An Analysis of Change management models

An Analysis of Change the executives models In this report, we have concentrated on change the executives inside an association or a venture. Change the executives is turning out to be essential to the point that these days an ever increasing number of organizations utilize this technique to improve the presentation. Bunches of progress the board models are utilized; they have made benefit to the organizations. Be that as it may, not all the models are appropriate to all the tasks or all the sorts of organizations; they have drawbacks just as focal points when utilizing them. In this report, we will examine three models as models: Kotters Eight Step Change Model, Lewins Change Management Model and McKinsey 7-S Model. Presentation Change the board is a systematic way to deal with taking care of with change, from the point of an association as well as on the individual level. A fairly ambiguous term, change the board has in excess of three unique measurements, adjusting to change, controlling change, and affecting change included. A proactive way to deal with taking care of with change is at the focal piece of every one of the three perspectives. For an association, change the board implies making the definition and usage of strategies and additionally advancements to deal with changes in the business condition and to benefit from evolving openings. Triumphant adjustment to change is as imperative inside an association for what it's worth in the regular world. Only like plants and creatures, associations and the people in them unavoidably run into changing conditions that they are inadequate to control. The more successfully you handle with change, the more plausible you are to prosper. Building organized strategies for tending to changes in the business condition or building methods for dealing with stress for tending to changes in the working environment may be engaged with adjustment. Subsequently, loads of progress the executives models are worked to help roll out the improvement the board increasingly viable. There are a few of progress the board models. We will examine three and choose which the best fit an association requiring numerous progressions is. We will examine both the points of interest and hindrances of these three change the executives models. When we talk about them further, we will see contrasts to every one of these models. There are likewise a great deal of similitudes among these models. It is fundamental that we have a methodical liberal of every one of the three change the executives models introduced. Issue Area Scope It as a rule doesnt matter how very much planned a venture is toward the start, change is an unavoidable piece of the undertaking usage process. A large portion of us tend to consider change regarding issues or negative outcomes. In spite of the fact that the facts demonstrate that change could be awful or could be acceptable. There are many of angles that are taken a gander at when the progressions are made and a right way ought to be received so as to accomplish the necessary objective. Our extent of this report centers around the accompanying: Step by step instructions to portray change the executives framework What are the standards of progress the board and the rules which should be seen when changes are required Components of progress the board frameworks Best models of progress the executives Despite the fact that there are a few models present in the market today however just that model which suits the profile of the undertaking ought to be embraced or whose usage isn't unclear to the remainder of the task group. In this investigation report we have principally centered around following three models of progress the executives: Kotter Model McKinsey 7-S Model Lewins Change Management Model Extra more our report features: Attributes of Each Model Strategy of their use. The significant requirements that could run over are booked underneath: Vulnerability between individuals actualizing change the executives models Correspondence hole between top administration and lower level. Time Vulnerability of the jobs and obligations System Our investigation was employedã‚â on the investigation of Change Management, standards various models of progress the board models were gotten by playing out the accompanying arrangement of exercises: Point Selection and Planning of Study We had a conceptualizing meeting where our colleagues got consented to take a shot at Conflict taking care of in Project Management and with the assistance of the investigation targets and necessities which were referenced by our course educator (Erika Bellander), at that point the examination was separated into the accompanying errands: presentation, issues, scope territory, speculations models identified with various clash circumstances in ventures, compromise techniques, strategies utilized in the study,ã‚â unwavering quality, legitimacy, results, conversations and suggestions. These were trailed by the arrangement of a duty grid and time planning. The status or progress of each errand were accounted for and as a rule transferred on bilda in any event daily before our week by week gatherings on each tuesdays. Online Discussions The IMPACTS bunch individuals who were cooperating on certain expectations had online conversations and challenges experienced during the errands executing were likewise as often as possible examine on line. We additionally helped each other by giving insights/contributions to one another by messages and we found this is increasingly viable method of correspondence. Assets Because of the time imperatives, the IMPACT gathering couldn't acquire any essential information for the investigation from the organizations/Industries on account of that our examination depended on optional sources which contains addresses notes, books and the web were consolidate with working experience of our colleagues. Results Presently a days each supervisor or pioneers in instruction are required to lead and oversee changes. It is huge as all things considered the overview has discovered that change is occurring at a developing beat, the check recommends that most change activities doesnt not measure up for example ebb and flow research suggested that under 65% of re-associations met their expressed points which are typically main concern improvement. The effect of disappointments to get viable change could likewise be grand for example loss of market position, end of senior administration, loss of partner dependability, loss of key representatives. To stay away from such disappointments there is need of colleague with the change the board standard and models and its results. In this area we will depict the essential change the executives standards and a few models for the change the board. Meaning of Change Management Change the executives is a game-plan where entire framework is altered by any pre-characterized structure or displayed by tailing it. Rule of Change Management There are a few standards followed to make change the board. By following these standards as a deliberate, structure, group pioneers can discover that how to deal with their very own change and how to choose the entire association all the while. In spite of the fact that there are numerous Principles of progress the executives yet not many of the Principles are following: Receiving a principled technique that shows dependability and incites receptiveness and conviction will see your change program all through the difficult situations. Here are five key standards of effective change management㠯⠼å ¡ Sponsorship The change program gets the noticeable help of key chiefs inside the association just as assets are prepared to the program. Arranging Arranging is attempted deliberately before program execution and focused on composing. Plans are listed as per transcendent partners and assets, objectives, dangers and other pertinent members. Estimation Program destinations are written in assessable terms and program progress is controlled and intercommunicated to significant partners. Commitment Partners are engaged with a legitimate two-sided correspondence based on receptiveness, complementary trust and regard. Bolster structures Program agents and change beneficiaries are given the assets and supporting frameworks required during the procedure of the usage and the repercussions. Change Management Guidelines In our investigation of this change the board model standard we have discovered the accompanying significant rules for the change the executives: Address the individual side methodicallly: At all occasions connect with and concur support from individual inside framework as each change makes people individual issues. At the point when new pioneers are approached to change at that point work will be changed and representatives typically make encounter which will prompt danger of speed of work, spirits and results. There is a typical methodology of progress the executives that start with the top supervisory crew and afterward connect with the partners and this idea should begin in beginning period of progress itself. Start at the top: When changes in association framework happens then everybody takes a gander at the top administration as the choices originates from them who that how this ought to be alongside its conventions. Top administration should cooperate by arranging and responsibility and they should speak with one another. Include each layer: When the game-plan of progress begins then we makes the procedure at that point structures its path and in usage stage begins which influence all degrees of the association. Authority at each level is must required with skill in information. Impart the message: One must remember that there ought not be any correspondence hole during the change the board. There is a serious mix-up which is regularly observed that a few directors accept that all individuals in the group comprehend the issues. There is generally need of normal and ideal messages which ought to be persuasive and pertinent. Correspondence must be from base to up and from up to down additionally with the goal that representatives may get data at perfect time. There is additionally need of right message to opportune individual to stay away from awful results. Get ready for unforeseen: Whenever change is made by arrangement then one as a rule has numerous issues looked during change the board procedure. There are some unexpected methods of response appeared by certain individuals. The explanation of response could

