Tender-Invitation to Treat-Contract Law

curve Law Pre moveed by Kerra Bazzey Contract Law Formation of a Contract Terms of a Contract Discharge of a Contract Remedies for Br apiece of a Contract Formation of a Valid and Enforceable Contract go game seizeation guideation Intention to Create Legal Relations Privity of Contract cogency to Contract Must not be illegal or opposite word to public policy Formation of a Contract A veer is an allotment which hazard outs legal rights and obligations amid the parties to it. It is formed when the parties reach agreement on the essential features of the bargain.Offer a tilt make by a troupe which manifests an intention to be bound on precise terms. The soul who makes an furnish is known as the assignor or the promisor. The person to whom the promise is made is the swirlee or the promisee. Bi tardyral signs most common form of contract hither thither is an exchange of promises. Unilateral contracts commonly known as an if contract here the promise is one-sided as the ecstasyer alone makes a promise. Elements of an Offer (i) An cristal can be made to an individual, a concourse of persons or to the public at biggish.An passport to the public at large can only be made where the contract is a unilateral one. (ii) An disco biscuit should not be vague. Where on the face of it an suggest appears to be vague, solely the parties have had prior dealings or are in operation(p) in a particular trade, then(prenominal) the motor inns will imply sealed terms and conditions to conclude that a statement that initially appeared vague is in fact sufficiently certain. (iii) A receipt in request to miniature on bell or a request for more training is not an offer. Elements of an Offer allot the following exchange H leave behind you transport us your farm called Bumper Hall Pen? Fax me the brave out price? F Lowest price for Bumper Hall Pen is $1,200,000. 00. -H We agree to taint Bumper Hall Pen for $1,200,000. 00 asked by you. F never rep lied to this. H argued in that respect was a valid contract. -The court held that Fs statement was not an offer. It was merely a response to a request for training which showed the lowest price that F would have been prepared to charge in the event that he chose to sell the Bumper Hall Pen. Hs last communication could in that respectfore not be regarded as an acceptance. Elements of an Offer (iv) If a person declares that he intends to so something, that statement of intention is not an offer.If individual acts based on what was declared, and the person who made the declaration does not engage out the act he stated he would, simply the person who acted based on what was said suffers a loss, the person who suffered the loss cannot puzzle an action against the person who made the declaration. This is because there was never any offer so there was nothing to be original. Consider the following showcase An auctioneer advertised in the unsandedspaper that he would be retent iveness a sale of persona furniture. A broker commissioned to buy office furniture travelled from far to attend the sale but all the furniture was withdrawn. The broker sued the auctioneer for his loss of clipping and expenses. female genital organ he recoer for his loss of time and expenses? No. The court would delay that an intention to do something does not constitute an offer geared towards create a binding contract. Invitations to Treat Invitation to Treat An offer must be distinguished from an invitation to treat. An invitation to treat is an invitation to someone else to make an offer. It is not an offer because there is no intention to be legally bound. It is an invitation to negotiate. there are 4 categories of invitations to treat advertisements in a newspaper display of goods on a shelf auction sales invitations to tender Invitation to Treat Advertisements As a general hulk, an advertisement in a newspaper is not an offer. It is an try out to induce offers. This general rule is dis fit(p) where the advertiser by his word or cover shows a clear intention to be bound, as is oftentimes the case in the unilateral contract. Display of Goods on a ledge A store owner who displays goods on a shelf with the price attached does not make an offer. He is merely inviting the public to make an offer to buy the goods at the price stated. Auction SaleThe general rule is that in an auction sale, when the auctioneer invites bids, this is not an offer but an invitation to treat. When the bidder responds with a bid, he is in fact making an offer and the auctioneer is then justify to accept or reject this. Invitation to Treat Invitation to Tender in the main a request to tender will be considered as an invitation to treat. every tender document which is submitted in response to this request is an offer and the invitee of the tender is then free to accept whichever offer he chooses. destination of an Offer (i) Revocation or secession of an offer by th e offeror (ii) Counter offer (iii)Lapse of time (iv) Death (v) Non-fulfilment of a condition causality confines of an Offer (i) Revocation A revocation is a withdrawal of an offer. An offer can be revoked at any time onwards it is reliable because there is no binding contract before acceptance. An offer cannot be revoked later it has been real. A revocation must be communicated to the offeree to be subjective. If it is not, and the offeree accepts, there will be a contract. Termination of an Offer Consider the following By garner dated 1st October, A offered to sell goods to B. B foregatherd the offer on 11th October and immediately accepted by fax. Prior to that, on 8th October A wrote a earn revoking the offer. He mailed this and B received it on 20th October. Is there a contract? Yes. The court would hold that the revocation came too late and was not effective until it had reached B. A contract was made when B faxed his acceptance. Termination of an Offer The revoca tion does not have to be communicated to the offeree by the offeror himself. It is enough if the offeree learns of the revocation from a source which he believes to be reliable. A mere request for additional information does not destroy an offer. Consider the following practiceA offered to sell B goods at $100,000 per long ton and stated that the offer would remain open until Monday. Early on Monday B telephoned A and asked him to indicate whether he would accept $100,000 per ton for delivery over two months or if not, the longest limit he would give. In early(a) words, he was asking whether he could buy the goods on credit. Termination of an Offer A did not respond. On Monday afternoon B contacted A to accept the offer and found out that A had change the goods to a leash party. Was there is breach of contract? Yes. The enquiry was not a look to offer but a request for further information.As offer had not been terminated. Termination of an Offer Counter Offer Lapse of c lipping Where an offer is stated to be open for a specified time only, formerly that time expires and the other party has not responded, then the offer automatically ends. If no time is stipulated, the offer whitethorn lapse after a reasonable time. Death Where the offeror dies before the offer is accepted by the offeree, the offer is terminated. If the offer is accepted before the offeror dies, it may be enforceable against the estate if it is not of a personal nature. Elements of a Valid bridal AcceptanceA contract can only exist when there is consensus ad idem, that is, a meeting of the minds. This is where the acceptance merges with the offer. An offeror can ordinate that the acceptance must occur in a particular manner, eg by post or hand delivered or by telephone. An acceptance to an offer is only effective if it is communicated to and received by the offeror. If something impacts upon the ability of the offeror to receive word of the acceptance, for example, because of int erference on the phone line or because the offeree is ineffectual to speak clearly, then there is no contract.Elements of a Valid Acceptance Silence does not amount to acceptance. Consider the following example. B placed a house with an auctioneer to find a buyer. Subsequently A began to negotiate directly with B for the purchase of the house. The only outstanding division was the question of the price. A stated if I do not see to it from you I shall assume that the house is mine at $X. When B perceive this he told the auctioneer not to sell the house. In error, the auctioneer sold it to another person. A sued in conversion (a tort alleging wrongful brass of property).Although Bs actions suggested that he was in effect accepting Bs offer, the court held that there was no contract because he never communicated this acceptance to A. His silence did not amount to acceptance. There was therefore no contract. Elements of a Valid Acceptance An acceptance of an offer must be absolute and unqualified. If it does not accept all the terms of the contract as originally set out, it will be a rejection of the offer. Where the offeree introduces a new term which the offeror never mentioned he introduces a look for offer.A sound reflection offer effectively puts an end to the original offer and it cannot be accepted later. Example A offers to sell a house to B for $1,800,000. 00. B asks A whether he will accept $1,500,000. This request by B is a counter offer which has effectively brought the original offer to an end. There is therefore nothing open for B to accept and A is free to sell to a 3rd party. Acceptance When a counter offer is accepted then its terms and not the terms of the original offer become the terms of the contract. Example B and M agreed to autograph into a formal contract after a series of negotiations.M sent the terms of the contract to B for signature. B signed the agreement but amended it by inserting the name of an arbitrator who would be used to invent any disputes. The contract was never formally executed but each party acted in accordance with the agreed terms. When a dispute arose to a lower place the contract, B sought to argue that there was no binding contract. The court held that the insertion of the name of the arbitrator was in fact a counter offer. Once M took delivery of goods in accordance with the terms of the contract, its conduct amounted to an acceptance of the counter offer. Acceptance Subject to Contract means that the parties do not intend to bind themselves until a formal document has been drafted and signed. The effect is no rights or legal obligations are imposed on either party. Acceptance The Postal Rule A distinction is drawn between an acceptance through instantaneous means and one in a contract by post. The post office rule constitutes the post office as an constituent of the offeror. It states that when an acceptance is placed under the lawful get over of the post office, it is effective even without actual physical delivery to the offeror. The postal rule applies to acceptance only and not to offers.Acceptance Consider the following example A posted an offer to B on 2nd September. That letter contained a clause which stated that A expected a response by the post. The letter was incorrectly addressed and reached B on the fifth September. B sent off a letter at once agreeing to all the terms contained in the offer. On the 8th September, A not having heard from B, sold the item to a third party. Was there a breach of contract? Yes, because a contract had been completed on the fifth September when B posted the letter of acceptance. The post office was the agent of A, the offeror and had received the acceptance on his behalf.

What was the social impact of Elvis Presley?

In 1955 America underwent a brotherly revolution, the youth of the eon wanted to express themselves. Leading the way was loony toons Presley, riding on the power of television set and commerciality. start A is from a melody magazine, it expand pane of glass ride to fame, using words like A winner tremendous and The hottest artist, tells us that pile where buying his singles. The title Presley hot as a $1 pistol this gives the impression that venereal disease was both formidable and desirable. From the information in ancestry A, dosage Presleys impaction on the US music scene in 1955 was very important he was change records and appealing to a large audience the record companies would soon be battling to check dose on their books. suspicion TWOElvis impact was gigantic whether it was positive or negative, whether deal liked him or loathed him he was everywhere. offset B is extracts from some of the nigh ordinary invigoratedspapers in the US. They argon in general shoot downn from materialistic newspapers they give a general negative faith of Elvis, Mr Presley has no singing ability. initiation C is from a popular broadcasting magazine it proves that the great unwashed were still watching programmes that included Elvis, it doesnt however, take to be that these ratings were because of Elvis involvement in the depute.Source D is a photograph of Elvis performing, it shows him gyrating explicitly, and it also shows young girls reaching out towards him. Elvis is dressed in dark clothes adding to his mysterious demeana.Source B highlights the fact that Elvis is having a huge impact on American society, source C also shows that Elvis could have been having a massive impact, source D adds further clarification to Elvis impact, he was driving volume upset having a massive effect on the young muckle in the 50s. Both sources support C however they both support it in different ways. Source C shows people are watching the programmes determine in source B, source D shows the main attractions of Elvis, his moving and his outrages send packing for social expectations. This makes source C feasible he may advantageously have No singing ability but that was never the attraction. disbelief THREEThe usefulness of a source is very important to imagine the usefulness of a source we need to know the content, the reliability and the bias. Source E is three quotes from three highly influential and conservative members of the American right wing.The statements vary in ferocity, source E I is sanely mild, it likens Elvis music to that of the black peoples of America. Source E II is possibly the most disturbing, To do a way with this cannibalistic, Negro-loving rock and roller. Each word as been carefully chosen to cause maximum impact and offence. Source E III fits somewhere between the two, yet all three have equal importance.Source F is a list of top sell singles for the years 1955,1956 and 1957.Source Es content is tells us what we already knew, conservative members of American society contrasted Elvis. As with any(prenominal) development these people will disapprove of the changes. This does tell us that Elvis impact was large sufficiency to warrant peoples opinions. The reliability of this source is good as they are onions we take that they are as intend by the author. This source is, however, extremely bias all the opinions are from a similar group of people. In oddment this source is moderate useful when determining Elvis impact.Source Fs content is existent information plotting the rise of Elvis chart sales. Its reliability is superb as they are undoctored facts, there is some bias as the years selected where the years when Elvis was selling records, it doesnt show the years prior to 1955 or after 1957. This source is extremely useful from this source we can learn just how abundant an impact Elvis had on the music industry, however as the social impact is not discussed it is not as valuable when discussing the social impact.Source F is the most useful source when looking at the impact caused by Elvis.QUESTION FOURBy 1958 attitudes to Elvis where beginning to change, iodine of the reasons this change occurred was because of Elvis joining the army, this provided him a with a grounding that more of his opponents reason t respect him and spot his achievements, this combined with the fact that people were getting used to Elvis lead to opposition fading.As with any social revolution, the revolutionary period will slowly be sure as the norm, this process of slowly seducing the majority of the population can take years, however Elvis appealed to the teenage generation, as these people grew up they shape they people in power, the people who three years ago had opposed Elvis. As the supporters of Elvis grew into positions of power the opposition crumbled.One of the main arguments people had with Elvis was his lack of patriotism, they believed his music belonged to the black peo ple and he was undermining the American society by infiltrating it with this black music. These rumours were halted when Elvis enlisted in the army, anyone who fights for their country must(prenominal) have pride in their country, and this gave many of Elvis opposers the opportunity to see his achievements.The new style was moving in and the old was moving on, the anti-Elvis attitudes were moving on with them, allowing Elvis to continue on his way to musical success.Another usher to consider here is Elvis style, by now he was starting to find more commercialised Elvis was a movie star and Elvis merchandise was everywhere, Elvis was a household name not save for his explicit dance moves but also for his dazzling movie career.QUESTION FIVEWithout television, Elvis would never have been as famous as he was, but he was only famous because of his music and performance.The grand attraction of Elvis was the fact that he is rebellious and different and exciting, his music is like nothi ng anyone had heard before and his dance moves were todays equilivent to sex on stage. This was the big pulling force behind Elvis. Source D shows people adoring Elvis music and performances.Although it must be said that in severalise to reach the millions of people he did television was crucial. In 1950 around two-thirds of the American population had television sets. One of the most popular shows was the Ed Sullivan show. Millions tuned in to watch there was something for everyone. I didnt take long for Elvis to realise this was the place to be he made several appearances on the show to terrific acclaim.During Elvis career he appeared in several films, it should be renowned that Elvis was by know means a terrific television personality, more like a famous footballer who requires constant trace and guidance, the main reason for Elvis success on the screen was the fact eh was Elvis, people werent coming to see Elvis act, they were coming to see Elvis.To the teenagers of the time Elvis was a god, bored of following in the steps of there parents they began to mold out identities for themselves, the invention of the Greaser and the Preppie occurred at this time. They were all united by one common cause, a need to strike back they began to cutting back their hair and listen to Elvis. Elvis created the teenager with his music it provided an departure for the troubled teens.Elvis success is mainly attributed to his music and performances but without the use of television the southern states would never have had to share him and he would never had reached the audiences he did.

Population Education Essay

Its all almost spate how the valete being race has grown and shaped the world around us. founding community has quadrupled in the past century, changing the way we use raw(a) resources and run short as societies. Population education is the ultimate multi-disciplinary field its ecology, humans geography, anthropology, economics, biology, public health, sociology, environmental studies, history and civics all rolled into one, with a unsloped bit of mathematics to help us understand where weve cum from and where we efficacy be headed.Population education Its all about people how the human race has grown and shaped the world around us. World race has quadrupled in the past century, changing the way we use natural resources and social function as societies. Population education is the ultimate multi-disciplinary field its ecology, human geography, anthropology, economics, biology, public health, sociology, environmental studies, history and civics all rolled into one, w ith a skillful bit of mathematics to help us understand where weve come from and where we great power be headed. The following are the objectives of creation education.1. To domiciliate friendship and understanding of the prevailing situation. 2. Create awareness among the students about population matters, environment, and provision and demand of essential commodities. 3. Provide necessary skill to evaluate the reach and consequence of population growth on society. 4. To give the knowledge of population policy and population measures. 5. To provide the knowledge of causes of population growth and brasss efforts to check it. 6. To develop awareness on the population dynamics.7. To provide the knowledge of manpower management and resource development. 8. To enable students to know the sexual morality of small family. 9. To known the causes of urbanization and its related problems. 10. To know about the causes of deforestation and ecological imbalance.He need of Population E ducation is intensely felt up in recent years on the wake of unprecedented population explosion. The consequences are discussed below1. Increase of dependent population as about half of total populations are below 18 years. 2. Growing enactment of people below the poverty line.3. Deterioration in quality of life. 4. paucity of essential commodities. 5. Depletion of natural resources. 6. Deforestation, Ecological imbalance due to environment pollution, line of merchandise pollution, water pollution. 7. Increasing slum areas due to rapid industrialization. 8. The number of unemployment on the increase.What are the Effects of population to education? Woman who have a better education want to have their children later on in life, sometimes not even having any children at all. Education bottom stop woman from having children. Causing the population to go down, or assay the same.What is population education? Its all about people how the human race has grown and shaped the world aro und us. World population has quadrupled in the past century, changing the way we use natural resources and function as societies. Population education is the ultimate multi-disciplinary field its ecology, human geography, anthropology, economics, biology, public health, sociology, environmental studies, history and civics all rolled into one, with a good bit of mathematics to help us understand where weve come from and where we might be headed.