Search For My Tongue Essay Example For Students

Quest For My Tongue Essay Gayness inside covered up by the British outside. The two artists express these social clashes with the utilization of point of view, social setting, abstract gadgets, symbolism and varieties to grammar. The similitudes in these sonnets show that social clash is bottomless and universal, though the distinctions give uniqueness among the social clashes. In Search for My Tongue, Beats sonnet includes the contention between native language and the remote tongue. These exceptionally physical items supplant her local language of Guajarati and unknown dialect of English. The utilization of this figurative similarity is far reaching, for example, in the French language, where the word langue implies both tongue and language. As indicated by Bath, in the event that you needed to/talk a remote tongue,/your first language would spoil (10-12). The contention between dialects proceeds in the subliminal world, where the first language consistently returns and blooms out of my mouth (38). So also Half-Caste is likewise a contention of societies, explicitly race. John Agar is a blended race of high contrast light a shadow (13). His life in Britain has purportedly stifled his dark, undesirable side. This dissent sonnet is the dark side endeavoring o be liberated Just as how Beats native language needs to grow(s) back (31). Agar frequently portrays himself as a large portion of an individual, remaining on one leg (2), Half-an eye (41), a large portion of a-fantasy (43), a large portion of a-shadow, (46). Shower scans for her two tongue yet just discovers one. Contrastingly, Half-position is a sonnet of outer clash among Agar and the opposing English society, though Search For My Tongue is about self-disclosure and interior clash. In Search for My Tongue, lines somewhere in the range of 1 and 14 are all in the second individual, which interfaces the sonnet to the peruser. It is increasingly emotional and sincere Han an account. Beats interior clashes are voiced out to the world, scanning for a response to the inquiry I pose to you, what might you do (3). Half-rank uses precisely the same system so as to accomplish an alternate objective. The second individual account is introduced between lines 4 and 37. He utilizes phrases like Explain housefly/hold up you mean (4-5), which legitimately focuses on the segregating British (you need confirmation of that from his sonnet) you put the on illustration with the sun dont go in England society, it fits truly well here . Outside clashes among Agar and the general public are quickly voiced. The two sonnets utilize the viewpoint of the it isn't second individual , JUDD revealed to me that on Search for my tongue sits associate with the peruser, yet one does it to apply the inner clashes to the outside world though different does it to be heard. Shower draws out her inside clashes so she can interface with the peruser. In Search for My Tongue, numerous abstract gadgets are accustomed to draw out these inside clashes. Her figurative tongues really represent dialects. She regularly changes between the questionable implications. For instance, she expresses that in the event that you had two results in your mouth,/and lost the first, the primary language, (4-5). Shower is giving heavenly characteristics to the physical tongue. In an another model, she expresses that your native language would decay,/spoil and bite the dust in your mouth (12-13). For this situation, Bath is making representations by giving exact, characteristic properties to a language. This shows how Bath is exchanging between the different implications. In Half-standing, Agar likewise draws on numerous models. Contrastingly, he utilizes suggestions or references to outer abstract works. The two obvious references are Picasso and Tchaikovsky. Put the lines Both of these specialists use differences to make a more prominent bit of work. As per Agar, a blended individual is a living case of excellence got from two differentiating societies. In spite of the fact that the importance of these implications isn't vague, they are regularly snide and direct. The distinctions in the utilization of scholarly gadgets have to do with the way that Bath is indistinct about her social clash, while Agar comprehends his social clash. The two writers utilize the abstract gadget of reiteration to communicate social clash. For instance, in Search for My Tongue, the words tongue and mouth are exceptionally bounteous. .u62b492310a2b22135a92058f189c023c , .u62b492310a2b22135a92058f189c023c .postImageUrl , .u62b492310a2b22135a92058f189c023c .focused content territory { min-stature: 80px; position: relative; } .u62b492310a2b22135a92058f189c023c , .u62b492310a2b22135a92058f189c023c:hover , .u62b492310a2b22135a92058f189c023c:visited , .u62b492310a2b22135a92058f189c023c:active { border:0!important; } .u62b492310a2b22135a92058f189c023c .clearfix:after { content: ; show: table; clear: both; } .u62b492310a2b22135a92058f189c023c { show: square; progress: foundation shading 250ms; webkit-change: foundation shading 250ms; width: 100%; obscurity: 1; change: darkness 250ms; webkit-change: mistiness 250ms; foundation shading: #95A5A6; } .u62b492310a2b22135a92058f189c023c:active , .u62b492310a2b22135a92058f189c023c:hover { haziness: 1; change: murkiness 250ms; webkit-progress: mistiness 250ms; foundation shading: #2C3E50; } .u62b492310a2b22135a92058f189c023c .focused content region { width: 100%; position: relati ve; } .u62b492310a2b22135a92058f189c023c .ctaText { fringe base: 0 strong #fff; shading: #2980B9; text dimension: 16px; textual style weight: striking; edge: 0; cushioning: 0; content design: underline; } .u62b492310a2b22135a92058f189c023c .postTitle { shading: #FFFFFF; text dimension: 16px; text style weight: 600; edge: 0; cushioning: 0; width: 100%; } .u62b492310a2b22135a92058f189c023c .ctaButton { foundation shading: #7F8C8D!important; shading: #2980B9; outskirt: none; outskirt span: 3px; box-shadow: none; text dimension: 14px; textual style weight: intense; line-tallness: 26px; moz-outskirt sweep: 3px; content adjust: focus; content adornment: none; content shadow: none; width: 80px; min-stature: 80px; foundation: url(https://artscolumbia.org/wp-content/modules/intelly-related-posts/resources/pictures/basic arrow.png)no-rehash; position: supreme; right: 0; top: 0; } .u62b492310a2b22135a92058f189c023c:hover .ctaButton { foundation shading: #34495E!important; } .u62b492310a2b22135 a92058f189c023c .focused content { show: table; stature: 80px; cushioning left: 18px; top: 0; } .u62b492310a2b22135a92058f189c023c-content { show: table-cell; edge: 0; cushioning: 0; cushioning right: 108px; position: relative; vertical-adjust: center; width: 100%; } .u62b492310a2b22135a92058f189c023c:after { content: ; show: square; clear: both; } READ: The Love Song of J. Alfred Prufrock Argumentative EssayThe word tongue closes lines 2, 5, 7, 11 and 37. The word mouth closes lines 4, 13, 34 and 38. Not exclusively does the reiteration unite the sonnet, it reinforces the message Bath is attempting to send. It looks like a trouble signal from an individual with desperate need. Likewise, John Agar rehashes the expression Explain housefly in lines 4, 10, 23 and 31 . This helps the peruser to remember the forceful tone in this insubordinate sonnet, and ties the sonnet together. Each time another thought is raised, Explain housefly is the early on line. Another way the artists endeavor to depict social clash is by the utilization of symbolism. Toward the finish of the sonnet, Strata Bath composes It becomes back, a stump of a shoot (31). This is a representation, contrasting the mother language with a developing bamboo. The analogy adds to the reasonable symbolism. Continuing,Grows longer, develops damp, becomes solid veins,alt ties the other tongue in knots,The bud opens, the bud opens in my mouth,alt pushes the other tongue aside. (32-35)These lines paint an express picture in the perusers mind, helping the writer go over with the significance. Additionally, John Agar likewise offers to the numerous faculties. The red a green (8) on the canvas (9) feed on the human feeling of sight. The dark key (28) and white key (29) in the orchestra (30) by Tchaikovsky (26) influence the human feeling of hearing. Together, it permits the peruser to completely encounter the possibility of Half-Caste. At long last, the two artists utilize an odd type of linguistic structure. In Search for My Tongue, Bath includes a full area of Gujarat. This represents the resurrection of the native language inside Baths subliminal psyche. Likewise, between lines 31 and 35, there are no disintegrates, supplanted by commas. This segment holds the symbolism clarified above, and periods would include pointless breaks. Essentially, Half-position has no accentuations. Along with the contrasting lingo, it shows the writer restricting his environmental factors. This is a type of dissent, since Agar isn't adhering to the general principles of composing set by his bigot rivals. Subsequently, the two writers express social clash with varieties to language structure. When perusing Search for My Tongue, a monolingual individual would not have the option to completely understand Baths social clash, aside from when it is portrayed truly. By permitting the peruser to picture two tongues in their mouth, Baths interior clashes are communicated remotely, permitting her to sympathize with her torment with the world. In any case, somebody who is bilingual may have just experienced comparable social clashes. Hence, this bilingual peruser will comprehend Search for My Tongue obviously superior to an ordinary monolingual peruser. Likewise, Half-standing, is additionally outfitted towards two unique sorts of individuals. An individual who isnt blended won't have the option to grasp this sonnet just as somebody who is blended. Likewise, Half-Caste fights discriminative English individuals. In a less discriminative culture, for example, Canada where the utilization of racial slurs like half-station is rare, it is a lot harder to fathom Agars social clashes. In this manner, both Half-standing and Search for my Tongue are both genuine instances of how social setting impacts how the sonnet is seen. Taking everything into account, the two sonnets are influenced by social setting, which directs the impact on the peruser. For instance, as recently expressed, a bilingual individual will have the option to understand Search for My Tongue superior to a monolingual individual. Be that as it may, Strata Bath needs to guarantee that the m

March Questions Omnibus 4

March Questions Omnibus 4 Lupe (who Im looking forward to seeing at CPW!) asked, is it pretty simple to travel on train or ? from Logan to MIT? Well be running a bus from Logan Airport to MIT all day Thursday, and back from MIT to Logan on Sunday. Just look for the person with the MIT sign near the baggage claim (make sure youve given us your flight information). If youre coming outside of the times were running the shuttle, you can take a taxi (~$25), or the subway ($1.25). The subway trip can be a little confusing for those not used to public transportation because it involves two transfers, but its not difficult: Blue line inbound to Green line inbound to Red line outbound, exit at Kendall/MIT station. CL wrote, hey Matt, I heard MIT are paying for flights for students to get to Boston (CPW). Is that true? n also.. If we register now, but when the time comes, we cant make it.. is there any penalty? cuz I might have a tournament that weekend.. but it all depends on how i perform next weekend. Good luck with the tournament! It is better to register now and then cancel (please try to cancel at least a few days in advance, if at all possible) than to not register by the deadline and then try to register late. Also, it is true that we are paying for some students transportation to CPW; for the most part, this is based on financial need. Ash wrote, Is there anyway to come late for it? as in late friday night, all of sat and leave sunday? Sure. Just let us know your dates when you register. Youll miss all of the academic stuff, but youll be around for housing stuff and parties. Michael wrote, What happens if I register without stating someone whom I have plans to stay with, and then realize I have someone I want to stay with? That is, a current MIT student? No problem! Let us know at [emailprotected], or call the office at (617) 253-3400. Thomas wrote, In my planning to attend CPW I called one of my friends who is a student at MIT. Although he was willing allow me to stay with him, he was wondering if there was anything he had to register or if I puting his name into the registration form is enough. Your friend must register as a host at the MIT Community CPW site. If he has any problems, he should email [emailprotected] Alex wrote, I cant come to CPW cause of an orch competition so I was just wondering what actually goes on during it? In other words, what am I missing? Centrally, CPW is about exposing you to MIT life classes, faculty, students, housing, student life, etc. to help you determine if you want to attend MIT. Youd stay with an MIT student, check out classes, meet your potential future classmates in short, get a taste of MIT. If youre already decided on MIT, CPW allows to meet your classmates, check out which dorm you might want to live in, etc. You can see the schedule of CPW events in your MyMIT portal. I wouldnt worry about it too much, though focus on your orchestra competition. Good luck! Currer Bell wrote, I already registered for CPW, but on the part where we have to answer questions that help us get matched up to our MIT student hosts, under perferences, do we have to indicate the gender preference of our host. Ex. I am female and would like to room with a female student, or is that a given. We will match you with a host of your gender. However, the majority of you will be housed in a co-ed dorm. Do let us know if you require or prefer single sex housing. nehalita asked, hows the tennis in MIT? =) You can learn more about varsity womens and mens tennis (and all of the other varsity sports) on their websites. There are plenty of tennis courts at MIT for recreational playing as well as intramural tennis. Somewhat relatedly, we have pretty nice squash facilities, too. Erek wrote, you edited your post. I wonder why. No big conspiracy here, Erek, its just that blogs.mit.edu doesnt have built-in preview functionality, so I usually post once and then edit. Ill probably be moving this blog to a Moveable Type platform this summer with more functionality. Eric Schmiedl wrote, In regards to the new SAT, you say youll address it after May 1st. Why the delay? Taking a break from thinking about admissions stuff? Well, were mostly focused on the Class of 2009 right now. In a month or so well turn our full attention to the Class of 2010, and the new SAT (and ACT and TOEFL) will be an important topic. Im Not Nemo! wrote, Heres a question about the Swim Test. I understand that the swimming test involves swimming 4 lengths of a 25 M pool, and only the last length can be done with a backstroke. What happens to the students who CANT SWIM?!?!?! Would taking a semester of Beginning Swimming substitute for passing the Swim Test? Or would the non-swimmers have to take Beginning Swimming over and over again until they can actually pass the swim test? In other words, is there a point at which MIT says, You tried to learn to swim and pass the swim test, thats sufficient. Or will MIT make us keep trying and trying to pass the test until we either drown or have to drop out? Ive never heard of anyone having to drop out because of the swim test. If you take the Swimming PE class, Im sure youll be fine. 05senior posted on the waitlisted thread, I have received several awards and had several accomplishments since I submitted my application. Would it be in my best interest to submit those now that I am on the waiting list? Absolutely! Waitlisted students should keep in touch with us and let us know about any cool new stuff. Wait listed applicant wrote, Matt, I have one quick question. Do you think that if we devote some time posting comments on these blogs might have an influence on the admissions process for the wait-listed applicants? I wouldnt count on blog-commenting as the best way to keep in touch with us. Letters and emails, and perhaps the occasional phone call, would be the methods I would recommend. gameboyguy13 wrote, You said you dont admit for the spring semester, right? Also, how likely is it that someone who was rejected this year would get in as a transfer student next year? We only admit freshmen to begin in the fall semester. We admit transfers for both the spring and fall semesters, but you must complete at least one full year of university before entering MIT as a transfer. I dont know how likely it is that someone not admitted in the freshman process would be admitted in the transfer process, but I personally know folks who have done just that. Need_clarification_numbers_class_2009 wrote, I do have a question on the numbers. I believe that MIT sent out less than 1500 letters to admitted students for the 2009 class. There were 400-500 students that were sent the waitlisted letter. Based on your comments, MIT is aiming for a class of 980 students for the class of 2009. So realistically, is there any remote chance for a waitlisted student to even be considered at all ?? I know that in the last 2 years, MIT did not take anyone off the waitlist. Given your high yield, should current waitlisted students even want to keep any hope at all ? Yes. The numbers of students we admitted was selected intentionally with the idea of our being able to go to the waitlist this year. The last two years, where we took no students from the waitlist, Id consider aberrations. waitlisted wrote, Do you remember the applications of rejectecd applicants for a subsequent year? In other words, if one reapplies as a Freshman again next year (by staying eligible) what information from the preceeding years application be brought to bear on the new application? Would essays, recommendations and transcripts be kept on file from the preceding year? Also, what would be the difference in a waitlisted reapplying vs a rejected reapplying, if any? Finally, for the waitlisted applicants this year, what sort of selection process will be used to admit them? Your entire application from the previous year will be in your application file in the year you apply. Your decision from the previous year will have no bearing on your next decision. When we go to the waitlist, staff will be asked for their input, and a small committee will make the final decisions. Anonymous wrote, How important does MIT consider math competitions to be? Do you consider making the USAMO to be a big deal? What about MOSP? Math and science accomplishments at the national level are a big deal. As Ive continually written, though, accomplishments are far from all that matters in MIT admissions. Jordan Sun wrote, Did MIT reject any RSI scholar applicants this year? People always tell me that RSI is the ticket of getting into MIT. I dont believe that in any the four years Ive worked here that every RSI student was admitted. Those who are admitted to RSI have many of the same qualities we look for in MIT applicants, but there is no magic ticket for MIT admissions. valent victoria (Lupes daughter, who Im also looking forward to seeing!) wrote, one of my favorite bands, the matches, plays in boston so much, so i am stoked about that next year. hey matt, have you checked out ted leo and the pharmicists? If not, add them to your collection! I dont yet know either The Matches or Ted Leo The Pharmacists, but I look forward to hearing them from your CD collection in the fall! And for all of the rest of you who have recommended music to me in this blog, I do fully expect for you to stop by my office (3-107) in the fall, CDs in hand =) MITmom (in response to the Matt looks like thread) wrote, no, no.. You look like Rob Morrow! Ill take that as a complement! (What math problem will Numbers work with tonight?) Though his Boston accent in Quiz Show could have used some work Michael also wrote, Grr. Im angry. Apparently, you were supposed to be at the NYC Admitted Students meeting, and you werent. Lana and I were angry. :p Yeah, sorry about that, change of plans instead of being in downstate New York this weekend with Internet, Ill be disconnected in upstate New York. For those of you who went to an admitted student party in your hometown, how was it?