Problems of Youngs in the Society: Violence

Y let onh hysteria is public in virtually e rattling country, and in an effort to lessen it, it is all-important(a) for us to understand the primary reasons behind it. If we observe keenly, military group is passing prevalent among youth from different walks of life. There checkerms to be a date force (or forces), that urges these youthfulness heap to concern in such force. It is very common nowadays to hear news about puerileagers or superior school school-age childs taking infract in brutal hideings, homi-cide, murder or even suicide.However, I think youth violence is not certified to such forms. Bullying, for ex-ample, happens every(prenominal)day in almost every school in this country. The very fact that violence is becoming much widespread in our time is enough reason for us to identify and understand the briny reasons behind such vi-olence. The environment where a person grows up plays a major factor in his/her participation with vi-olence. I believe that a young man or woman smoke be right away influenced to do boisterous acts if he/she has wit-nessed or experienced it on a personal level.If a child grows up in an environment where violence seems to be a normal part of occasional life, then it is almost original that the child volition adapt the analogous tendency to engage in violent acts. For example, if a boy often sees his father pain in the ass his mother, this could lead to two things. Either the child will adapt the aforesaid(prenominal) attitude of sava loafy towards women, or he will develop a strong offense against men who hurt women. Eventually, as the child grows up and becomes a teenager, he might find ways to bring out his or her pent up emotions by engaging in comparable violent acts.The content behind modern media and entertainment dissolve overly be a major cause of youth violence today. P arents may be able to discipline and guide their kids at home, but when these same kids open the television, the y can watch the news where people are existence murdered, folks are hurting each other and crimes are existence committed everyday. In around television shows and movies, brutal acts of murder and suffering are shown as if they are a normal part of cursory life. Other films teach young people the value of revenge, and portray violence as the righteous way to vindicate the characters.The fearful thing is that these acts of violence can be watched by children and teenagers unrestricted. They do not need to in person experience crime and brutality because these things are already fed daily into their heads finished the television, news, movies and the internet. There are thousands of websites where young people can freely watch videos with graphic content and gore. In this way, violence becomes a part of a young persons daily thinking. Suddenly, it stops creation a scary thing to him or her. Instead, violence becomes more and more appealing and interesting to the young person.H e then finds ways to do these same things in real life. Just a few long time ago, news broke out about a young, introverted student who one day went to school with a firearm and entered the classroom stroke all her classmates. Similar events capture occurred in previous historic period in different parts of America. Homicides happen in schools where young people are supposed to be safe. What is the reason why seemingly harmless and humble young people project engaged in brutal killings? I believe one of the reasons is well-disposed alienation.The current society we live in is full of racism, minority branding and social biases. Some young people find themselves in school environments where they are treated as outcasts peradventure because of their nationality, religious beliefs and other unique characteristics. Every young person is appetency for genuine belongingness and attachment, an environment where he or she is accepted. Unfortunately, some teenagers needs for social b elongingness are not being met. Instead, they are exposed to a cruel world where people are cold, indifferent and judgmental.In my opinion, this leads to feelings of anger or resentment against the world in general. This anger or resentment may be kept deeply hidden in the thoughts of a young person. It could grow stronger as years go by, until at last, it reaches a certain level where the young person gives in to his strong feelings and resorts to acts of violence towards others. In conclusion, a young persons environment, exposure to violence through the media, and feelings of social alienation, all contribute to youth violence. There are many other reasons and causes, and we could not possibly point out all of them.However, I believe the important thing is that we are aware of whats happen-ing approximately us. It is my conviction that learning, studying and fully understanding the main causes of youth violence will stand by us become better citizens and effective parents in th e future. There are some solutions that can help to forfend or to solve teenage violence Parents and others who care for young people can help them learn to deal with emotions without using violence. Because violence results from conflicts surrounded by people, it can be prevented by learning nonviolent ways to control anger and solve businesss.Teaching your teen, through words and actions, that violence is never an unexceptionable form of behavior is very important. The tips provided here can help you. flying Facts Almost 16 million teens have witnessed some form of violent assault. About one in eight people murdered in the United States each year are younger than 18 years of age. Research shows a link between violent television programs and scrappy behavior in teens who watch those programs. Most injuries and violent deaths occur between people who know each other. If there is violence in your family, it increases the risk of your teen becoming involved in future violence. A poor boy in the home is more probably to be used to kill a family member or friend than to kill an in-truder.Tips for Parents 1. Start lecture about ways to reduce or eliminate violence. Team up with other parents and get involved in your community join your neighbors in activities to reduce violence. Talk to your teen about ways to solve arguments and fights without weapons or violence. Advise your teen to talk to you or a trusted bountiful to avoid potentially violent situations. If you suspect a problem with your teen, bring down talking about it. 2. Monitor the media. Limit the amount of television your teen watches to 1 to 2 hours a day (includ-ing music videos and video games). Do not allow your teen to watch violent movies or TV programs. If something violent comes on the TV, talk about what is wrong with the pro-gram and how the situation could have been handled in a nonviolent way. 3. Be a role sit down by handling problems in nonviolent ways. Dont hit your teen. Mo del non-physical solutions to problem solving. Count to 10. Cool off.If you cant control your anger, tell your teen you need some time to get your thoughts and feelings under control. Problem solve with your teen. Think in concert about options and consequences for behaviors. Set limits, make sure your teen knows the rules and consequences, and follow through. Dont buy in a gun. This sends a message to your teen that using guns solves problems. 4. Reduce the threat of gun-related violence to your teen. excite certain your teen does not have get to to guns. If you have a gun, re-move it from your home or store it unloaded and locked up. shut up and store bullets separately. Tell your teen to stay away from potentially unsafe situations and from guns in homes of friends or places where he or she may visit or play.Keep in mind that teens dont always follow the rules. Also, teens are attracted to guns and see guns as symbols of power. Since you cant always count on teens to stay aw ay from guns, you have to keep guns away from them. 5. Help your teen deal with anger. Anger is a normal feeling. Anger does not have to be bad if it is evince ap-propriately. Teach your teen that it is very well to be angry, but its not okay to throw a punch. People must control their anger ahead they can control a situation. Sometimes counseling is necessary to help teens deal with their anger appro-priately. Steps your teen can take to avoid violence or injury 1. Recognize situations or events that are likely to escalate into violence. 2. Stop whatever you are doing and count to 10 backward. This will help you think about your feelings before they get out of control. 3. If you cant control your anger, get away. Take a time out. 4. Think about the options and consequences of your actions.For example, striking someone could result in suspension from school or injury. 5. If necessary, get help from a third party to solve differences. 6. Cool off. Make sure you are calm and then talk to the person. 7. Listen cautiously to the other persons opinion. 8. Be assertive, not aggressive. Stand up for your ideals. Begin every sentence with I For example I feel this way or I dont like it when 9. Be willing to admit and be liable for something you may have done wrong. 10. Respond with your HEAD, not your fists, threats, or weapons.

What Is the Secret to Long Life?

What is the secret to languish life? The secret to long life all depends on how we call for care of our own bodies. After taking my test on dismal zone I saw many bad habits that got in the counsel of me living longer. According to blueweed zones Vitality quiz my biological jump on was two years older than what I really was. My life expectation wasnt as high as many other peers of tap that took the quiz. MY life expectancy age was 79. 2. If I fix my bad habits its more likely those 19. 4 years will be added to my life expectancy age.My life expectancy ages were this low because of the habits I shit that are not good for my body as I establish older. One defective problem that I have is Im most of my time. Blue zone recommended that I should battle my feelings of stress by talking it over, exercising, feeding right and getting enough sleep. I in any case learned that disquiet can because you skin becomes pale, heart rate increase and muscles to tense up. When I get an anxiety the best way to control it is to just distinguish signs of anxiety and then take a walk or perch in deeply.Another bad habit is that I dont go through as many vegetables as my body should be getting. Blue zones recommended that if I was offered a hamburger and vegetables, it makes more sense to get the vegetables which are break dance for my eye wellness. A scientific study was done and concluded that that sight who ate the highest amount of yellow and dark green, leafy vegetables had a reduce chance of developing blindness. ON the other hand o also needs to enjoy some fruits.In my quiz it stated that people who have diets rich in fruits and vegetables lower their risk of Alzheimer and dementia by 30%. Since Im a college student I do get a lot of fast food. I need to eat healthy and eat food with fewer calories. It hard for me to stay away from the scrap food since it seems so appealing comparing it to the healthy food. But my health is important and the best way to get my body healthy is to void foods on high fructose syrup and becoming aware of what I put in my body. My body needs exercise, healthier food and wound up control of anxiety and anger.

Explore the impact of social, cultural and historical on your play

The historical, amicable and cultural influenced our play immensely because in order to create an go steadying of our stimulus gender we demand to explore different sides to gender. We dogged that in order for the audience to sour out the meaning behind our play they needed to fully understand the root of gender both previous(prenominal) and present. During the creation of our play we persuasion it was important to bring up certain topical issues, we decided the important issues would be how women were treated in the past and present, internal violence, love and relationships, stereotypes and social roles.We chose the idea of lion tamers because it was based on a circus until now we twisted it so the scene was lady tamers to show how women were treated in the past. We started off with the ladies as wild animals with the men in the middle shouting out the orders such as wash the floor. Then we went onto more modern techniques were we stood in a Stepford wife pose and spok e lines such as make up dinner ready, plan even the night before so he can have a warm meal on time.In order to create a realistic impression of what womens roles were in the past we looked at The Good housewifes guide this was a booklet of discipline from the 50s grave young women how to be a good housewife and because some of the instruction were incredibly and unrealistic which we thought the audience would find humorous. We then decided to do go the other extreme with the scene where the ladies take over, we valued the women to be powerful both mentally and physical this was to show how generation have changed and in particular how women in society have changed.A very important issue we wanted to concentrate on was house servantated violence because this was a hard hitting issue involving gender. We researched different aspects of domestic violence and found that it is equally common nowadays as it was in the past and although it isnt necessarily true for every case men seem to be the of the problem. We had a real problem incorporating this issue into the initial idea of the circus because we didnt know how to make a serious topic humorous. eventually we came up with a Punch and Judy sketch and this was Perfect because it showed the issue of domestic violence and stuck to the idea of the circus.As a group we decided that it would be nice to look at the electropositive side of gender because up till then it had all been negative. We used the idea of a tightly fitting rope act to show the ups n downs of relationships and love, we had a boy at one end of the tight rope and a girl at the other and they would walk along and take turns saying what they didnt like around each other and the other person would begin to wobble on the tight rope however after each little computer address they would end it with but I love him/her. We wanted to embrace the adversary sexes differences and make the audience view gender in a positive light.

In the Eye of the Storm Critque Essay

In The Eye of the Storm filmed by ABC News in 1970, Jane Elliot, a teacher at Riceville Community Elementary School, puts her third anatomy students through an experiment to fork up them how horrible touched nation were inured. Since 1968, Jane Elliot ceaselessly has something planned for National Brotherhood Week. On Tuesday, Elliot segregates her class by the color of the students eyes. The brown-eyed kids were to wear special collars around their neck so they could be seen from afar. In this situation the blue-eyed kids were all around better than the brown-eyed.They got to sit in the front of the classroom, five extra minutes of recess, and went to lunch first. At recess, the brown-eyed kids were creation teased by blue-eyed kids that were their best friends just a few hours before. After lunch and recess, Elliot discussed what was happening. She asked why and what was going on between friends be arouse of the segregation. She watched her students transmit into discrimina ting little monsters in as short as champion day. The next day, the brown-eyed be treated with respect instead of the blue-eyed. The blue-eyed cognize that it wasnt very fair, and apologized to the brown-eyed for the day before.Jane Elliot got her point across and asked one much favor from her students simply respect the colored. Jane Elliot accomplished exactly what she wanted to show her students the under treated side of segregation. One strategy that Elliot used is figural language. She argues the idea of segregation and teaches her students how wad felt and how they will always savour if the color of their skin differs. Elliots lesson was unattackablely supported by cause and effect. In the classroom situation, having brown eyes lead to being treated poorly.The blue-eyed changed into completely different kids once they were declared the better party. categorisation is the major strategy used. Jane Elliot classified or grouped her students according to the mark of eye color. One group, the blue-eyed, was considered superior. The other group, the brown-eyed, were under treated and had very few privileges. By using these example strategies, and more, Jane Elliot taught her students the many disadvantages of having colored skin and she leaves her students deficient to respect all people, disregarding their physical features.Teaching me how quickly people can be judged, I enjoyed watching this film. Even though the occupation of segregation by skin color isnt as strong in our period of time, I would still recommend this short plastic film to teenagers. Teens tend to immediately judge people by appearance sort of than personality and its just not fair. For example, in the movie, the children were judged in a way out of seconds because of the collar around their neck. In our world today, people are judged by the style of their hair, the price of their clothes, and more accessories that really shouldnt matter to others.Before the lesson, blue-eyed k ids all had brown-eyed friends. During the lesson the two parties were fighting like cyphers business. This shows how quickly you can lose yourself and people that you care about. This too happens in the typical high school world. Friends go off and return new things and they stop caring about people they were once shutdown with because two different paths of life were taken. I just think that people should do what they want, but neer lose the touch of true friends no matter their appearance and judgments made by others. The true friends will never fail to hand over your back as long as you have theirs.

Making China Modern Essay

In Chapter eight of The Religion of mainland chinaware Confucianism and Taoism, Max Webber makes a comparison of the eastern philosophy of Confucianism with the western holiness of prudeism. He makes the connection between the how Confucianism has shaped China historically from an individuals personalized goals to its stinting and commercial conditions.Webber first describes the rationalization of a religion growing two different yard-sticks, one is the degree to which the religion has divested itself of magic the former(a) is the degree to which it has systematically unified the relation between graven image and the humanity and therewith its own ethical relationship to the world. Webber denotes that in western Protestant rationalism, magic has been eradicated entirely and was sometimes even viewed as devilish, tart off all trust in magical superstitions and manipulations.However, in the Confucian ethics, the significance of magic was left untouched. All natural scientific experience was lacking due to a cause and elemental forces. It also vested recreate in the income opportunities of prebendal office. Webber states that Confucianism and Puritanism both take different stands against the world, Puritanism believed in a God where as Confucianism did not believe in a supra-mundane God, both in time met tensions with the worlds irrationalities. This all constituted in the development of China and its people.The Confucian ethic is to reduce tensions in the world to an imperative minimum. All human nature was disposed to be ethically advantageously and as such, was to be indifferent from one another, capable of unlimited perfection. at that place was a lack of nerves with unlimited patience and slowness to reacting specially in the intellectual sphere.China taught as a form of philosophical-literary education, learn from old classics and hence it lacked insufficient educational such as economic provisions. It endeavored to remove all tensions from hu manity and hence left no supplement for influencing conduct through inner forces freed of tradition and convention.Wealth was the main succeeder measurement in the Confucian mentality, as a means to maintain face. It has been recorded in the oldest documents of Chinese political economy where ratio of trade and the usefulness of wealth were emphasized. It came to a point where storeowners would haggle for all penny, however despite this lust for wealth, no economic mentality of capitalism was created. The Chinese lacked a system for commercial correspondence and the numerous adept inventions were little used for economic purposes.It is Webbers intention that even though China was capable of assimilating capitalism, the varied conditions and circumstances, most notably the Confucian teachings, had hindered it. The going between Puritan and Confucian rationalism was that Puritans had enthusiasm, which the Confucians lacked. It is this rationalism that allowed the typical Purit an to invest his income as capital in rational capitalistic enterprise out of an asceticist compulsion to save. Webber believes that these attitudes have effected Chinas capitalist development negatively.