Women s Rights Of Women Essay - 855 Words

Outline Thesis: There has been a history of women being treated unfairly in society leading discrimination. The perception of women in society The history of women gaining their rights The current position of women in society today Women Right Women are considered intellectually inferior to men from the being of time. Contributing to them being treated unfairly in society leading to discrimination in religion, workforce and home life. The perception of women in society is a negative one all around the world. Women are limited to only bearing children and doing housework. Furthermore, Women are blamed for all the evil in the world. For example, In Greek mythology, Pandora a woman is the one that opened the forbidden box and released evil into the world. Women are not only blamed for all the evil in the world, but is considered nothing without a man. For instance, Women in India families have to pay a dowers to their future husbands family in order to get married. They also have to pay for the wedding making it undesirable to have a daughter. When their husband s die society treat them as nothing as outcasts and invaluable. They are often blamed for their husbands death and is expected to mourn them forever. â€Å"The estimated 40 million women widows in the country go from being called â€Å"she† to â€Å"it† when they lose their husbands† ( Barrera, Corbacho, page 1). Some widows are even forced into prostitution because of their limited options of surviving. India i s not theShow MoreRelatedWomen s Rights Of Women Essay1455 Words   |  6 Pagesa myriad of women have expressed through outlets such as public assemblies, literature, and speeches. There have been three waves of the women’s movement, each targeting a variety of issues within each era. The third wave was in 1995, where Hillary Clinton spoke in Beijing, China, claiming that women’s rights were the same as human rights, that every aspiring girl deserved the civil liberties that every man was given around the world. Moreover, the movement had shifted towards women in developingRead MoreWomen s Rights Of Women1265 Words   |  6 Pagesstands in the way of women being equal to men? Journalist Carlin Flora suggests the following, â€Å"While not all claims to humanity are universal and no one context, culture or continent can truly represent all peoples, the following three examples from very different contexts, cultures and continents show that some violations of womenâ €™s human rights are universal. In particular, it is still the case the world over that a woman’s reproductive rights, which impact on her right to life, are still seenRead MoreWomen s Rights Of Women881 Words   |  4 PagesTwenty –first century ladies are discovering it a daunting task to keep up both sexual orientation parts as an aftereffect of the women s activist development. They are presently assuming liability for both the supplier and the nurturer, battling like never before to acquire and keep a superior personal satisfaction. Woman s rights has supported in equivalent vocation opportunity, battling to get ladies acknowledged into the employment advertise, and what initially began as ladies strengtheningRead MoreWomen s Rights Of Women Essay1647 Words   |  7 Pagesthe early 1920’s, women thought they had achieved the unachievable. They could finally work, keep their earned wages, marry whomever they please, and even vote. After reaching their goal and fighting vigorously, women could taste equality and the freedom they deserved. While women still have the right to work in today’s society, women are not exactly treated equal in the workplace. Regardless of the past and the extreme measures taken to ensure equal opportunities for both men and women, there are manyRead MoreWomen s Rights Of Women1590 Words   |  7 Pagesthe 1920s, women were ignored in every aspect of their life. From politics, to social situations, women were constantly looked at as lesser. The 20s was a decade of women ready to fight for their rights. From gaining social freedoms, to getting political rights, the 20s was the first decade of feminism. Many women played key roles in the fight for women s rights through speeches, marches, and much more. The women that fought for their rights in the 1920s completely changed how women live their livesRead MoreWomen s Rights Of Women1230 Words   |  5 PagesWomen’s suffrage has stretched from the 1800’s to present day, as women have struggled to have the same civil and constitutional rights as men in politics and be appreciated as equals in the workforce. Groups of women known as suffragists questioned the customary views of women’s roles. Eventually our nation has evolved and realized that male-controlled societies suppress women’s rights. From the beginning steps taken in 1850 to 2013 with women earning combat roles in the military, women’s rolesRead MoreWomen s Rights Of Women1206 Words   |  5 Pagesto speak of women and the role of women in this election, the subject of women is tiresome but necessary in a world where gender is still existent as an obstacle for most. I cannot identify what woman is. I am basing my definition from our modern understanding of woman, our general view, and the popular experience. People are using younger women voting for Bernie Sanders as proof of gender’s irrelevant in this election, that women have achieved their rights. Even if women ‘have rights now’ it doesRead MoreWomen s Rights Of Women1393 Words   |  6 Pages Women all over the world are being treated different than men. Iran is one of the places that women are being treated the worst. From restrictions to punishments, women in Iran are being treated with no respect, and that is not okay. Women’s rights activists have tried to get it to change, and have traveled to many places to try and get more people to join their movement. There are many issues with women not having the same rights as men. One of the main problems is that they are treated lessRead MoreWomen s Rights Of Women1272 Words   |  6 PagesThroughout history, women have fought a strenuous battle for equal rights. Many men, and even some women, all over the world believe that women do not share the same value and importance to society as men do. On September 5, 1995, Hillary Clinton spoke at the 4th World Conference on Women, on behalf of women all over the world. Clinton raised awareness on how women s rights are being violated and why it is important to recognize women s rights as equal to everyone else’s rights. Even today, in 2016Read MoreWomen s Rights Of Women1052 Words   |  5 PagesThe family has traditionally been the basic unit of Chinese society where women have long been charged with upholding society s values in their roles as wives and mothers. Especially in the Qing Dynasty, women were required to balance society s i deals with the reality of raising a family and maintaining a household. Throughout the imperial period and into the beginning of the twentieth century, the relationship among family members was prescribed by Confucian teachings. The revered philosopher

University of Dallas GPA, SAT ACT Admissions Data

School Annual Day Free Essays

This is a request to the entire guest, please get settle down in few minutes, we are about to start our function. We will start our function with national anthem. Kindly stand out at your places. We will write a custom essay sample on School Annual Day or any similar topic only for you Order Now On behalf of **** school family, I welcome you all with great pleasure, for this Annual Day Celebration. It’s an honour to call our Chief Guest†¦Ã¢â‚¬ ¦ We are the world. We are the children. We are the ones who make a brighter day. I’m sure, all of you present here, must have heard this song performed by michael jackson. Children are the future of every nation across the world. It is today’s generation which can go ahead and make the world a better place. Children are our tomorrow – our future. Bright faces that you are going to see here today, while performing on stage, showing their talents and receiving prizes will be the citizens of tomorrow who are going to make a difference in our society. I hope you all are going to appreciate them, as well as to teachers also, who have putted lot of efforts. Thank you XXX Sir, Good afternoon to all of you, as we all know today we are gathered here to celebrate our Annual Day. Nowadays, only academic excellence is not enough to make any child as outstanding performer. They should be good at extar- curricular activities also. From this prospective our teachers have putted lot of efforts with the little brainees for all the performances. Wishing them luck we will start†¦.. How to cite School Annual Day, Papers