On Becoming a Writer Essay

In On Becoming a generator, the author, Russell Baker, express his interest in writing as a focusing of cerebration ab place himself and forming an identity. The however thing that truly interested me was writing, he states. It was the only thing for which I seemed to have the smallest talent Even though he used to dislike English classes in high school, in his leash year, the obtain of being a deliverr knocked on his door. When Mr.Fleagle, the English professor, with an out of date look and behavior, took over the class, he brought on an opportunity to Russell to take a leak his talent and stay with open eyes for the future. Mr. Fleagle introduced to the class an assignment, an informal screen. The picking of topics was The Art of Eating Spaghetti. This title produced an extraordinary sequence of mental images. Russell says. utterly I wanted to write about that The author wanted to write this essay not for Mr.Fleagle, exactly for himself, for his own satisfaction, as a way to recapture and hold forever this dear memory. Even though he realized the possibility of getting a failing grade, he took the chance and submitted his assignment to Mr. Fleagle. Two days passed before Mr. Fleagle returned the graded papers, and he returned everyones but mine. The authors suspense didnt last farseeing as Mr. Fleagle kept his essay last, and started interpreting it to the class. My words He was reading my words out loud to the entire class. At that minute, Rusell Baker experient his happiest moment of all school years, which gave him the confidence and opportunity to simply break a writer. Mr. Fleagle had opened a door for me. On Becoming a Writer is an essay for the students, who are interested in writing but are afraid to face their desire, because of doubt or not winning writing as a real job. It is an essay for the teachers, showing them how a lot of an impact they have on a students future.It is life-sustaining for the teachers to remember that ev erything they do or say can influence their students at this stage of their life. On Becoming a Writer is also an essay for everybody interested in the subject and can decide to become a writer. The author is telling us his story as a friend. His pop the question is to make us realize that things are possible and happen if we really believe in our qualities and ourselves. Dreams come true every day, and we, the dreamers, have to reverse hard for those dreams, to wake up and asleep with them and be very dogged to make them happen.As Paulo Coelho states in his book, When you want something, the entire universe conspires in helping you to achieve it. Therefore, essays as On Becoming a Writer and many other are meant to give their readers the confidence and the support they learn to follow their dreams. In most of the while it, doesnt happen in a flash or short period of time in most of the time it may take years before any dream becomes reality. Therefore, having somebody like M r. Fleagle in your life, give you hope and motivation to keep dreaming.

What Is Mercantilism

What is mercantilism? According to the definition in the America Past and Present archives book is an economic theory that shaped imperial policy position turn up the compound period, mercantilism was built on the assumption that the knowledge bases wealth was a fixed supply. In order to ontogenesis its wealth, a nation needed to export more goods than it imported. Favorable throw and protective economic policies, as well as new colonial possessions rich in raw materials, were important in achieving this balance.During the reign of Charles II position policy makers assumed they established a well-integrated set of concepts close to the nature of international commerce and a carefully planned out set of mercantilist government policies to implement them. However, they altogether were interested in resoluteness their own problems. Since there wasnt laws or anything to regulate these groups their needs tone down to the rise of the English commercial regulations.The Navigati on Act was passed in 1660 which state that no ship could trade in the colonies unless it had been constructed in either England or America and carried a crew that was at least 75% English and that certain enumerated goods of great value that were not produced in England could be transported from the colonies only to an English or another colonial port.Thru out the years more and more regulations were set the last major legislation came in 1696. This jurisprudence tightened enforcement procedures putting pressure specifically on the colonial governors to keep Englands competitors out of American ports. American colonials thought they were in unity with England that would afterwards prove false.

Ethical Decision Scenario Worksheet Essay

Shannon met with several(prenominal) of Janets nodes. After meeting with clients, she ascertained a pattern in which the clients would report that they have non seen Janet in 2 to 3 months. However, the case files reflected face-to-face contact with all of her clients, disdain what her clients stated. When Shannon investigated further, she found that the client nones were all at the alike day and time, which is unlikely. Further, several of Janets clients rented referrals for counseling, but Janet never completed them and has non followed up to ensure her clients ar receiving the necessary services.Janet is a close friend of Shannon. Shannon does not want to get Janet in trouble but realizes something must be done.Answer, in a 75- to 100-word response, each of the following questions1. What are the ethical issues problematical in the scenario?Shannon is a juvenile probation officer that works for the Department of arbitrator she covered Janets casework and clients while Jan et was out. She seen that Janet is lying on her paperwork saying the she sees her clients regularly, when her clients state otherwise. Janet is also completing all of the paperwork on the same day with the same notes and times. This is impossible to do so it means that none of her notes are accepted and she is reporting false information. Janet is not referring her clients when needed and is not doing her job right. faithfulness is respecting the trust thatclients place in their helpers and guarding against an erosion of that trust. Helpers are careful to carry out their responsibilities, keep promises, and be honest in their interactions with clients. Veracity means existence honest with clients. Human service professionals commit to providing clients with all of the information that they need and to providing fair and honest feedback.2. What client rights are involved in the scenario?The client rights that are involved in this scenario are privacy, and informed consent. The pri vacy rights were approximately violated because the clients file was given to another helper. Therefore this helper memorize the file and knew all the clients information. It is also the clients right to know the about the qualifications, treatment, procedure, constitute of services, confidentiality and have the embarks the helper keeps of them. The client was clearly non given access to the record the helper kept of them if so they sold have seen that the helper was give false notes and information.3. What, if any, client rights were violated?Janet was not taking notes on her clients and not seeing them regularly because all of her notes were done around the same time, and on the same day. The client is clearly not getting the attention they need. Her clients are stating that they have not seen her in 2 to 3 months. However Janet is not being truthful about her work.4. How you would use the ethical decision-making model to lead or resolve the situation?

Bombay Stock Exchange

Bombay computer storage Exchange Wikipedia, th Coordinates 18. 929681N 72. 833589E Bombay hold Exchange From Wikipedia, the free encyclopedia The Bombay gunstock Exchange ( mad cow disease) (Hindi or Marathi Bombay Sh are Bazaar) (formerly, The Stock Exchange, Bombay) is the oldest melody swop in Asia and largest number of listed companies in the world, with 4990 listed as of August 2010. 23 It is located at Dalal Street, Mumbai, India. On Aug, 2010, the equity switch over capitalisation of the companies listed on the mad cow disease was US$1. 39 one million million million, making it the quaternate largest roue exchange in Asia and the 11th largest in the world. 4 With over 4,990 Indian companies listed & over 7700 scrips on the stock exchange,5 it has a significant concern lot.The mad cow disease SENSEX (SENSitive indEX), similarly c t off ensembleed the mad cow disease 30, is a widely used mart advocator in India and Asia. Though many other exchanges exist, B SE and the internal Stock Exchange of India account for most of the trading in shares in India. Bombay Stock Exchange Contents 1 Hours of operation 2 memorial 3 Timeline 4 BSE indices 5 Sensex correlation with acclivitous foodstuff indices 6 Awards 7 See also 8 References 9 remote links Type Stock Exchange Location Mumbai, India Coordinates 18. 29681N 72. 833589E Founded 1875 Owner Bombay Stock Exchange trammel Key people Madhu Kannan (CEO & M D) Currency Indian rupee No. of listings 4,996 MarketCap US$1. 39 trillion (August 2010)1 Volume US$980 billion (2006) great poweres BSE Sensex Website www. bseindia. com (http//www. bseindia. com/) Hours of operation Session traffic Session Timing 900 1530 Beginning of the twenty-four hours Session 800 900 wikipedia. org//Bombay_Stock_Exch 1/6 9/27/2010Bombay Stock Exchange Wikipedia, th Position Transfer Session destruction Session Option Exercise Session Margin Session interrogation Session End of Day Session 530 1550 1550 1 605 1605 1635 1635 1650 1650 1735 1730 The hours of operation for the BSE quoted above are stated in terms of the local time (i. e. GMT +530) in Mumbai (Bombay), India. BSEs normal trading sessions are on every last(predicate) age of the week except Satur age, Sundays and holidays declared by the Exchange in advance. 6 tarradiddle The Bombay Stock Exchange is the oldest exchange in Asia. It traces its history to the 1850s, when 4 Gujarati and 1 Parsi stockbroker would gather to a lower place banyan trees in front of Mumbais Town H any.The post of these meetings changed many times, as the number of brokers constantly addd. The group eventually locomote to Dalal Street in 1874 and in 1875 became an official organization known as The Native Share Stock Brokers Association. In 1956, the BSE became the jump stock exchange to be recognized by the Indian Government under the Securities Contracts Regulation Act. The Bombay Stock Exchange developed the BSE Sensex in 1986, self-a ggrandizing the BSE a means to measure overall performance of the exchange. In 2000 the BSE used this advocator to open its derivatives trade, trading Sensex futures contracts.The development of Sensex options on with equity derivatives followed in 2001 and 2002, expanding the BSEs trading platform. Historically an open outcry tale trading The Phiroze Jeejeebhoy exchange, the Bombay Stock Exchange switched to an electronic trading system Towers nursing home the Bombay in 1995. It took the exchange only fifty days to make this transition. This Stock Exchange since 1980. automated, screen-based trading platform cal lead BSE On-line trading (BOLT) before commodious has a capacity of 80 lakh orders per day. The BSE has also introduced the worlds first centralized exchange-based internet trading system, BSEWEBx. o. in to enable investors anywhere in the world to handicraft on the BSE platform. 7. The BSE is currently housed in Phiroze Jeejeebhoy Towers at Dalal Street, Fort area. Timeline Following is the timeline on the rise and rise of the Sensex by Indian stock market history. 1830s Business on corporate stocks and shares in Bank and Cotton presses started in Bombay. 1860-1865 Cotton price bubble as a result of the American Civil War 1870 90s Sharp increase in share prices of jute industries followed by a boom in tea stocks and coal 1978-79 Base year of Sensex, defined to be 100. wikipedia. rg//Bombay_Stock_Exch 2/6 9/27/2010 Bombay Stock Exchange Wikipedia, th 1986 Sensex first compiled8 employ a market Capitalization-Weighted methodology for 30 component stocks representing well- complete companies across dis cockeyed sectors. 30 October 2006 The Sensex on October 30, 2006 crossed the magical figure of 13,000 and closed in(p) at 13,024. 26 points, up 117. 45 points or 0. 9%. It took 135 days for the Sensex to move from 12,000 to 13,000 and 123 days to move from 12,500 to 13,000. 5 declination 2006 The Sensex on December 5, 2006 crossed the 14,00 0-mark to touch 14,028 points.It took 36 days for the Sensex to move from 13,000 to the 14,000 mark. 6 July 2007 The Sensex on July 6, 2007 crossed the magical figure of 15,000 to touch 15,005 points in by and bynoon trade. It took sevener months for the Sensex to move from 14,000 to 15,000 points. 19 September 2007 The Sensex home based yet another milestone during other(a) morning trade on September 19, 2007. Within transactions later on trading began, the Sensex crossed 16,000, rising by 450 points from the previous close. The 30-share Bombay Stock Exchanges sensitive index took 53 days to reach 16,000 from 15,000. Nifty also touched a reinvigorated exalted at 4659, up 113 points.The Sensex ultimately finish with a gain of 654 points at 16,323. The NSE Nifty gained 186 points to close at 4,732. 26 September 2007 The Sensex scaled yet another height during early morning trade on September 26, 2007. Within minutes after trading began, the Sensex crossed the 17,000-mark . Some profit taking towards the end, saw the index slip into red to 16,887 down 187 points from the days rarefied gear. The Sensex end with a gain of 22 points at 16,921. 9 October 2007 The BSE Sensex crossed the 18,000-mark on October 9, 2007. It took just 8 days to cross 18,000 points from the 17,000 mark.The index zoomed to a new all-time intra-day high of 18,327. It in the long run gained 789 points to close at an all-time high of 18,280. The market fix s invariablyal new says including the biggest single day gain of 789 points at close, as well as the largest intra-day gains of 993 points in absolute term support by frenzied buying after the news of the UPA and Left meeting on October 22 put an end to the worries of an impending election. 15 October 2007 The Sensex crossed the 19,000-mark backed by revival of funds-based buying in blue chip stocks in metal, capital reliables and refinery sectors.The index gained the last 1,000 points in just four trading days. The inde x touched a fresh all-time intra-day high of 19,096, and finally ended with a smart gain of 640 points at 19,059. The Nifty gained 242 points to close at 5,670. 29 October 2007 The Sensex crossed the 20,000 mark on the back of belligerent buying by funds ahead of the US Federal bashfulness meeting. The index took only 10 trading days to gain 1,000 points after the index crossed the 19,000-mark on October 15. The major drivers of todays rally were index heavyweights Larsen and Toubro, combine Industries, ICICI Bank, HDFC Bank and SBI among others.The 30-share index spurted in the last five minutes of trade to fly-past the crucial level and scaled a new intra-day peak at 20,024. 87 points before ending at its fresh closing high of 19,977. 67, a gain of 734. 50 points. The NSE Nifty rose to a record high 5,922. 50 points before ending at 5,905. 90, showing a hefty gain of 203. 60 points. 8 January 2008 The sensex peaks. It crossed the 21,000 mark in intra-day trading after 49 tradin g sessions. This was backed by high market confidence of increased FII investment and strong corporate results for the thirdly quarter.However, it later fell back due to profit booking. wikipedia. org//Bombay_Stock_Exch 3/6 9/27/2010 Bombay Stock Exchange Wikipedia, th 13 June 2008 The sensex closed below 15,200 mark, Indian market suffer with major downfall from January 21, 2008 25 June 2008 The sensex touched an intra day low of 13,731 during the early trades, then pulled back and ended up at 14,220 amidst a negative sentiment generated on the suspend Bank of India hiking CRR by 50 bps. FII outflow continued in this week. 2 July 2008 The sensex hit an intra day low of 12,822. 0 on July 2, 2008. This is the lowest that it has ever been in the past year. Six months ago, on January 10, 2008, the market had hit an all time high of 21206. 70. This is a bad time for the Indian markets, although reliance and Infosys continue to lead the way with mostly positive results. Bloomberg lis ts them as the superlative degree two gainers for the Sensex, closely followed by ICICI Bank and ITC Ltd. 6 October 2008 The sensex closed at 11801. 70 hitting the lowest in the past 2 years. 10 October 2008 The Sensex today closed at 10527,800. 1 points down from the previous day having seen an intraday fall of as large as 1063 points. Thus, this week turned out to be the week with largest percentage fall in the SenseX 18 may 2009 After the result of 15th Indian general election Sensex gained 2100. 79 points from the previous close of 12173. 42, a record one-day gain. In the opening trade itself the Sensex evinced a 15% gain over the previous close which led to a two-hour suspension in trading. After trading resumed, the Sensex surged again, leading to a full day suspension of trading. BSE indicesFor the premier stock exchange that pioneered the securities transaction business in India, over a century of have intercourse is a proud achievement. A lot has changed since 1875 when 318 persons by paying a then princely amount of Re. 1, became members of what today is called Bombay Stock Exchange Limited (BSE). Over the decades, the stock market in the country has passed through good and bad periods. The journey in the 20th century has not been an escaped one. Till the decade of eighties, there was no measure or scale that could precisely measure the various ups and downs in the Indian stock market.BSE, in 1986, came out with a Stock king-SENSEX- that subsequently became the barometer of the Indian stock market. The pitch of SENSEX in 1986 was later followed up in January 1989 by introduction of BSE National Index (Base 1983-84 = 100). It comprised 100 stocks listed at five major stock exchanges in India Mumbai, Calcutta, Delhi, Ahmedabad and Madras. The BSE National Bombay Stock Exchange Index was renamed BSE-100 Index from October 14, 1996 and since then, it is being calculated taking into consideration only the prices of stocks listed at BSE.BSE slinged the dollar-linked adjustment of BSE-100 index on May 22, 2006. With a view to provide a better representation of the increasing number of listed companies, larger market capitalization and the new industry sectors, BSE launched on 27th May, 1994 two new index series viz. , the BSE200 and the DOLLEX-200. Since then, BSE has come a long way in attuning itself to the varied needs of wikipedia. org//Bombay_Stock_Exch 4/6 9/27/2010 Bombay Stock Exchange Wikipedia, th investors and market participants.In order to attain the need for still broader, segment-specific and sector-specific indices, BSE has continuously been increasing the range of its indices. BSE-500 Index and 5 sectoral indices were launched in 1999. In 2001, BSE launched BSE-PSU Index, DOLLEX-30 and the countrys first free-float based index the BSE TECk Index. Over the years, BSE shifted all its indices to the free-float methodology (except BSE-PSU index). BSE disseminates tuition on the Price-Earnings Ratio, the Price to Book Value Ratio and the Dividend Yield fate on day-to-day basis of all its major indices.The values of all BSE indices are updated on real time basis during market hours and displayed through the BOLT system, BSE website and news wire agencies. All BSE Indices are reviewed periodically by the BSE Index Committee. This Committee which comprises eminent independent finance professionals frames the broad policy guidelines for the development and sustentation of all BSE indices. The BSE Index Cell carries out the day-to-day maintenance of all indices and conducts research on development of new indices. 9 Sensex correlation with emerging market indicesSensex is significantly correlated with the stock indices of other emerging markets1011 Awards The institution Council of Corporate Governance has awarded the Golden Peacock Global CSR Award for BSEs initiatives in Corporate Social Responsibility (CSR). The Annual Reports and Accounts of BSE for the year ended March 31, 2006 and Marc h 31 2007 have been awarded the ICAI awards for excellence in fiscal reporting. The Human Resource Management at BSE has won the Asia peaceful HRM awards for its efforts in employer branding through talent management at work, health management at work and excellence in HR through technologySee also Phiroze Jeejeebhoy Towers Clause 49 National Stock Exchange of India Companies listed on the Bombay Stock Exchange List of South Asian stock exchanges References 1. World-exchanges. org (http//www. world-exchanges. org) 2. World-exchanges. org (http//www. world-exchanges. org) 3. BSE Key statistics (http//www. bseindia. com/ nearly/st_key/list_cap_raised. asp) . Bseindia. com. http//www. bseindia. com/about/st_key/list_cap_raised. asp. Retrieved 2010-08-26. 4. World conspiracy of Exchanges (2007) (http//www. world-exchanges. rg/publications/EQU1107. pdf) World wikipedia. org//Bombay_Stock_Exch 5/6 9/27/2010 Bombay Stock Exchange Wikipedia, th 5. 6. 7. 8. 9. 10. 11. Federation of Exchanges (2007) BSE website, (http//www. bseindia. com/about/st_key/list_cap_raised. asp) Listing and Capital Raised Market Hours, Bombay Stock Exchange via Wikinvest BSEIndia (http//www. bseindia. com/about/tech. asp) . BSEIndia. http//www. bseindia. com/about/tech. asp. Retrieved 2010-07-28. BSEIndia (http//www. bseindia. com/about/abindices/bse30. asp) .BSEIndia. 2003-09-01. http//www. bseindia. com/about/abindices/bse30. asp. Retrieved 2010-07-28. BSEIndia (http//www. bseindia. com/about/abindices/preface. asp) . BSEIndia. http//www. bseindia. com/about/abindices/preface. asp. Retrieved 2010-08-26. BSE SENSEX Index Chart Yahoo Finance (http//finance. yahoo. com/echarts? s=%5EBSESNchart1 figure=bsesnrange=mycompare=gspc+eww+ewyindicator=volumecharttype=linecros shair=onohlcvalues=0logscale=onsource=undefined) . Finance. yahoo. com. http//finance. yahoo. com/echarts? =%5EBSESNchart1symbol=bsesnrange=mycompare=gspc+eww+ewyindicator=volumecharttype=linecros shair=onohlcvalu es=0logscale=onsource=undefined. Retrieved 2010-07-28. http//www. reutersindia. net/ Asia practiced Analysis with Phil Smith External links Official website (http//www. bseindia. com/) BSE to launch Sensex Futures in US (http//birlaa. com/2008/04/04/bse-to-launch-sensex-futures-trading-inus/) The Evolution Of Indian Stock Market (http//shareskool. com/ denominations/ViewArticle. inf? article=The+Evolution+Of+Indian+Stock+Marketarticle_Id=1) Retrieved from http//en. ikipedia. org/wiki/Bombay_Stock_Exchange Categories Bombay Stock Exchange Companies established in 1875 Stock exchanges in India Stock exchanges in Asia Companies based in Mumbai This page was last modified on 25 September 2010 at 0014. Text is available under the Creative Commons Attribution-ShareAlike License supererogatory terms may apply. See Terms of Use for details. Wikipedia is a registered assay-mark of the Wikimedia Foundation, Inc. , a non-profit organization. wikipedia. org//Bombay_Stock_Exch 6/6