Water Management Problem in Developing Countries †Free Samples

Question: Discuss about the Water Management Problem in Developing Countries. Answer: Introduction: Freshwater is an extremely precious but finite resource which is imperative for sustaining life. It is because water is crucial in every aspect of life. It is to be understood that adequate water supply should be present for people of present as well as future generations. In addition to this the quality and quantity of water flow need to be maintained for the ecosystem functions. In several developing countries the availability of water is subject to large seasonal or inter-annual fluctuations. Water is essential for food production, economic growth, environmental support and the sustainability of life. Water is utilized for domestic uses as well as industrial for the purpose of day-to-day activities. The purpose statement which this report aims to address is about the water management problem in the developing countries of the World as the depletion of water reserves is a major issue and for sustaining life on earth, water is utmost important. Findings: Problems: The value of water and water management has been major issues and several debates have been carried out regarding this issue. There are 261 river basins which cross the political boundaries of two or more countries. Around 45.3% of the land surface accounts for around 80% of the global river run off and it also affects around 40% of the total population on earth. Severe mismanagement of water is a serious issue in countries like India specifically (Worthington, 2013). The two major problems are floods and salty groundwater (Dinar Zilberman, 2012). Solutions: The solution for management of floods is large scale irrigation projects to help management and protect from environmental hazards. Plantations can also improve the impact of water flow on soil erosion. The possible solutions are the use of gypsum, the use of molasses and cane sugar extracts and also the cultivation of salt resistant varieties. Discussion: The main challenges for the achievement of water security are meeting basic needs, securing the food supply, protection of the ecosystems, sharing the water resources, management of the risks, valuing of the water as well as governing the water wisely. Meeting of the basic needs includes a preparatory process of water management, understanding the fact that water and sanitation are most basic of the human needs and they are essential for health as well as well being and also for the empowerment of people (Marlow et al., 2013). The proper and equitable allocation of water is necessary for food production, specifically of the poor and the vulnerable. The water supply should also be maintained for the integrity of the ecosystems by the sustainable management of water resources (Loehr, 2012). Risk management needs to be properly done in order to provide security from floods, droughts, pollution and other water related hazards. The water needs to be managed in a way which reflects the cost of their provision and hence the need for equity should also be taken into account. In order to ensure the proper governance the involvement of the public and the interests of all the stakeholders need to be kept in mind (Boyd Tucker, 2012). Conclusion: The competition over shared resources, especially water cannot be a root cause of social, economic as well as political tension. This needs to be kept in mind in cases where water is scarce, wherever the place is or not. Surface water resources are derived from rivers, even within countries and the activities are designed to develop and also develop a coordinated strategy. It can be safely said that the greatest economic benefits of the improved supply of water, sanitation as well as water resources management will be experienced in those countries where there are the greatest water challenges. Thus investing in improved water and sanitation, drinking and major other uses is beneficial for the developing countries and specifically its poor people. Investments in public health and management of water leads to better adaptive capabilities to climate variability and also improved services of ecosystem. There are economic highlights of investing in water as well. Increased productivity and production within the economic sectors might be one of the reasons which might influence the people to invest in water. Recommendations: The people need to be made aware of the existing scenario of the availability of water specifically as well as other natural resources. It will also encourage the people to rediscover the specific elements of the ecosystem that contribute to the environment and sustainability nad hence protect and conserve them. Institutions or processes to learn from experiences of the developed countries need to be employed so that the same mistakes are not repeated (Faria Bagajewicz, 2012). The developed countries need to fulfil the commitments made at UNCED in Rio regarding the funding of environmental protection projects in the developing countries. The governments should closely link their national policies with regional and international policies in order to achieve maximum progress in areas of water pollution prevention linked strategy and also other areas like water, natural resource recovery, biodiversity protection and so on. All countries need to maintain their commitments regarding the proposals for follow up activities on water conservation along with other environmental components (Schultz Engman, 2012). References: Boyd, C. E., Tucker, C. S. (2012).Pond aquaculture water quality management. Springer Science Business Media. Chapter 7. Conclusions and recommendations. (2017).Fao.org. Retrieved 5 October 2017, from https://www.fao.org/docrep/005/y4502e/y450 Dinar, A., Zilberman, D. (Eds.). (2012).The economics and management of water and drainage in agriculture. Springer Science Business Media. Faria, D. C., Bagajewicz, M. J. (2012). A new approach for global optimization of a class of MINLP problems with applications to water management and pooling problems.AIChE Journal,58(8), 2320-2335. Loehr, R. (2012).Agricultural waste management: problems, processes, and approaches. Elsevier. Marlow, D. R., Moglia, M., Cook, S., Beale, D. J. (2013). Towards sustainable urban water management: A critical reassessment.Water research,47(20), 7150-7161. Schultz, G. A., Engman, E. T. (Eds.). (2012).Remote sensing in hydrology and water management. Springer Science Business Media. Worthington, E. B. (Ed.). (2013).Arid land irrigation in developing countries: environmental problems and effects. Elsevier.

War Poets and the five senses. Essay Example For Students

War Poets and the five senses. Essay Anthem for Doomed Youth fully utilizes sound, though the language Owen uses is simple and poignant. stuttering rifles rapid rattle shrill, demented choirs of wailing shells these quotes, when read, immediately evoke the sounds of artillery and gunfire, common sounds in the Great War. Owen utilizes this to give the sense of overbearing, foundation shaking explosions and to give the reader an auditory feeling of being In the trenches. Arbitrary and abstract Ideas expressed In this way become very real when reading them out loud to yourself. Smell is perhaps the most primal of all the five senses. Though imagery and sound are used most often in film and other media, smell is forgotten. However, smell is one of the most powerful of all the senses in its ability to affect the reader. Who has ever ergot the stench of rotting meat, or of gunpowder. Siegfried Seasons the rank of smell poets can access the deeper parts of the human psyche, and instill deep emotions in the reader without the reader even realizing it. We will write a custom essay on War Poets and the five senses. specifically for you for only $16.38 $13.9/page Order now Owen and Swanson knew this and both utilize it often in their poetry. Relating to the topic, tangible means to be perceptible by the senses; Earlier on in the evolutionary sense we evolved from animals whose primary sense was smell, and to become tangible, an abstract issue must affect the primary or base emotions. Smell is the most effective in this. Taste is lesser known in poetry because it is so difficult to adequately describe, though Owen tries in Dulcet Et. Obscene as cancer, bitter as the cud of vile, incurable sores on innocent tongues Taste is perhaps the most difficult of the senses to accurately describe, thus is also harder to use to make abstract ideas less so. Touch is one of the most effective senses a poet can manipulate to make abstract ideas more tangible. Through invoking the sense of touch, a poet can stir the reader to easily imagine what the poet wants. Most of all in war poetry, touch is embodied in he sense of pain, for war is the cause of more pain than anyt hing else. Wilfred Owens poetry almost always speaks of pain, death and suffering, and indeed this is true in almost all war poetry. Everyone has experienced physical pain at some stage in their life thus the usage of pain in poetry is always going to affect the reader, for every reader understands pain. Pain is perhaps the primary feeling during wartime. Emotional or physical, none leave the trenches without experiencing it and by using it in poetry, the reader understands with perfect clarity what the poet is describing, just by imagining their own pain. The five senses are the most important things in poetry, for while an abstract idea may be perfect in its conception and tone, it cannot truly speak to a reader without allowing the reader to feel the poetic message in a more primal way. Wilfred Owen and Siegfried Swanson surely understood this as the senses are strong components of their respective works. This allows their poetry to speak to any reader, and explains their huge popularity among the poetic world. The five senses are difficult to describe and harder to use, but without them abstract issues such as in Dulcet Et Decorum Est would be difficult indeed to appreciate.