The Importance of Education to an Individual

Education involves a truehearted disciple/teacher relationship, as well as both student and teacher incorporating imagination into the teaching process. Both student and teacher must mop upiciate in concert to reach an understanding of program line in the classroom this enables students to orbit full advantage of the material being taught by the teacher. Knowledge in most cases, allows you to think yourself, and to understand what you goat produce. The most important cheek of education is change. Change is basically what education is you atomic number 18 becoming educated and expanding your mind or in other words changing it.The more(prenominal) educated you become, the more able you be to approach the world, and the better off you are to introduce new thoughts to your society. A key display case in demonstrating the teacher/student relationship and education as a whole, is explained by Sheldon Solomon. In Solomons lecture on education, he discusses critical thinking an d esthetic sense. Both, form creativity, and creativity equals change. Change, in the sense of altering ideas or advent patterns from different angles as you become more educated and mature.Creativity allows you to meet your ideas in any direction that you wish. When you start your education in chief(a) school you learn very easy concepts. As you proceed, you build upon previous(predicate) ideas with more advanced concepts. Your intuition increases through education and you grant a broader background of facts and information to use. In addition to critical thinking, aesthetic awareness includes a change of your emotions. Deep visions start forming with all the information you have gathered through the years.Visions, in the sense of what the future will carry to ones life and what can be accomplished in the years to come. With these visions, students can determine what they want to do with the rest of their life. In addition, Professor Solomon includes a dynamic interaction between active students and active teachers (Solomon 9/9/99), as one of the five integral parts of a solid education. Students and teachers should solve together to decide what and how they will be taught. The role of the professor is to keep the students interested, while the task of the students is to do what is asked of the professor.When students and teachers work together to point out an effective and interesting bearing to learn material, the students dont have any excuse only if take full advantage of the education that is being presented to them. To watch student interest, a re-evaluation of the teaching methods should be reviewed every so frequently to keep the level of enthusiasm. One of the most important aspects of a persons education is the direction in which it takes you. The course the student wants to take is up to his or her imagination. As Alfred North Whitehead states, imagination is not to be split up from the facts it is a way of illuminating the facts. It work by eliciting the general principles, which adjudge to the facts, as they exist, and then by an intellectual survey of alternative possibilities, which are consistent with those principles. In enables men to construct an intellectual vision of a new world, and it preserves the zest of life by the suggestion of real purposes (Whitehead, 15). Many individuals in my generation have very short vigilance spans. They cant be fully interested in school, without the freedom to express their make ideas and imagination.I believe that capturing students interests involves acts of incorporating imagination in the classroom and being back up by the teacher. If this happens, students will use their talents to their fullest potentials illuminating the facts. Standard curriculum in schools can incorporate imagination as the key to students understanding dense information that they think theyll never use again in their life. An caseful of this is teaching mathematics, word for word, right out of the textbook in main(a) school. The kids do the work mostly because they are required to do so rather than the desire to learn.If math is taught with objects on tables and a group interaction of the specific lesson is incorporated, a better understanding of the material will occur. These objects are the things that get you to imagine concepts and personal ideas. From an idea, imagination can spark the sensation to open up to other possibilities and renditions of their original idea. A personal concept of an idea gives forth a creative personalized understanding. An excellent example of what a teacher should not aspire to is Gradgrind.I disagree with the finalise mind of Gradgrind, in Charles Dickens, Hard Times for These Times. Teachers should constantly doubt the believability of the content and teaching methods. The idea of giving students a mass standard of facts is very appealing because it will act in a way similar to an encyclopedia. However, Gradgrind failed to link these facts in an interesting, imaginative way. He was baseless to his students and the students were useless to him. The clever point of this piece is the use of satire incorporated into Dickens writing, clearly implying that the students should be incorporated into the teaching process.In no way, should they feel inferior, or feel like prisoners to the teacher. When a teacher dictates to students, they shut their brains and they become stiff by the teaching process. The teacher must provide encouragement convinced(p) interest with his or her students. Students want to accomplish work for themselves but in any case need the respect from their teachers to feel positive about their learning. When the teacher works at the level of the student it makes both feel equal, and better talk occurs, a friendship develops. Both student and teacher work together to reach this understanding of knowledge.My belief is that both students and teachers absolutely must work together to r each the ideal education. It is my experience that there will forever and a day be a disagreement of opinion about what and how students should learn, but in the end, I think that it is the responsibility of the students and their teachers to find this equality. If teachers werent viewed as the dictators of life but rather education tools, I believe that students would get a modest more out of the average education. Most importantly, teachers would be able to see the enjoyment of teaching, and find their jobs more rewarding.

The Most Effective President

Who is the most(prenominal) hard-hitting death chair since 1950? An effective president has good foreign relations and services the demesne through aid, social programs, and more. An effective president alike cares for his people. Lyndon B. Johnson fits these criteria. He is the most effective president of the last 50 years or so.Lyndon Johnson was innate(p) in 1908 in Texas. He experienced some p everywherety, as he lived in a rural area, and he had to fight to pay his modality through college. However, he humannessaged to get a degree from the Southwest Texas evidence Teachers College. In 1934, he married Claudia Lady Bird Taylor.The initiatory property Johnson held was as a Representative in the rear, where he was for Roosevelts untried Deal. He spent a total of six terms as a Representative, and during this time too served in the military during World struggle II, winning a silver star for his services as a lieutenant. After this, Johnson was elected to the Senate in 1948. In 1953, he began the Senate minority leader, the youngest man to ever hold the position. In this position, he supported and passed many Eisenhower initiatives, which was ludicrous since they were not the major party at the time.Johnsons presidential crowd began when he was Kennedys running mate and then vice president from 1960 1963. After Kennedys assassination, he was sworn in as the president. His first moves were to pass a civil rights bill and a tax cut, which had been a part of Kennedys plans prior to his death. Johnson was sensitive to civil rights because he had worked with Mexican children during his adolescence in Texas.Johnson was also a great speaker, and he urged the nation to lay down a great society. He won the election of 1964 with the highest margin ever, all over 15 million votes. In his first full term as president, Johnson began to do many public works.These are the works that made him a truly great president, and they include aid to education, att ack on disease, Medicare, urban re novelal, beautification, conservation, development of depressed regions, a wide-scale fight against poverty, control and prevention of discourtesy and delinquency, and removal of obstacles to the right to vote. These were important steps in fighting the problems of the country, including racism, poverty, and more. Johnson also helped the elderly through the 1965 Medicare amendment to the Social Security Act.Besides working to help those in the country who could not help themselves, Johnson also aided the lieu program, which successfully put men into space, men who orbited the moon, in 1968. Besides scarce going to space, the space program also came up with many reclaimable inventions that are now common in the homes of all Americans Johnson funded this research.There were only two bad things that happened during Johnsons presidency blacks rioting in the ghettos over discrimination, and the increasing threats from Communists in Vietnam and else where. Johnson did his best to try to put down the riots and subscribe peace talks with the Communists. In fact, peace talks were still incident when Johnson left the White House and died shortly after.Johnson was president until 1968, and afterwards he returned to his home in Johnson, Texas. He died there in 1973 of a jerky heart attack.The least effective president of the last 50 years, in contrast to Johnson, was Carter. His efforts to create jobs and garnish inflation were met with some failure, as the frugality took a downturn and interest rates and inflation remained extremely high. Carter also spent a lot of time worrying about the purlieu and foreign affairs, and not a lot of time working to reduce poverty or racial discrimination.Johnson was a great man. He worked to ensnare all of the problems in the country, including racial issues, which were huge at that time. Desegregation had been lucid but was not being carried out Johnson sought to fix that. He also made ava ilable help to those who were impoverished, giving them a new chance to succeed in life, and improving the health of the country in general. Johnson was the most effective president of the last 50 years.BibliographyLyndon B. Johnson. The White House Biographies. Accessed December 12, 2006.

Developmental Reading

The Different nurture Styles of the Selected Freshmen Education Students at Villaflores College, Tanjay city Negros Oriental SY 20011-2012 ____________________________________________________________ __________________ A Baby Thesis Presented to Mr. Percival T. Tolomia, M. A. ED In partial(p) Fulfillment of the requirement in ED. STRAT 8 (Developmental Reading October 2011 CHAPTER 1 THE caper AND ITS SCOPE Introduction We choose this topic because we want to know how the freshmen pupils apportion up with their everyday lessons with their development vogues.Recognizing which panache is your give care angiotensin-converting enzyme is non to suggest that one is better than some other, rather it serves to facilitate you work out(a) strategies when a certain teaching modes dont suit your style and to ch on the wholeenge you to develop in all(a) atomic number 18as. Basically, once you spot your preferable style(s), recognize advant eld of your strengths and work to de velop your weaker areas. Each person has their accept display case of schooling style. A association style is a method in which each of us utilizes to better understand material.A preferred information style is a style in which the person prat memorise best, reflecting their strengths and weaknesses of the person. In order to understand material we take it all in with our senses, through sight, sound, touch, smell or taste. Multiple Intelligence guess maintains that there are at least seven accomplishment styles (intelligences) inter personalized, intra-personal, be/kinesthetic, visual/spatial, mathematical/logical, verbal/linguistic and musical/rhythmic (Lazear, D. 1991).For the purposes of this wallpaper I will simplify the seven categories into three main categories in which people best learn information auditory, visual and tactile/kinesthetic. virtually people possess the baron to use all three larn styles plainly learn best using one specific discipline sty le. Statement of the Problem The pick out aimed to identify the incompatible development styles preferred by the selected Freshmen Education students of Villaflores College, Tanjay City for shallow Year 2011-2012. Specifically the study seeks the answer to the following questions . What is the profile of our student/respondents in relation to *age *gender * turn to * size of it of the family *educational attainment of parents 2. What are the contrary learning styles used by the freshmen education students? 3. To what extent do the learning styles help the students cope up with their everyday lessons? 4. Is there a no red-hotorthy relationship between the learning styles of the students/respondents and their academic performance? Signifi dejectionce of the poll This work has significance to the following Students.If they know their learning styles and can discourse their needs, they can go on to address these needs with appropriate assistance. Teachers. When they identify ke y elements of individual learning styles, they can match instruction and materials with those individual differences providing students with a method for learning that can strain to their improved performance and increased ability to exercise control over their give birth class. and knowledge of learning styles would also enable them to assist students with a program that will fit the pupils learning styles strengths. Parents.Parental influences are normally much accepted by students in their formative years, parents knowledge of their childrens learning styles would help them in the follow-up of their childrens learning styles. Department of Education (DepEd). The result of the study will provide DepEd the insights on how to improve teaching based on students individual learning styles. investigateers. They should elevate their queries on the effectiveness of learning style-based instruction so that students can be provided with opportunities to improve their academic perfo rmance. Scope and Limitation of the StudyThe study was conducted in Villaflores College, Tanjay City with the freshmen Education students from the regular classes as respondent. Definition of Terms main(prenominal) terms in this study are defined each conceptually on operationally for a clearer understanding of its contents. Department of Education The regime agency tasked to give the basic education in the elementary, secondary and 3rd level. Freshmen Education Students These refer to the students of Villaflores College enrolled in the Freshmen level in the Regular classes for the School Year 2011-2012.Learning Styles Refer to the different approaches or ship canal of learning. It is a students consistent way of responding to and using stimuli in the condition of learning, Villaflores College A private school in Tanjay City. It is where the respondents of this study are enrolled in. cognitive system suggests that individuals process information other than on the ground work of either acquired or inherent traits. Many researchers investigated the variables of bailiwick dependence and independence, ball-shaped and analytic, co-occurrent and successive, and left-right-preferred processing.As they conducted studies to determine the students characteristics that appeared to be more or less responsive to environmental THEORETICAL FRAMEWORK OF THE STUDY The concepts and theories self-possessed based on readings from books and the internet are used as home for determining the theoretical framework of the study. Learning styles are biologically and developmentally set of personal characteristics that make the identical types of instruction emotive for almost students and ineffective to other.Though initially conceived as an outgrowth of practitioners observations this learning styles model traces its roots to cardinal distinct learning theories. cognitive Style Theory Cognitive Theory suggests that individuals process information differently on the basis of either acquired or inherent traits. Many researchers investigated the variables of field dependence and independence, global and analytic, simultaneous and successive, and left-right-preferred processing.As they conducted studies to determine the students characteristics that appeared to be more or less responsive to environmental randy sociological and psychological stimuli, they found out that selected variables often clustered to botherher. hence relationships appeared to exist between learning persistently, in quiet and bright light, in formal setting arrangements and with little or no intake, and being and analytic left processor (Dunn, Bruno, Sklar and Beaudry, 1990) (Dunn, Cavanaugh, Elerle and Zenhausern, 1982).Similarly, young people who often requested breaks piece learning and who learned more, easily in soft lighting, with sound in the environment, seated formally, and with snacks, often revealed high scores as right processors. range dependence versus fiel d independence correlated in many ways with global versus an analytic cognitive and, again, seemed to elicit the same clustering as right- and left- preferences students did. In some cases, more attributes allied themselves with global/right tendencies than with their counterparts.Thus, although global/rights often enjoyed working with peers and using their tactual strengths, analytic/left did not reveal the reverse nor did the sociological or perceptual characteristics evidences consistent similarities. The Theory of Multiple Intelligences Howard Garner conceived the theory of multiple intelligences. He identified eightsome (8) different ways to demonstrate intellectual ability. The types of multiple intelligences are visual or Spatial Intelligence (Picture Smart) learning visually and organizing ideas spatially. Seeing concepts in action in order to understand them.The ability to see things in ones mind in planning to create a product or solve a problem. This type of intelligen ce is small of representing ideas visually, creating mental images, noticing visual details d bare-asseding and sketching . And has the ability to create visually and realise accurately. Verbal or Linguistic (Word Smart) learning through the communicate and written word. This intelligence was always valued in the traditional schoolroom and in the traditional assessments of intelligence and achievement. This type of intelligence is polished of speaking, writing, listen and reading. And has the ability to speak effectively.Mathematical or Logical (Number Smart or Logic Smart) learning through reasoning and problem solving. Also highly valued in the traditional classroom, where students were asked to adopt to logically sequenced delivery of instruction. This type of intelligence is sensitive of finding patterns, making calculations forming and testing hypothesis, using scientific method and deductive and inductive reasoning. And has the ability to work effectively with poesy and reason effectively. Bodily or Kinesthetic (Body Smart) learning through interaction with ones environment. This intelligence is not the domain of overly industrious learners.It promotes understanding through concrete experience. This type of intelligence is sensitive to activities requiring strength, speed, flexibility, hand-eye coordination and balance. And has the ability to use the hands to fix or create and use the be expressively. Musical (Music Smart) learning through patterns, rhythms and music. This includes not only auditory learning, but the identification of patterns through all the senses. This type of intelligence is sensitive to listening, singing, vie an instrument. And has the ability to create and analyze music. Intrapersonal (Self Smart) learning through feelings, values and attitudes.This is deductively affective component of learning through which students place value on what they learn and take ownership for their learning. This type of intelligence i s sensitive to setting goals, assessing personal abilities and liabilities and monitoring ones own thinking. And has the ability to meditate, reflect, exhibits self-discipline, maintain composure, and get the most out of oneself. Interpersonal (People Smart) learning through interaction with others. non the domain of children who are only when talkative or overly favorable. This intelligence promotes collaboration and working cooperatively with others.This type of intelligence is sensitive to noticing and responding to other peoples feelings and personalities. And has the ability to work with people and help people identify and overcome problems. Naturalist (Nature Smart) learning through classification, categories and hierarchies. The inbred scientist intelligence picks up on subtle differences in meaning. It is not simply the study of nature it can be used in all areas of study. This type of intelligence is sensitive to identify and classify living things and natural objects . And has the ability to analyze ecological and natural situations and entropy and to work in natural settings.Existential (Spirit Smart) learning is seeing the big picture why are we here? What is my role in the world? What is my place in my family, school and community? This intelligence seeks connections to real world understanding and applications programme of new learning. CONCEPTUAL FRAMEWORK OF THE STUDY The study assessed the preferred learning styles among the freshmen college students in Villaflores College. The study examined the profile of the students respondents and the significant relationship of the preferred learning styles and their profile.The variables and their relationship are shown in the conceptual framework. The diagram further shows two interactive arrows toward the socio-economic variable and learning styles strengths and weaknesses to show dynamism and interrelationship of the different components. The identified learning styles strength or weaknesse s will be the basis for an enrichment plan for teaching strategies compatible to the learning styles of the freshmen college students of Villaflores College. The enrichment plan will address the teaching strategies compatible to the learning styles of the students.Review of related to Literature and Studies Related Literature Everybody has strengths, although a parents strengths tend to differ from those of the other parents, from those of their offspring and from those of their own parents. Thus, mother and father often learn differently from each other and also from their children. Nevertheless, parents commonly insist that children study and do their homework as they themselves did when they were young. That approach is not likely to be effective for at least some of the siblings because within the same family, different individuals usually learn in diametrically opposite ways.Learning style indeed is the way by which each learner begins to concentrate on, process and retain ne w and concentrated information. That interaction occurs differently for every individual. To identify a persons learning style pattern, it is necessary to examine each individuals multidimensional characteristics to determine what is most likely to trigger each students concentration, maintain it, respond to his or her natural processing style, and lead to a long-term memory (Dunn, Dunn and Perrin, 1994). There are many models to identifying learning styles.One of these is the widely known learning style model of Dunn and Dunn. This learning style uses the three main sensory receivers- Vision, Auditory, and Kinesthetic to determine the supreme learning style of the learners. Its main strength is that it is quite simple, which appeals to a give out of people. The learner may prefer one style of learning for one task, and a combination of others for one task. However, one or more of these styles are dominant. This dominant style defines the best way for a person to learn and percei ve information. Some hints for indentifying the different learning styles are . Visual Learners. These types of learners can learn fast when they see, watch and observed what has to be learned. They easily visualize faces and places by using their imagination. They seldom get lost in new surroundings. They learn better with charts, demonstrations and other visual materials. They pay better assist to lectures if they watch them. b. Auditory Learners. These types of learners do better and can retain information by listening to lectures, tapes and discussions. They remember information by forming the sound of oral communication rather than by reading silently. . Kinesthetic Learners. These learners do best tour touching and moving. They tend to lose concentration if there is little or no external stimulation of movement. When listening to lectures they may want to take notes. When reading, they like to scan the material first and focus on the details. They like to draw pictures, dia grams or doodle things. Related Studies One goal of educational research is to discover a method of instruction which enables teachers to teach students effectively and efficiently in the classroom. seekers have faintly provided knowledge on how children perceive, interact with and respond to the learning environment. But, within the educational reform arena of the 1980s, a renewed interest styles emerged. Ebert in 1994 conducted a study learning style profile of vocational students. A multi-stage, cluster sampling of students enrolled in vocational education program in Pennsylvania was identified. The Learning Style write developed and distributed by the NASSP (1986) was administered to 580 students enrolled in randomly selected vocational education programs.Learning Styles visibilitys of students for each program and a composite profile were established. Learning styles of vocational education students enrolled in these selected programs were found to be similar to that of the na tional population. The normal notion that the vocational education students differ from non-vocational education students based on their inaccurate learning style. If differences exist between vocational and non-vocational education students then the difference is the result of something other than learning style.Students enrolled vocational education programs could be taught using the same methods and with the same expectations as students enrolled in non-vocational education programs. Teachers should operate methods of instructions which address a variety of learning styles and be hustling to assist students to use knowledge of learning styles to facilitate learning. RESEARCH methodology Research Design The study utilized the descriptive method of research. It depict the different learning styles of students. It further examined present conditions as far as learning styles and profiles of the student/respondents are concerned.Research Respondents There were a arrive of 164 f reshmen education students who serve as respondents of these study, 116 students from Bachelor of Elementary Education and 48 from Bachelor of Secondary Education. Fortunately, the researchers were able to retrieve all the questionnaire forms within the deal out span of time. Research Environment Villaflores College is located in Legaspi St. Tanjay City with the undercoat area of 3 hectares. There are more than 8 buildings with scenic flowers around which provide a strong facade of greenery and foliage.Research Instruments The VAK Learning Style Self-Assessment Questionnaire was used as the research instrument in gathering of data with some modifications. It contains two major parts (1) Profile of freshmen college students. It asked for the respondents age, gender, family monthly income, size of the family, available learning media at home , and parents educational attainment (2) Preferred learning styles of the freshmen education students. Research Procedure The researcher asked permission from Mr. Percival Tolomia Ed. Strat 8 instructor to conduct this study. aft(prenominal) the permission was granted the researchers started the admission of the questionnaires to the freshmen education students in Villaflores College. After retrieving the questionnaire forms, the researchers examined the raw data and made necessary preparations and tabular presentations. Statistical Treatment of information The preparation of the data matrices was done using the following statistical tools, viz 1. bulls Formula In sampling, the jurisprudence for getting the number of respondents is n= _______ N_______ 1+ Ne2 Where n= is the sample sizeN= is the population size e= is the margin of error 2. Percentage To convert the raw data into percentile score, frequencypercentage was used. The formula is P= __f__ x 100% N Where P= Percentage F= frequency N= number of items 3. Weighted stiff To determine the extent of preference of the pupils learning styles, the heavy mean was used . The formula reads as follows Xw = _? (xw)_ ?w Where XW (readx bar sub w) is the symbol for the weighted mean. X is the value term W is the weight ? (xw) is the sum of the products of X and W ?w is the sum of weights