Definition and Examples of Primary Verbs in English

Definition and Examples of Primary Verbs in English The primary verbs in English grammar are the verbs be, have, and do- all three of which can function as either main verbs or auxiliary verbs. Primary verbs are sometimes referred to as ​primary auxiliaries. The Different Functions of Primary Verbs To BeMargaret is a brilliant student. (lexical verb)Margaret is applying to Yale. (auxiliary verb)To HaveFrank has a good job. (lexical verb)Frank has just returned from a business trip. (auxiliary verb)To DoNana does the crossword puzzle in the Sunday paper. (lexical verb)Nana doesnt go out much anymore. (auxiliary verb) Primary Verbs as Auxiliaries In one of their uses, the primary verbs precede a main, lexical verb. When used in this way, they may be said to be functioning as auxiliary verbs within the clause. This is illustrated in (17): (17a) He is speaking to her now.(17b) I have visited my grandmother every Christmas since I was a child.(17c) You didnt eat your lunch.In simple terms, auxiliary verbs are additional verbs (or helping verbs, as EFL teachers often say). In Modern English, primary be is used as an auxiliary in either the progressive construction, illustrated in (17a), or in the passive construction, illustrated in (18):(18) She was spoken to yesterday.When used as an auxiliary, have appears in perfect constructions, as shown in (19):(19a) He has spoken to her.(19b) He had spoken to her yesterday.When used as an auxiliary, do appears in negative and interrogative constructions:(20a) I didnt speak to her yesterday.(20b) Did you speak to her yesterday? Notice that it is the job of the primary verb to carry the tense inflection for the entire verb phrase (VP), while the main verb conveys the semantic content. Primary Verbs and Modal Verbs Primary and modal verbs do not follow the same grammatical rules. In particular: Primaries have -s forms; modals do not:is has, doesPrimaries have nonfinite forms; modals do not:to be, being, been(David Crystal, Rediscover Grammar, 3rd ed. Pearson Longman, 2003)​ Be as Auxiliary of the Progressive and of the Passive [I]n a sense we can answer the question of how many primary auxiliaries there are with either four or three; the verb be does double duty as the auxiliary of the progressive and the auxiliary of the passive. Since these are quite different functions, and since it is quite easy to distinguish them, it is best to view them as two different primary auxiliaries which have the same form. It is easy to distinguish the two uses. First of all, the progressive be and the passive be are followed by different forms of the verb, ing form (be eating) and part (be eaten), respectively. Second, passive sentences have some particular characteristics: for instance, in a passive sentence you can usually have a by phrase (be eaten by a shark).Functions of DoWe often use the verb do as a stand-in auxiliary, much in the same way as we use primary and modal auxiliaries. Like primary verbs, it can function as an auxiliary or as a principal verb because it has a full verb inflectional paradigm.Do as an auxi liary verb:This! Why, father, what do you mean? This is home! [Porter]Does everybody at the academy dress like that? [Gogol] Do as a lexical verb:But that the most acceptable service of God is doing good to man. [Franklin]Sane people did what their neighbors did so that if any lunatics were at large, one might know and avoid them. [Eliot]The thick iron ferrule is worn down, so it is evident that he has done a great amount of walking with it. [Doyle] Because of the flexibility of this verb (it is also used to form questions, negatives, and for emphasis), it is important to pay close attention to how it is used. When it is used as an auxiliary, like the primary and modal verbs, it will occupy the initial position in the verb phrase, and there will always be a non-finite lexical verb to follow. When it is used as a lexical verb, it may be preceded by an auxiliary verb or simply stand alone. Sources Martin J.  Endley,  Linguistic Perspectives on English Grammar: A Guide for EFL Teachers. Information Age Publishing, 2010 Kersti Bà ¶rjars and Kate Burridge,  Introducing English Grammar, 2nd ed. Hodder, 2010 Bernard ODwyer,  Modern English Structures: Form, Function, and Position. Broadview Press, 2000