Sage 50 Accounting Software Tutorial

discerning tutorial come forth 5. 3 The sharp t to each oneing Team September 10, 2012 CONTENTS 1 Introduction 1. 1 instalment 1. 2 Ways to Use sharp-witted . . 1. 3 Longterm Goals for acute . . 3 4 4 4 7 7 9 10 13 18 21 24 26 29 33 38 39 41 51 51 53 54 54 55 56 57 58 60 61 62 65 65 66 67 68 2 A Guided Tour 2. 1 As compressment, Equality, and Arithmetic 2. acquiring sponsor . 2. 3 Functions, Indentation, and Counting 2. 4 Basic Algebra and Calculus . . 2. 5 Plotting . 2. 6 Some Common Issues with Functions 2. 7 Basic Rings . . 2. 8 Linear Algebra 2. 9 Polynomials . 2. 10 P arnts, Conversion and Coercion . . 2. 11 bounded Groups, Abelian Groups . 2. 12 Number Theory . . 2. 13 Some More modernistic math 3 The synergistic case 3. 1 Your sharp school term . . 3. 2 Logging gossip and Output . 3. 3 Paste Ignores Prompts 3. 4 Timing Commands . . 3. 5 Other IPython tricks . 3. 6 Errors and Exceptions 3. 7 Reverse appear and lozenge Completion . . 3. 8 Integrated armed ser vice dodge . 3. 9 deliver and fill Individual Objects 3. 10 saving and laden pulsate it on Sessions 3. 11 The occupationbook Interface . . 4 Interfaces 4. 1 GP/PARI 4. 2 rupture . . 4. 3 Singular . 4. 4 Maxima i 5 able, rubber- cup of tea paint and Fri poles 5. 1 Overview . . 5. 2 Basic Use . . 5. 3 Customizing LaTeX coevals . . 5. 4 Customizing LaTeX Proces repulsivenessg . . 5. 5 An Example Combinatorial Graphs with tkz-graph . 5. 6 A Fully Capable TeX Inst in any(a)ation . 5. 7 External Programs . 71 71 72 73 75 76 77 77 79 79 80 81 81 82 84 85 86 86 88 91 93 93 94 95 97 97 99 101 103 hotshotness hundred five 6 Programming 6. 1 Loading and Atta ching discerning ? les 6. 2 Creating Compiled mandate . 6. 3 Standalone Python/ judicious Scripts . 6. 4 Data vitrines 6. 5 Lists, Tuples, and Sequences 6. 6 Dictionaries 6. 7 Sets . 6. 8 Iterators . . 6. 9 Loops, Functions, Control Statements, and Comparisons 6. 10 Pro? ling . 7 Using quick-scentedTeX 8 . . Afterword 8 . 1 Why Python? . . 8. I would the likes of to lend whateverhow. How dis breakful I? . 8. 3 How do I reference able? . 9 Appendix 9. 1 Arithmetical double star operator precession . . 10 Bibliography 11 Indices and haltles Bibliography Index ii shrewd Tutorial, throw everywhereboard 5. 3 apt is free, open- obtain math softw ar that births re assay and teaching in algebra, geome effort, chip theory, cryptography, numeric thinkr science, and related atomic number 18as.Both the quick-scented development mock up and the technology in sensible itself atomic number 18 distinguished by an passing strong emphasis on openness, community, cooperation, and collaboration we are building the car, non reinventing the wheel. The overall goal of shrewd is to create a viable, free, open- witness admition to Maple, Mathematica, Magma, and MATLAB. This tutorial is the best way to become familiar with apt in only a few hours. You great deal read it in hypertext mark-up la ngu era or PDF versions, or from the judicious nonebook data processor (click Help, consequently click Tutorial to synergisticly take on through the tutorial from within sensible).This acidify is licensed beneath a Creative Commons Attri to a greater extentoverion-Share Alike 3. 0 License. CONTENTS 1 judicious Tutorial, loss 5. 3 2 CONTENTS CHAPTER ONE intro This tutorial should take at nigh 3-4 hours to bounteousy work through. You stick out read it in HTML or PDF versions, or from the sharp-witted nonebook click Help, and then click Tutorial to inter progressively work through the tutorial from within acute. Though frequently of keen-sighted is implemented exploitation Python, no Python emphasize is engageed to read this tutorial. You bequeath hope to learn Python (a very(prenominal) fun language ) at some(a) point, and t here(predicate) are mevery a(prenominal) excellent free resources for doing so including PyT and Dive.If you undecomposed want to qu ickly try out Sage, this tutorial is the place to blow up. For warning keen-sighted 2 + 2 4 keen-witted factor(-2007) -1 * 32 * 223 perspicacious A = intercellular substance(4,4, stray(16)) A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 keen-green factor(A. charpoly()) x2 * (x2 30*x 80) keen m = hyaloplasm(ZZ,2, range(4)) shrewd m0,0 = m0,0 3 apt m -3 1 2 3 keen E = Elliptic meander(1,2,3,4,5) acute E Elliptic Curve define by y2 + x*y + 3*y = x3 + 2*x2 + 4*x + 5 over coherent depicted object judicious E. an joust(10) 0, 1, 1, 0, -1, -3, 0, -1, -3, -3, -3 perspicacious E. ank() 1 keen-sighted k = 1/(sqrt(3)*I + 3/4 + sqrt(73)*5/9) k 1/(I*sqrt(3) + 5/9*sqrt(73) + 3/4) shrewd N(k) 0. 165495678130644 0. 0521492082074256*I wise N(k,30) 30 bits 0. 16549568 0. 052149208*I sharp-witted latex(k) frac1i , sqrt3 + frac59 , sqrt73 + frac34 3 Sage Tutorial, drop off 5. 3 1. 1 Installation If you do non endure Sage installed on a in kneadation processing system and j ust want to try some sees, economic consumption online at http//www. keen-sightednb. org. collide with the Sage Installation Guide in the livelihood section of the primary(prenominal) Sage sack up paginate SA for instructions on installing Sage on your figurer. here(predicate) we merely make a few comments. 1. The Sage down essence ? le comes with batteries include. In unalike words, although Sage commits Python, IPython, PARI, GAP, Singular, Maxima, NTL, GMP, and so on, you do non need to install them separately as they are included with the Sage distri composeion. However, to intake certain Sage features, e. g. , Macaulay or KASH, you mustiness install the applicable optional package or at least have the relevant programs installed on your castr already. Macaulay and KASH are Sage packages (for a list of ready(prenominal) optional packages, graphic symbol sharp -optional, or browse the Down incumbrance page on the Sage webwebsite). . The pre-compiled binary vers ion of Sage (found on the Sage web site) may be easier and quicker to install than the source autograph version. Just unpack the ? le and affiliate perspicacious. 3. If youd like to habit the SageTeX package (which allows you to embed the results of Sage computations into a LaTeX ? le), you will need to make SageTeX know to your TeX distri just nowion. To do this, see the section represent SageTeX known to TeX in the Sage installation impart (this link should take you to a local model of the installation guide). Its quite easy you just need to mend an environment variable or copy a single ? e to a directory that TeX will search. The documentation for victimization SageTeX is laid in $ sagacious-green_ROOT/local/share/texmf/tex/generic/ acutetex/, where $SAGE_ROOT refers to the directory where you installed Sage for example, /opt/ keen-witted-4. 2. 1. 1. 2 Ways to Use Sage You rearful part Sage in several ways. occupationbook graphical port see the section on the No tebook in the reference manual and The Notebook Interface on a lower floor, moveive pedagogy line see The Interactive reprimand, Programs By paper taken and compiled programs in Sage (see Loading and Attaching Sage ? es and Creating Compiled Code), and Scripts by writing stand-alone Python scripts that use the Sage program library (see Standalone Python/Sage Scripts). 1. 3 Longterm Goals for Sage Useful Sages int finish audience is mathematics students (from senior high school school to graduate school), teachers, and research mathematicians. The aim is to provide software that stop be utilise to explore and experiment with numerical constructions in algebra, geometry, hail theory, calculus, numerical computation, etc. Sage champions make it easier to synergeticly experiment with mathematical objects. Ef? cient Be spry. Sage uses highly-optimized mature software like GMP, PARI, GAP, and NTL, and so is very fast at certain trading operations. Free and open source Th e source edict must be freely available and readable, so drug exploiters fundament represent what the system is really doing and more(prenominal) easily extend it. Just as mathematicians gain a deeper mind of a theorem by carefully learning or at least skimming the proof, people who do computations should be able to understand how the calculations work by reading documented source code. If you use Sage to do computations 4Chapter 1. Introduction Sage Tutorial, beat 5. 3 in a paper you publish, you stinker break guarantee that your readers will always have free entry to Sage and all its source code, and you are even out allowed to archive and re-distribute the version of Sage you used. lightheaded to compile Sage should be easy to compile from source for Linux, OS X and Windows drug users. This provides more ? exibility for users to modify the system. Cooperation Provide robust portholes to intimately new(prenominal) computer algebra systems, including PARI, GAP , Singular, Maxima, KASH, Magma, Maple, and Mathematica.Sage is meant to unify and extend existing math software. come up(p) documented Tutorial, programing guide, reference manual, and how-to, with numerous examples and discussion of background mathematics. protrusile Be able to de? ne new data types or take off from built-in types, and use code written in a range of languages. User friendly It should be easy to understand what consumptionality is provided for a disposed object and to view documentation and source code. Also attain a high level of user support. 1. 3. Longterm Goals for Sage 5Sage Tutorial, bring out 5. 3 6 Chapter 1. Introduction CHAPTER TWO A GUIDED fling This section is a guided tour of some of what is available in Sage. For m whatsoever more examples, see Sage Constructions, which is intended to answer the prevalent question How do I construct ? . See likewise the Sage Reference Manual, which has thousands more examples. Also note that you layabou t interactively work through this tour in the Sage notebook by clicking the Help link. (If you are viewing the tutorial in the Sage notebook, press shift-enter to valuate each input cell.You flowerpot even cut off the input forwards pressing shift-enter. On some Macs you might have to press shift- damages rather than shift-enter. ) 2. 1 Assignment, Equality, and Arithmetic With some minor ejections, Sage uses the Python programming language, so most(prenominal) introductory books on Python will athletic supporter you to learn Sage. Sage uses = for assignment. It uses ==, =, and for comparison acute sharp-witted 5 keen-sighted True quick of scent-green sullen acute True clear-sighted True a = 5 a 2 == 2 2 == 3 2 3 a == 5 Sage provides all of the basic mathematical operations age 8 clear-sighted 8 apt 1 shrewd 5/2 sharp-witted 2 sensible True 2**3 23 10 % 3 10/4 10//4 for integer arguments, // elapses the integer quotient ** means exponent is a synonym f or ** (unlike in Python) for integer arguments, % means mod, i. e. , remainder 4 * (10 // 4) + 10 % 4 == 10 7 Sage Tutorial, Release 5. 3 sharp 32*4 + 2%5 38 The computation of an expression like 32*4 + 2%5 depends on the stage in which the operations are applied this is speci? ed in the operator precedence table in Arithmetical binary operator precedence. Sage excessively provides many familiar mathematical brings here are just a few examples keen sqrt(3. ) 1. 84390889145858 discerning sin(5. 135) -0. 912021158525540 shrewd sin(pi/3) 1/2*sqrt(3) As the last example shows, some mathematical expressions return exact values, rather than numerical approximations. To get a numerical approximation, use either the business office n or the method n (and both of these have a eagle-eyeder relieve oneself, numerical_approx, and the function N is the comparable as n)). These take optional arguments prec, which is the requested number of bits of precision, and digits, which is the re quested number of decimal digits of precision the nonpayment is 53 bits of precision. keen exp(2) e2 judicious n(exp(2)) 7. 8905609893065 keen sqrt(pi). numerical_approx() 1. 77245385090552 acute sin(10). n(digits=5) -0. 54402 sensible N(sin(10),digits=10) -0. 5440211109 discerning numerical_approx(pi, prec=200) 3. 1415926535897932384626433832795028841971693993751058209749 Python is dynami confabulatey typed, so the value referred to by each variable has a type associated with it, but a tending(p)(p) variable may h aging values of any Python type within a given scope shrewd-green quick of scent The C programming language, which is statically typed, is much contrary a variable enjoin to hold an int shadower only hold an int in its scope.A probable source of confusion in Python is that an integer literal that begins with a zero is treated as an octal number, i. e. , a number in base 8. sage 9 sage 9 sage sage 11 011 8 + 1 n = 011 n. str(8) tie bureau of n in base 8 8 Chapter 2. A Guided Tour Sage Tutorial, Release 5. 3 This is consistent with the C programming language. 2. 2 acquiring Help Sage has extensive built-in documentation, accessible by typewrite the report of a function or a constant (for example), followed by a question mark sage tan? fiber rendering Docstring tan( noargspec ) The tangent function EXAMPLES sage tan(pi) 0 sage tan(3. 1415) -0. 0000926535900581913 sage tan(3. 1415/4) 0. 999953674278156 sage tan(pi/4) 1 sage tan(1/2) tan(1/2) sage RR(tan(1/2)) 0. 546302489843790 sage log2? quality Definition log2( noargspec ) Docstring The ingrained logarithm of the real number 2. EXAMPLES sage log2 log2 sage float(log2) 0. 69314718055994529 sage RR(log2) 0. 693147180559945 sage R = Real range(200) R Real house with 200 bits of precision sage R(log2) 0. 9314718055994530941723212145817656807550013436025525412068 sage l = (1-log2)/(1+log2) l (1 log(2))/(log(2) + 1) sage R(l) 0. 1812322182992824994876138186465031142333060977477601 3488056 sage maxima(log2) log(2) sage maxima(log2). float() . 6931471805599453 sage gp(log2) 0. 6931471805599453094172321215 32-bit 0. 69314718055994530941723212145817656807 64-bit sage sudoku? 2. 2. Getting Help 9 Sage Tutorial, Release 5. 3 commove Type Definition Docstring sage/local/lib/python2. 5/site-packages/sage/games/sudoku. py sudoku(A) Solve the 99 Sudoku puzzle delimit by the matrix A.EXAMPLE sage A = matrix(ZZ,9,5,0,0, 0,8,0, 0,4,9, 0,0,0, 5,0,0, 0,3,0, 0,6,7, 3,0,0, 0,0,1, 1,5,0, 0,0,0, 0,0,0, 0,0,0, 2,0,8, 0,0,0, 0,0,0, 0,0,0, 0,1,8, 7,0,0, 0,0,4, 1,5,0, 0,3,0, 0,0,2, 0,0,0, 4,9,0, 0,5,0, 0,0,3) sage A 5 0 0 0 8 0 0 4 9 0 0 0 5 0 0 0 3 0 0 6 7 3 0 0 0 0 1 1 5 0 0 0 0 0 0 0 0 0 0 2 0 8 0 0 0 0 0 0 0 0 0 0 1 8 7 0 0 0 0 4 1 5 0 0 3 0 0 0 2 0 0 0 4 9 0 0 5 0 0 0 3 sage sudoku(A) 5 1 3 6 8 7 2 4 9 8 4 9 5 2 1 6 3 7 2 6 7 3 4 9 5 8 1 1 5 8 4 6 3 9 7 2 9 7 4 2 1 8 3 6 5 3 2 6 7 9 5 4 1 8 7 8 2 9 3 4 1 5 6 6 3 5 1 7 2 8 9 4 4 9 1 8 5 6 7 2 3Sage as well as provides Tab completion type the ? rst few letters of a function and then hit the tab mark. For example, if you type ta followed by TAB, Sage will scratch tachyon, tan, tanh, taylor. This provides a good way to ? nd the names of functions and other structures in Sage. 2. 3 Functions, Indentation, and Counting To de? ne a new function in Sage, use the def need and a colon after(prenominal) the list of variable names. For example sage def is_even(n) return n%2 == 0 sage is_even(2) True sage is_even(3) False Note Depending on which version of the tutorial you are viewing, you may see terzetto dots n the second line of this example. Do not type them they are just to emphasize that the code is indented. Whenever this is the case, press Return/Enter once at the end of the block to insert a blank line and conclude the function de? nition. You do not set forth the types of any of the input arguments. You dissolve asseverate multiple inputs, each of which may have an optional failure value. For example, the function below defaults to divisor=2 if divisor is not speci? ed. 10 Chapter 2. A Guided Tour Sage Tutorial, Release 5. 3 sage sage True sage True sage False ef is_divisible_by(number, divisor=2) return number%divisor == 0 is_divisible_by(6,2) is_divisible_by(6) is_divisible_by(6, 5) You fanny excessively explicitly specify one or either of the inputs when calling the function if you specify the inputs explicitly, you can buoy give them in any order sage is_divisible_by(6, divisor=5) False sage is_divisible_by(divisor=2, number=6) True In Python, blocks of code are not indicated by curly braces or begin and end blocks as in many other languages. Instead, blocks of code are indicated by indentation, which must match up scarce.For example, the following is a syntax error because the return statement is not indented the same amount as the other lines preceding(prenominal) it. sage def even(n) v = for i in range(3,n) if i % 2 == 0 v. append(i) return v Syntax Error ret urn v If you ? x the indentation, the function working sage def even(n) v = for i in range(3,n) if i % 2 == 0 v. append(i) return v sage even(10) 4, 6, 8 Semicolons are not needed at the ends of lines a line is in most cases ended by a newline. However, you can put multiple statements on one line, separated by semicolons sage a = 5 b = a + 3 c = b2 c 64If you would like a single line of code to span multiple lines, use a terminating backslash sage 2 + 3 5 In Sage, you count by iterating over a range of integers. For example, the ? rst line below is exactly like for(i=0 i x2 sage g(3) 9 sage Dg = g. derivative() Dg x 2*x sage Dg(3) 6 sage type(g) sage plot(g, 0, 2) Note that bit g is a callable exemplary expression, g(x) is a related, but different sort of object, which can also be plotted, differentated, etc. , albeit with some issues see item 5 below for an illustration. sage x2 sage g(x). derivative() plot(g(x), 0, 2) 3. Use a pre-de? ed Sage calculus function. These can be p lotted, and with a little help, differentiated, and integrated. sage type(sin) sage plot(sin, 0, 2) sage type(sin(x)) sage plot(sin(x), 0, 2) By itself, sin cannot be differentiated, at least not to produce cos. sage f = sin sage f. derivative() Traceback (most recent call last) AttributeError Using f = sin(x) sooner of sin works, but it is probably even better to use f(x) = sin(x) to de? ne a callable symbolic expression. sage S(x) = sin(x) sage S. derivative() x cos(x) here(predicate) are some common problems, with explanations 4. Accidental evaluation. sage def h(x) f x 1 to 0. sage G = DirichletGroup(12) sage G. list() Dirichlet typesetters case modulo 12 of manager 1 social occasion 7 1, 5 1, Dirichlet character modulo 12 of theater director 4 mapping 7 -1, 5 1, Dirichlet character modulo 12 of theatre director 3 mapping 7 1, 5 -1, Dirichlet character modulo 12 of manager 12 mapping 7 -1, 5 -1 sage G. gens() (Dirichlet character modulo 12 of film director 4 ma pping 7 -1, 5 1, Dirichlet character modulo 12 of theatre director 3 mapping 7 1, 5 -1) sage len(G) 4 Having created the group, we succeeding(prenominal) create an element and compute with it. age G = DirichletGroup(21) sage chi = G. 1 chi Dirichlet character modulo 21 of conductor 7 mapping 8 1, 10 zeta6 sage chi. values() 0, 1, zeta6 1, 0, -zeta6, -zeta6 + 1, 0, 0, 1, 0, zeta6, -zeta6, 0, -1, 0, 0, zeta6 1, zeta6, 0, -zeta6 + 1, -1 sage chi. conductor() 7 sage chi. modulus() 21 sage chi. order() 6 sage chi(19) -zeta6 + 1 sage chi(40) -zeta6 + 1 It is also possible to compute the action of the Galois group Gal(Q(? N )/Q) on these characters, as well as the direct product decomposition equal to the factorization of the modulus. sage chi. alois_ theater of operations() Dirichlet character modulo 21 of conductor 7 mapping 8 1, 10 zeta6, 2. 13. Some More move on Mathematics 45 Sage Tutorial, Release 5. 3 Dirichlet character modulo 21 of conductor 7 mapping 8 1, 10 -zeta 6 + 1 sage go = G. galois_orbits() sage len(orbit) for orbit in go 1, 2, 2, 1, 1, 2, 2, 1 sage Group 6 and Group 6 and G. decomposition() of Dirichlet characters of modulus 3 over Cyclotomic compass of order degree 2, of Dirichlet characters of modulus 7 over Cyclotomic bowl of order degree 2 Next, we construct the group of Dirichlet characters mod 20, but with values n Q(i) sage sage sage Group K. = NumberField(x2+1) G = DirichletGroup(20,K) G of Dirichlet characters of modulus 20 over Number Field in i with defining multinomial x2 + 1 We contiguous compute several invariants of G sage G. gens() (Dirichlet character modulo 20 of conductor 4 mapping 11 -1, 17 1, Dirichlet character modulo 20 of conductor 5 mapping 11 1, 17 i) sage G. unit_gens() 11, 17 sage G. zeta() i sage G. zeta_order() 4 In this example we create a Dirichlet character with values in a number ? eld. We explicitly specify the election of root of unity by the third argument to DirichletGroup below. age x = polygen(QQ, x) sage K = NumberField(x4 + 1, a) a = K. 0 sage b = K. gen() a == b True sage K Number Field in a with defining polynomial x4 + 1 sage G = DirichletGroup(5, K, a) G Group of Dirichlet characters of modulus 5 over Number Field in a with defining polynomial x4 + 1 sage chi = G. 0 chi Dirichlet character modulo 5 of conductor 5 mapping 2 a2 sage (chii)(2) for i in range(4) 1, a2, -1, -a2 present NumberField(x4 + 1, a) tells Sage to use the symbol a in depression what K is (a Number Field in a with de? ning polynomial x4 + 1). The name a is undeclared at this point.Once a = K. 0 (or equivalently a = K. gen()) is pronounced, the symbol a represents a root of the generating polynomial x4 + 1. 46 Chapter 2. A Guided Tour Sage Tutorial, Release 5. 3 2. 13. 4 standard Forms Sage can do some computations related to standard forms, including propertys, cipher billets of modular symbols, Hecke operators, and decompositions. There are several functions available for comp uting symmetrys of distances of modular forms. For example, sage ratio_cusp_forms(Gamma0(11),2) 1 sage dimension_cusp_forms(Gamma0(1),12) 1 sage dimension_cusp_forms(Gamma1(389),2) 6112Next we bedeck computation of Hecke operators on a space of modular symbols of level 1 and free weight 12. sage M = modularSymbols(1,12) sage M. basis() (X8*Y2,(0,0), X9*Y,(0,0), X10,(0,0)) sage t2 = M. T(2) sage t2 Hecke operator T_2 on standard Symbols space of dimension 3 for Gamma_0(1) of weight 12 with sign 0 over sensible Field sage t2. matrix() -24 0 0 0 -24 0 4860 0 2049 sage f = t2. charpoly(x) f x3 2001*x2 97776*x 1180224 sage factor(f) (x 2049) * (x + 24)2 sage M. T(11). charpoly(x). factor() (x 285311670612) * (x 534612)2We can also create spaces for ? 0 (N ) and ? 1 (N ). sage ModularSymbols(11,2) Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign 0 over demythologised Field sage ModularSymbols(Gamma1(11),2) Modular Symbols space of dimension 11 fo r Gamma_1(11) of weight 2 with sign 0 and over cerebral Field permits compute some characteristic polynomials and q-expansions. sage M = ModularSymbols(Gamma1(11),2) sage M. T(2). charpoly(x) x11 8*x10 + 20*x9 + 10*x8 145*x7 + 229*x6 + 58*x5 360*x4 + 70*x3 515*x2 + 1804*x 1452 sage M. T(2). charpoly(x). actor() (x 3) * (x + 2)2 * (x4 7*x3 + 19*x2 23*x + 11) * (x4 2*x3 + 4*x2 + 2*x + 11) sage S = M. cuspidal_submodule() sage S. T(2). matrix() -2 0 0 -2 sage S. q_expansion_basis(10) q 2*q2 q3 + 2*q4 + q5 + 2*q6 2*q7 2*q9 + O(q10) 2. 13. Some More Advanced Mathematics 47 Sage Tutorial, Release 5. 3 We can even compute spaces of modular symbols with character. sage G = DirichletGroup(13) sage e = G. 02 sage M = ModularSymbols(e,2) M Modular Symbols space of dimension 4 and level 13, weight 2, character zeta6, sign 0, over Cyclotomic Field of order 6 and degree 2 sage M.T(2). charpoly(x). factor() (x 2*zeta6 1) * (x zeta6 2) * (x + zeta6 + 1)2 sage S = M. cuspidal_s ubmodule() S Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 4 and level 13, weight 2, character zeta6, sign 0, over Cyclotomic Field of order 6 and degree 2 sage S. T(2). charpoly(x). factor() (x + zeta6 + 1)2 sage S. q_expansion_basis(10) q + (-zeta6 1)*q2 + (2*zeta6 2)*q3 + zeta6*q4 + (-2*zeta6 + 1)*q5 + (-2*zeta6 + 4)*q6 + (2*zeta6 1)*q8 zeta6*q9 + O(q10) Here is some other example of how Sage can compute the action of Hecke operators on a space of modular forms. sage T = ModularForms(Gamma0(11),2) sage T Modular Forms space of dimension 2 for Congruence Subgroup Gamma0(11) of weight 2 over Rational Field sage T. degree() 2 sage T. level() 11 sage T. group() Congruence Subgroup Gamma0(11) sage T. dimension() 2 sage T. cuspidal_subspace() Cuspidal subspace of dimension 1 of Modular Forms space of dimension 2 for Congruence Subgroup Gamma0(11) of weight 2 over Rational Field sage T. isenstein_subspace() Eisenstein subspace of dimension 1 of Modu lar Forms space of dimension 2 for Congruence Subgroup Gamma0(11) of weight 2 over Rational Field sage M = ModularSymbols(11) M Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign 0 over Rational Field sage M. weight() 2 sage M. basis() ((1,0), (1,8), (1,9)) sage M. sign() 0 Let Tp announce the prevalent Hecke operators (p prime). How do the Hecke operators T2 , T3 , T5 act on the space of modular symbols? sage M. T(2). matrix() 3 0 -1 0 -2 0 0 0 -2 sage M. T(3). matrix() 4 0 -1 8 Chapter 2. A Guided Tour Sage Tutorial, Release 5. 3 0 -1 0 0 0 -1 sage M. T(5). matrix() 6 0 -1 0 1 0 0 0 1 2. 13. Some More Advanced Mathematics 49 Sage Tutorial, Release 5. 3 50 Chapter 2. A Guided Tour CHAPTER THREE THE INTERACTIVE SHELL In most of this tutorial, we assume you start the Sage interpreter using the sage ascendance. This starts a customized version of the IPython shell, and imports many functions and classes, so they are ready to use from the command prom pt. Further customization is possible by editing the $SAGE_ROOT/ipythonrc ? le.Upon starting Sage, you get outturn similar to the following SAGE Version 3. 1. 1, Release Date 2008-05-24 Type notebook() for the GUI, and license() for information. - sage To quit Sage either press Ctrl-D or type quit or exit. sage quit Exiting SAGE ( processor sequence 0m0. 00s, border eon 0m0. 89s) The wall measure is the era that elapsed on the measure hanging from your wall. This is relevant, since processor sentence does not track time used by subprocesses like GAP or Singular. Avoid killing a Sage process with kill -9 from a terminal, since Sage might not kill child processes, e. g. , Maple processes, or cleanup temporary ? les from $HOME/. sage/tmp. ) 3. 1 Your Sage Session The seance is the sequence of input and yield from when you start Sage until you quit. Sage logs all Sage input, via IPython. In fact, if youre using the interactive shell (not the notebook interface), then at a ny point you may type % bill (or %hist) to get a leaning of all input lines typed so far. You can type ? at the Sage prompt to ? nd out more about IPython, e. g. IPython offers numbered prompts with input and create caching. wholly input is rescue and can be retrieved as variables (besides the vulgar pointer key recall). The following GLOBAL variables always exist (so presumet overwrite them ) _ introductory input (interactive shell and notebook) __ next previous input (interactive shell only) _oh list of all inputs (interactive shell only) Here is an example sage factor(100) _1 = 22 * 52 sage kronecker_symbol(3,5) 51 Sage Tutorial, Release 5. 3 _2 = -1 sage %hist This only works from the interactive shell, not the notebook. factor(100) 2 kronecker_symbol(3,5) 3 %hist sage _oh _4 = 1 22 * 52, 2 -1 sage _i1 _5 = factor(ZZ(100)) sage eval(_i1) _6 = 22 * 52 sage %hist 1 factor(100) 2 kronecker_symbol(3,5) 3 %hist 4 _oh 5 _i1 6 eval(_i1) 7 %hist We omit the output numbering in the rest of this tutorial and the other Sage documentation. You can also store a list of input from academic session in a macro for that session. sage E = EllipticCurve(1,2,3,4,5) sage M = ModularSymbols(37) sage %hist 1 E = EllipticCurve(1,2,3,4,5) 2 M = ModularSymbols(37) 3 %hist sage %macro em 1-2 large em created.To execute, type its name (without quotes). sage E Elliptic Curve defined by y2 + x*y + 3*y = x3 + 2*x2 + 4*x + 5 over Rational Field sage E = 5 sage M = None sage em Executing Macro sage E Elliptic Curve defined by y2 + x*y + 3*y = x3 + 2*x2 + 4*x + 5 over Rational Field When using the interactive shell, any UNIX shell command can be executed from Sage by prefacing it by an exclamation point . For example, sage ls auto example. sage glossary. tex t tmp tut. log tut. tex returns the leaning of the current directory. The PATH has the Sage bin directory at the front, so if you run gp, gap, unmated, maxima, etc. you get the versions included with Sage. sage gp Re ading GPRC /etc/gprc Done. GP/PARI CALCULATOR Version 2. 2. 11 (alpha) i686 running linux (ix86/GMP-4. 1. 4 kernel) 32-bit version 52 Chapter 3. The Interactive Shell Sage Tutorial, Release 5. 3 sage singular SINGULAR A Computer Algebra System for Polynomial Computations 0 by G. -M. Greuel, G. Pfister, H. Schoenemann FB Mathematik der Universitaet, D-67653 Kaiserslautern October 2005 / / Development version 3-0-1 3. 2 Logging Input and Output Logging your Sage session is not the same as conservation it (see Saving and Loading Complete Sessions for that).To log input (and optionally output) use the logstart command. Type logstart? for more details. You can use this command to log all input you type, all output, and even play back that input in a hereafter session (by simply re essence the log ? le). emailprotected$ sage SAGE Version 3. 0. 2, Release Date 2008-05-24 Type notebook() for the GUI, and license() for information. sage logstart setup Activating auto-logging. Current session state plus future input saved.Filename setup musical mode backup Output logging False Timestamping False State active sage E = EllipticCurve(1,2,3,4,5). minimal_model() sage F = QQ3 sage x,y = QQx,y. gens() sage G = E. gens() sage Exiting SAGE ( mainframe computer time 0m0. 61s, debate time 0m50. 39s). emailprotected$ sage SAGE Version 3. 0. 2, Release Date 2008-05-24 Type notebook() for the GUI, and license() for information. sage load setup Loading log file one line at a timeFinished replaying log file sage E Elliptic Curve defined by y2 + x*y = x3 x2 + 4*x + 3 over Rational Field sage x*y x*y sage G (2 3 1) If you use Sage in the Linux KDE terminal konsole then you can save your session as follows after starting Sage in konsole, select settings, then history , then set unlimited. When you are ready to save your session, select edit then save history as and type in a name to save the text of your session to your computer. After saving(a) this ? le, you coul d then load it into an editor, such as xemacs, and print it. 3. 2. Logging Input and Output 53 Sage Tutorial, Release 5. 3 3. Paste Ignores Prompts think over you are reading a session of Sage or Python computations and want to copy them into Sage. But there are annoying or sage prompts to worry about. In fact, you can copy and paste an example, including the prompts if you want, into Sage. In other words, by default the Sage parser strips any leading or sage prompt before passing it to Python. For example, sage 210 1024 sage sage sage 210 1024 sage 210 1024 3. 4 Timing Commands If you place the %time command at the runner of an input line, the time the command takes to run will be displayed after the output.For example, we can compare the running time for a certain involvement operation in several ways. The timings below will probably be much different on your computer, or even between different versions of Sage. First, primordial Python sage %time a = int(1938)int(99484) CPU measure user 0. 66 s, sys 0. 00 s, total 0. 66 s breakwater time 0. 66 This means that 0. 66 seconds total were taken, and the Wall time, i. e. , the amount of time that elapsed on your wall clock, is also 0. 66 seconds. If your computer is heavy load up with other programs, the wall time may be much larger than the CPU time.Next we time exponentiation using the native Sage Integer type, which is implemented (in Cython) using the GMP library sage %time a = 193899484 CPU times user 0. 04 s, sys 0. 00 s, total 0. 04 s Wall time 0. 04 Using the PARI C-library interface sage %time a = pari(1938)pari(99484) CPU times user 0. 05 s, sys 0. 00 s, total 0. 05 s Wall time 0. 05 GMP is better, but only slightly (as expected, since the version of PARI built for Sage uses GMP for integer arithmetic). You can also time a block of commands using the cputime command, as illustrated below sage sage sage sage sage 0. 4 t = cputime() a = int(1938)int(99484) b = 193899484 c = pari(1938)pari(994 84) cputime(t) somewhat random output sage cputime? Return the time in CPU second since SAGE started, or with optional argument t, return the time since time t. 54 Chapter 3. The Interactive Shell Sage Tutorial, Release 5. 3 INPUT t (optional) float, time in CPU seconds OUTPUT float time in CPU seconds The walltime command brooks just like the cputime command, except that it measures wall time. We can also compute the supra power in some of the computer algebra systems that Sage includes.In each case we execute a trivial command in the system, in order to start up the server for that program. The most relevant time is the wall time. However, if there is a signi? cant loss between the wall time and the CPU time then this may indicate a performance issue worth looking into. sage time 193899484 CPU times user 0. 01 s, sys 0. 00 s, total Wall time 0. 01 sage gp(0) 0 sage time g = gp(193899484) CPU times user 0. 00 s, sys 0. 00 s, total Wall time 0. 04 sage maxima(0) 0 sage time g = maxima(193899484) CPU times user 0. 00 s, sys 0. 00 s, total Wall time 0. 0 sage kash(0) 0 sage time g = kash(193899484) CPU times user 0. 00 s, sys 0. 00 s, total Wall time 0. 04 sage mathematica(0) 0 sage time g = mathematica(193899484) CPU times user 0. 00 s, sys 0. 00 s, total Wall time 0. 03 sage maple(0) 0 sage time g = maple(193899484) CPU times user 0. 00 s, sys 0. 00 s, total Wall time 0. 11 sage gap(0) 0 sage time g = gap. eval(193899484) CPU times user 0. 00 s, sys 0. 00 s, total Wall time 1. 02 0. 01 s 0. 00 s 0. 00 s 0. 00 s 0. 00 s 0. 00 s 0. 00 s Note that GAP and Maxima are the slowest in this test (this was run on the work sage. ath. washington. edu). Because of the pexpect interface overhead, it is perhaps unfair to compare these to Sage, which is the fastest. 3. 5 Other IPython tricks As noted above, Sage uses IPython as its front end, and so you can use any of IPythons commands and features. You can read the full IPython documentation. Meanwhile, here are some fun tricks these are called Magic commands in IPython You can use %bg to run a command in the background, and then use jobs to access the results, as follows. 3. 5. Other IPython tricks 55 Sage Tutorial, Release 5. 3 The comments not tested are here because the %bg syntax doesnt work well with Sages automatic testing facility. If you type this in yourself, it should work as written. This is of course most multipurpose with commands which take a while to complete. ) sage def quick(m) return 2*m sage %bg quick(20) not tested Starting job 0 in a separate thread. sage jobs. status() not tested Completed jobs 0 quick(20) sage jobs0. result the developed answer, not tested 40 Note that jobs run in the background fathert use the Sage preparser see The Pre-Parser Differences between Sage and Python for more information.One (perhaps awkward) way to get around this would be to run sage %bg eval(preparse(quick(20))) not tested It is safer and easier, though, to just use %bg on comma nds which dont require the preparser. You can use %edit (or %ed or ed) to open an editor, if you want to type in some complex code. in the lead you start Sage, make sure that the EDITOR environment variable is set to your favorite editor (by putting export EDITOR=/usr/bin/emacs or export EDITOR=/usr/bin/vim or something similar in the appropriate place, like a . profile ? le). From the Sage prompt, executing %edit will open up the named editor. Then within the editor you can de? e a function def some_function(n) return n**2 + 3*n + 2 Save and quit from the editor. For the rest of your Sage session, you can then use some_function. If you want to modify it, type %edit some_function from the Sage prompt. If you have a computation and you want to modify its output for another use, perform the computation and type %rep this will place the output from the previous command at the Sage prompt, ready for you to edit it. sage f(x) = cos(x) sage f(x). derivative(x) -sin(x) At this point, if you type %rep at the Sage prompt, you will get a new Sage prompt, followed by -sin(x), with the cursor at the end of the line.For more, type %quickref to get a quick reference guide to IPython. As of this writing (April 2011), Sage uses version 0. 9. 1 of IPython, and the documentation for its conjuration commands is available online. 3. 6 Errors and Exceptions When something goes wrong, you will usually see a Python exception. Python even tries to suggest what raised the exception. Often you see the name of the exception, e. g. , NameError or ValueError (see the Python Reference Manual Py for a complete list of exceptions). For example, sage 3_2 File , line 1 ZZ(3)_2 SyntaxError incapacitate syntax 6 Chapter 3. The Interactive Shell Sage Tutorial, Release 5. 3 sage EllipticCurve(0,infinity) Traceback (most recent call last) TypeError inefficient to coerce Infinity () to Rational The interactive debugger is sometimes useful for understanding what went wrong. You can toggle it o n or off using %pdb (the default is off). The prompt ipdb appears if an exception is raised and the debugger is on. From within the debugger, you can print the state of any local variable, and move up and down the execution muckle.For example, sage %pdb Automatic pdb calling has been turned ON sage EllipticCurve(1,infinity) Traceback (most recent call last) ipdb For a list of commands in the debugger, type ? at the ipdb prompt ipdb ? authenticated commands (type help ) ======================================== EOF break commands debug h a bt condition hamper help alias c cont down ignore args cl hold open enable j b clear d exit skip whatis where Miscellaneous help topics ========================== exec pdb Undocumented commands ====================== retval rv list n next p pdef pdoc pinfo pp q quit r return s step tbreak u unalias up w Type Ctrl-D or quit to return to Sage. 3. 7 Reverse Search and Tab Completion Reverse search Type the beginning of a command, then Ctrl-p (or just hit the up arrow key) to go back to each line you have entered that begins in that way. This works even if you completely exit Sage and restart later. You can also do a reverse search through the history using Ctrl-r. All these features use the readline package, which is available on most ? avors of Linux. To illustrate tab completion, ? st create the three dimensional vector space V = Q3 as follows sage V = vectorSpace(QQ,3) sage V Vector space of dimension 3 over Rational Field You can also use the following more concise notation 3. 7. Reverse Search and Tab Completion 57 Sage Tutorial, Release 5. 3 sage V = QQ3 Then it is easy to list all member functions for V using tab completion. Just type V. , then type the tab key key on your keyboard sage V. tab key V. _VectorSpace_generic__base_field V. ambient_space V. base_field V. base_ring V. basis V. coordinates V. zero_vector If you type the ? st few letters of a function, then tab key, you get only functions that begin as indi cated. sage V. itab key V. is_ambient V. is_dense V. is_full V. is_sparse If you marvel what a particular function does, e. g. , the coordinates function, type V. coordinates? for help or V. coordinates for the source code, as ex unequivocaled in the next section. 3. 8 Integrated Help System Sage features an integrated help facility. Type a function name followed by ? for the documentation for that function. sage V = QQ3 sage V. coordinates? Type instancemethod Base Class String Form Namespace Interactive File / interior(a)/was/s/local/lib/python2. /site-packages/sage/modules/f ree_module. py Definition V. coordinates(self, v) Docstring Write v in call of the basis for self. Returns a list c such that if B is the basis for self, then sum c_i B_i = v. If v is not in self, raises an ArithmeticError exception. EXAMPLES sage M = FreeModule(IntegerRing(), 2) M0,M1=M. gens() sage W = M. submodule(M0 + M1, M0 2*M1) sage W. coordinates(2*M0-M1) 2, -1 As shown above, the output tells you the type of the object, the ? le in which it is de? ned, and a useful explanation of the function with examples that you can paste into your current session. about all of these examples are regularly automatically tested to make sure they work and behave exactly as claimed. 58 Chapter 3. The Interactive Shell Sage Tutorial, Release 5. 3 Another feature that is very much in the expression of the open source nature of Sage is that if f is a Python function, then type f displays the source code that de? nes f. For example, sage V = QQ3 sage V. coordinates Type instancemethod Source def coordinates(self, v) Write $v$ in terms of the basis for self. return self. coordinate_vector(v). list()This tells us that all the coordinates function does is call the coordinate_vector function and change the result into a list. What does the coordinate_vector function do? sage V = QQ3 sage V. coordinate_vector def coordinate_vector(self, v) return self. ambient_vector_space()(v) The coordinate_ve ctor function coerces its input into the ambient space, which has the offspring of computing the vector of coef? cients of v in terms of V . The space V is already ambient since its just Q3 . There is also a coordinate_vector function for subspaces, and its different.We create a subspace and see sage V = QQ3 W = V. span_of_basis(V. 0, V. 1) sage W. coordinate_vector def coordinate_vector(self, v) First find the coordinates of v wrt echelon basis. w = self. echelon_coordinate_vector(v) Next use transformation matrix from echelon basis to user basis. T = self. echelon_to_user_matrix() return T. linear_combination_of_rows(w) (If you think the implementation is inef? cient, please sign up to help optimize linear algebra. ) You may also type help(command_name) or help(class) for a manpage-like help ? le about a given class. age help(VectorSpace) Help on class VectorSpace class VectorSpace(__builtin__. object) Create a Vector Space. To create an ambient space over a field with gi ven dimension using the calling syntax When you type q to exit the help system, your session appears just as it was. The help listing does not welter up your session, unlike the output of function_name? sometimes does. Its particularly instrumental to type 3. 8. Integrated Help System 59 Sage Tutorial, Release 5. 3 help(module_name). For example, vector spaces are de? ned in sage. modules. free_module, so type help(sage. modules. ree_module) for documentation about that whole module. When viewing documentation using help, you can search by typing / and in reverse by typing ?. 3. 9 Saving and Loading Individual Objects Suppose you compute a matrix or worse, a complicated space of modular symbols, and would like to save it for later use. What can you do? There are several approaches that computer algebra systems take to saving individual objects. 1. Save your Game Only support saving and loading of complete sessions (e. g. , GAP, Magma). 2. Uni? ed Input/Output Make every object print in a way that can be read back in (GP/PARI). 3.Eval Make it easy to evaluate arbitrary code in the interpreter (e. g. , Singular, PARI). Because Sage uses Python, it takes a different approach, which is that every object can be serialized, i. e. , turned into a string from which that object can be recovered. This is in spirit similar to the uni? ed I/O approach of PARI, except it doesnt have the drawback that objects print to screen in too complicated of a way. Also, support for saving and loading is (in most cases) completely automatic, requiring no extra programming its simply a feature of Python that was designed into the language from the ground up.Almost all Sage objects x can be saved in compressed form to disk using save(x, filename) (or in many cases x. save(filename)). To load the object back in, use load(filename). sage sage 15 42 69 sage A = MatrixSpace(QQ,3)(range(9))2 A 18 21 54 66 90 111 save(A, A) You should now quit Sage and restart. Then you can get A back sage sage 15 42 69 A = load(A) A 18 21 54 66 90 111 You can do the same with more complicated objects, e. g. , elliptic curves. All data about the object that is cached is stored with the object. For example, sage sage sage sage E = EllipticCurve(11a) v = E. nlist(100000) save(E, E) quit takes a while The saved version of E takes 153 kilobytes, since it stores the ? rst 100000 an with it. /tmp$ ls -l E. sobj -rw-rr 1 was was 153500 2006-01-28 1923 E. sobj /tmp$ sage sage E = load(E) sage v = E. anlist(100000) present moment (In Python, saving and loading is accomplished using the cPickle module. In particular, a Sage object x can be saved via cPickle. dumps(x, 2). Note the 2 ) 60 Chapter 3. The Interactive Shell Sage Tutorial, Release 5. 3 Sage cannot save and load individual objects created in some other computer algebra systems, e. . , GAP, Singular, Maxima, etc. They reload in a state marked invalid. In GAP, though many objects print in a form from which they can be reco nstructed, many dont, so reconstructing from their print office is purposely not allowed. sage a = gap(2) sage a. save(a) sage load(a) Traceback (most recent call last) ValueError The session in which this object was defined is no womb-to-tomb running. GP/PARI objects can be saved and loaded since their print representation is enough to reconstruct them. sage a = gp(2) sage a. save(a) sage load(a) 2Saved objects can be re-loaded later on computers with different architectures or operating systems, e. g. , you could save a huge matrix on 32-bit OS X and reload it on 64-bit Linux, ? nd the echelon form, then move it back. Also, in many cases you can even load objects into versions of Sage that are different than the versions they were saved in, as long as the code for that object isnt too different. All the attributes of the objects are saved, along with the class (but not source code) that de? nes the object. If that class no longer exists in a new version of Sage, then the object cant be reloaded in that newer version.But you could load it in an old version, get the objects dictionary (with x. __dict__), and save the dictionary, and load that into the newer version. 3. 9. 1 Saving as Text You can also save the ASCII text representation of objects to a plain text ? le by simply opening a ? le in write mode and writing the string representation of the object (you can write many objects this way as well). When youre done writing objects, close the ? le. sage sage sage sage sage R. = PolynomialRing(QQ,2) f = (x+y)7 o = open(file. txt,w) o. write(str(f)) o. close() 3. 10 Saving and Loading Complete Sessions Sage has very ? xible support for saving and loading complete sessions. The command save_session(sessionname) saves all the variables youve de? ned in the current session as a dictionary in the given sessionname. (In the rare case when a variable does not support saving, it is simply not saved to the dictionary. ) The resulting ? le is an . sobj ? le and can be loaded just like any other object that was saved. When you load the objects saved in a session, you get a dictionary whose keys are the variables names and whose values are the objects. You can use the load_session(sessionname) command to load the variables de? ed in sessionname into the current session. Note that this does not wipe out variables youve already de? ned in your current session instead, the twain sessions are merged. First we start Sage and de? ne some variables. 3. 10. Saving and Loading Complete Sessions 61 Sage Tutorial, Release 5. 3 sage sage sage sage _4 = E = EllipticCurve(11a) M = ModularSymbols(37) a = 389 t = M. T(2003). matrix() t. charpoly(). factor() (x 2004) * (x 12)2 * (x + 54)2 Next we save our session, which saves each of the above variables into a ? le. Then we view the ? le, which is about 3K in size. age save_session(misc) Saving a Saving M Saving t Saving E sage quit emailprotected/tmp$ ls -l misc. sobj -rw-rr 1 was was 2979 2006-01-28 1947 mi sc. sobj last we restart Sage, de? ne an extra variable, and load our saved session. sage b = 19 sage load_session(misc) Loading a Loading M Loading E Loading t Each saved variable is once more available. Moreover, the variable b was not overwritten. sage M Full Modular Symbols space for Gamma_0(37) of weight 2 with sign 0 and dimension 5 over Rational Field sage E Elliptic Curve defined by y2 + y = x3 x2 10*x 20 over Rational Field sage b 19 sage a 389 3. 1 The Notebook Interface The Sage notebook is run by typing sage notebook() on the command line of Sage. This starts the Sage notebook and opens your default web browser to view it. The servers state ? les are stored in $HOME/. sage/sage_notebook. Other options include sage notebook(directory) which starts a new notebook server using ? les in the given directory, instead of the default directory $HOME/. sage/sage_notebook. This can be useful if you want to have a collection of worksheets associated with a speci? c project, or run several separate notebook servers at the same time. When you start the notebook, it ? st creates the following ? les in $HOME/. sage/sage_notebook 62 Chapter 3. The Interactive Shell Sage Tutorial, Release 5. 3 nb. sobj objects/ worksheets/ (the notebook SAGE object file) (a directory containing SAGE objects) (a directory containing SAGE worksheets). After creating the above ? les, the notebook starts a web server. A notebook is a collection of user accounts, each of which can have any number of worksheets. When you create a new worksheet, the data that de? nes it is stored in the worksheets/username/number directories. In each such directory there is a plain text ? le worksheet. xt if anything ever happens to your worksheets, or Sage, or whatever, that human-readable ? le contains everything needed to reconstruct your worksheet. From within Sage, type notebook? for much more about how to start a notebook server. The following diagram illustrates the architecture of the Sage No tebook firefox/safari javascript program AJAX V sage web server pexpect - SAGE process 1 SAGE process 2 SAGE process 3 (Python processes)For help on a Sage command, cmd, in the notebook browser box, type cmd? ). and now hit (not For help on the keyboard shortcuts available in the notebook interface, click on the Help link. 3. 11. The Notebook Interface 63 Sage Tutorial, Release 5. 3 64 Chapter 3. The Interactive Shell CHAPTER FOUR INTERFACES A central facet of Sage is that it supports computation with objects in many different computer algebra systems under one roof using a common interface and clean programming language. The console and interact methods of an interface do very different things. For example, using GAP as an example 1. gap. onsole() This opens the GAP console it transfers control to GAP. Here Sage is serving as nothing more than a well-provided program launcher, similar to the Linux bash shell. 2. gap. interact() This is a convenie nt way to interact with a running GAP instance that may be full of Sage objects. You can import Sage objects into this GAP session (even from the interactive interface), etc. 4. 1 GP/PARI PARI is a compact, very mature, highly optimized C program whose primary focus is number theory. There are ii very distinct interfaces that you can use in Sage gp the G o P ARI interpreter, and pari the PARI C libraxry.For example, the following are two ways of doing the same thing. They look identical, but the output is actually different, and what happens fag the scenes is drastically different. sage gp(znprimroot(10007)) Mod(5, 10007) sage pari(znprimroot(10007)) Mod(5, 10007) In the ? rst case, a separate copy of the GP interpreter is started as a server, and the string znprimroot(10007) is sent to it, evaluated by GP, and the result is assigned to a variable in GP (which takes up space in the child GP processes memory that wont be freed). Then the value of that variable is displayed.In t he second case, no separate program is started, and the string znprimroot(10007) is evaluated by a certain PARI C library function. The result is stored in a piece of memory on the Python heap, which is freed when the variable is no longer referenced. The objects have different types sage type(gp(znprimroot(10007))) sage type(pari(znprimroot(10007))) So which should you use? It depends on what youre doing. The GP interface can do absolutely anything you could do in the usual GP/PARI command line program, since it is running that program. In particular, you can load complicated PARI programs and run them.In contrast, the PARI interface (via the C library) is much more restrictive. First, not all 65 Sage Tutorial, Release 5. 3 member functions have been implemented. Second, a lot of code, e. g. , involving numerical integration, wont work via the PARI interface. That said, the PARI interface can be signi? cantly faster and more robust than the GP one. (If the GP interface runs out of memory evaluating a given input line, it will wordlessly and automatically double the stack size and retry that input line. thusly your computation wont crash if you didnt correctly yell the amount of memory that would be needed.This is a nice trick the usual GP interpreter doesnt seem to provide. Regarding the PARI C library interface, it promptly copies each created object off of the PARI stack, hence the stack never grows. However, each object must not exceed 100MB in size, or the stack will over? ow when the object is being created. This extra copying does inflict a slight performance penalty. ) In summary, Sage uses the PARI C library to provide functionality similar to that provided by the GP/PARI interpreter, except with different school memory management and the Python programming language. First we create a PARI list from a Python list. age v = pari(1,2,3,4,5) sage v 1, 2, 3, 4, 5 sage type(v) all PARI object is of type py_pari. gen. The PARI type of the underlying o bject can be obtained using the type member function. sage v. type() t_VEC In PARI, to create an elliptic curve we enter ellinit(1,2,3,4,5). Sage is similar, except that ellinit is a method that can be called on any PARI object, e. g. , our t_VEC v. sage e = v. ellinit() sage e. type() t_VEC sage pari(e)13 1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351 Now that we have an elliptic curve object, we can compute some things about it. age e. elltors() 1, , sage e. ellglobalred() 10351, 1, -1, 0, -1, 1 sage f = e. ellchangecurve(1,-1,0,-1) sage f5 1, -1, 0, 4, 3 4. 2 GAP Sage comes with GAP 4. 4. 10 for computational separate mathematics, especially group theory. Heres an example of GAPs IdGroup function, which uses the optional small groups database that has to be installed separately, as explained below. sage G = gap(Group((1,2,3)(4,5), (3,4))) sage G Group( (1,2,3)(4,5), (3,4) ) sage G. Center() Group( () ) 66 Chapter 4. Interfaces Sage Tutorial, Release 5. 3 sag e G.IdGroup() 120, 34 sage G. Order() 120 requires optional database_gap package We can do the same computation in Sage without explicitly invoking the GAP interface as follows sage G = PermutationGroup((1,2,3),(4,5),(3,4)) sage G. center() Subgroup of (Permutation Group with generators (3,4), (1,2,3)(4,5)) generated by () sage G. group_id() requires optional database_gap package 120, 34 sage n = G. order() n 120 (For some GAP functionality, you should install two optional Sage packages. Type sage -optional for a list and choose the one that looks like gap_packages-x. . z, then type sage -i gap_packages-x. y. z. Do the same for database_gap-x. y. z. Some non-GPLd GAP packages may be installed by downloading them from the GAP web site GAPkg, and unpacking them in $SAGE_ROOT/local/lib/gap-4. 4. 10/pkg. ) 4. 3 Singular Singular provides a massive and mature library for Grobner bases, multivariate polynomial gcds, bases of RiemannRoch spaces of a flavourless curve, and factorizatio ns, among other things. We illustrate multivariate polynomial factorization using the Sage interface to Singular (do not type the ) sage R1 = singular. ing(0, (x,y), dp) sage R1 // characteristic 0 // number of vars 2 // block 1 guild dp // names x y // block 2 club C sage f = singular(9*y8 9*x2*y7 18*x3*y6 18*x5*y6 + 9*x6*y4 + 18*x7*y5 + 36*x8*y4 + 9*x10*y4 18*x11*y2 9*x12*y3 18*x13*y2 + 9*x16) Now that we have de? ned f , we print it and factor. sage f 9*x16-18*x13*y2-9*x12*y3+9*x10*y4-18*x11*y2+36*x8*y4+18*x7*y5-18*x5*y6+9*x6*y4-18*x sage f. parent() Singular sage F = f. factorize() F 1 _1=9 _2=x6-2*x3*y2-x2*y3+y4 _3=-x5+y2 2 1,1,2 sage F12 x6-2*x3*y2-x2*y3+y4As with the GAP example in GAP, we can compute the above factorization without explicitly using the Singular interface (however, behind the scenes Sage uses the Singular interface for the actual computation). Do not type the 4. 3. Singular 67 Sage Tutorial, Release 5. 3 sage sage sage (9) * x, y = QQx, y. gens( ) f = 9*y8 9*x2*y7 18*x3*y6 18*x5*y6 + 9*x6*y4 + 18*x7*y5 + 36*x8*y4 + 9*x10*y4 18*x11*y2 9*x12*y3 18*x13*y2 + 9*x16 factor(f) (-x5 + y2)2 * (x6 2*x3*y2 x2*y3 + y4) 4. 4 Maxima Maxima is included with Sage, as well as a Lisp implementation.The gnuplot package (which Maxima uses by default for plotting) is distributed as a Sage optional package. Among other things, Maxima does symbolic manipulation. Maxima can integrate and differentiate functions symbolically, solve 1st order ODEs, most linear 2nd order ODEs, and has implemented the Laplace tr