Financial Analysis of Custom Snowboards Inc Term Paper

Financial Analysis of Custom Snowboards Inc - Term Paper Example As we are aware that there has been an immense amount of economic turmoil all around the world. Custom Snowboards Inc. was also severely impacted as the customers decreased their expenditure on leisure and sports. However, the company did not have to suffer like other companies did and it suffered from a 4% decline in Sales. Horizontal Analysis An increase in Sales Expenses are fairly consistent Interest income increased by 28% and interest expense decreased by 5% Current assets increased by more than 100% and total assets by 3.6% whereas total current liabilities had no significant impact Retained Earnings increased by more than 70% Vertical Analysis Gross Profit is 30% of Sales General and admin expenses are less than 20% of sales on average during years 12, 13, & 14 On average, current assets constitute approx. 50% of the total assets Cash comprises of more than 15% of the total assets and has the highest constituency whereas receivable come second Current Liabilities are under 10 % of the Total liabilities and equity Trend analysis - Trend analysis is the percentage changes in items of the financial statement during successive years. We can also call it an extension of the Horizontal Analysis and indicates the direction of change. The snapshot shows the sales trend during years 12, 13, & 14 respectively. ... dit risk Loaned out funds wont be no longer available for operational and other bank use Risk of incorrect assessment of interest rate (Fitzsimmons,n.d.) The bank also looks at several other things in a company's financial statements. It also looks at the Debt-ratio, Interest Coverage ratio, current income status of the company as well as its credit history and overall stability of the Enterprise. Custom Snowboards Inc. Debt-ratio is currently 49%, which is less than its competitor. Moreover, another red flag comes when we look at the Financial Statements, specifically the Income Statement and see that Net Income has suffered a sharp decline by 74% due to a sharp decline in Sales. As the bank is concerned with the stability, the declining sales and income statement pose a risk to the lender in terms of ability of Custom Snowboards to cover its debt. Risk Mitigation Credit Risk is the major risk that banks are concerned with, The financial statements of Custom Snowboards Inc. show sta bility and gradual growth The trend analysis shows that the sales would grow gradually making sure that the company would be able to meet its obligations Horizontal and vertical analysis show that the company is not under huge current and long term liabilities and the expenses are not very high Custom Snowboards Inc. is a growing concern As far as the debt-ratio is concerned, a positive aspect is that although it is higher than the competitor, it has declined from last year. The company's Income Statement does not show a very positive picture, however, it is mainly due to the massive economic recession. Moreover, if we look at the Balance Sheet, we that the Working Capital is positive and the company has enough financial strength to meet its short term obligations and remain operational.

Natural Selection Essay Example | Topics and Well Written Essays - 250 words - 2

Natural Selection - Essay Example that when a certain species is bred with another one from different part of the world, it leads to creation of new patterns of species that are well adapted to the environment. It is a dangerous idea since it bases its argument on the ground that species once developed or created can never transform which is not correct. For instance, gene duplication is able to form different species resulting from the same parental organism mainly because of polyploidization. Human activity such as mining and construction dismantle animal homes thus rendering them homeless and at the same leaving them vulnerable to preditators and extreme climates that make their survival hard. Global climate change and environmental pollution leads to production of poisonous gases such as carbon dioxide that endanger some species such as marine life. This is because they consume poisonous chemicals that either kill them or alter their reproductive system. On the same front, change in temperatures and climate conditions leads to prolonged dry spells which wipes away animal homes thus hindering evolution of new

The Effect Of Internet Piracy

The Effect Of Internet Piracy Both the music and gaming industry claim to suffer from major financial losses due to internet piracy. In 2002, Software publishers claimed that, the worldwide piracy rate for PC business software was 39%, which translated into a $13.08 billion loss in revenue. The music industry also recorded losses of up to $4.6 billion as a result of 1.8 billion illegal downloads. (International Planning and Research Corporation 2003). All these figures indicate significant losses to the relevant copyright owners. (Hui, Kai-Lung, and I.P.L. Png (2003)) Many analysts believe it is due to peer-to-peer (P2P) technologies which lead to the illegal downloading. This type of piracy is known as End-user piracy, which differs greatly from For-profit piracy. End-user piracy seems to be a lot more difficult to control. The music/game industry and policy makers address this issue by reinforcing copyright laws and implementing technological protection and also targeting the developers and users of P2P networks. The ongoing Eircom vs. The Pirate Bay debate is an example of this preventative action. But many believe downloading is a form of sampling and also leads to the exposure effect, leading people to find and try new music in order to make more informed purchases which in turn can lead to an increase in CD sales around the world. (Peitz and Waelbroeck (2003)) The harm caused by piracy also depends on publishers pricing strategies. When it seems more beneficial for potential shoppers to resort to private copying, publishers could raise the price of the legitimate item to extract the increased consumer surplus. If this happens, directly treating all pirated copies as lost sales would overstate the harm caused by piracy. However, similarly, if publishers deliberately set low prices to discourage copying, then the number of copies would understate the lost revenue (Kai-Lung et al (2003)) There are two ways of copying non-authorized digital products; by obtaining original material from family or friends, or by downloading it directly from the internet. The process of copying music, film or software is very easy, all someone needs is the product and a storage device like a hard-drive or cd-recorder. Digital goods also copy across perfectly when coming direct from the source. On the other hand, downloading from P2P file-sharing websites has a number of considerable disadvantages. Lower quality copies are generally produced and users can spend hours looking for the right download file. Also, frequently, due to the lack of install guides for software and lack of song lyrics, this effort can lead to wasted time. Lastly, files such as music and video files can be badly compressed or incomplete. (Martin Peitz et al (2003)) Literature Review To illegally copy or distribute unauthorized or counterfeit music, video or software of any type is known as internet piracy. Software is now one of the most heavily distributed products on the internet (Microsoft.com, 2010). This, now a criminal offence, includes the illegal reproduction and duplication of copyrighted computer software, music and films (Hohn, Muftic, Wolf, (2006)). However the biggest problem in this digital time we live in, as stated by Lysonski Durvasula, (2008), is the undoubtable fact that the process of downloading music over the internet is reasonably easy. With just a few clicks of a button you can download an artists entire discography, and with the speed of internet access these days it is on your computer in a matter of minutes. Piracy is most rampant in young people. As seen in the survey conducted by Gallup Poll (2003), 83% of the young people said that downloading of music for free was totally acceptable. In another survey conducted by Freestone and Mitchell (2004) evidence was found to suggest that downloading music was seen as least wrong of other criminal internet acts, because they felt no harm was being done to others. It was also found the majority of college students said that downloading music and films was neither an offence or illegal. (T. Ramayah, Noor Hazlina Ahmad, Lau Guek Chin, May-Chiun, Lo (2009)) This is mostly because of the creation of these P2P networks like Bit-comet the Pirate Bay and the total digitalisation of music, video and software. It is my belief that because of this process of digitalisation the sale of CDs around the world has declined. Most reports seem to suggest that P2P networks have a direct negative impact on the digital industry, be it music or games. Essentially, there are four communication channels that can be used for Internet piracy: The World Wide Web, a normalised set of standards for storing, getting and displaying information in a client/server environment. FTP (File Transport Protocol) a protocol for getting and sending files from a remote computer. Peer to Peer computing (P2P), a form of distributed processing that links computers via the Internet or pirate networks so that they can share processing tasks. Electronic Mail (e-mail), used for the computer-to-computer exchange of messages and usually the pirated files are sent as attachments, limited to 25mb using Googles Gmail. (T. Ramayah et al (2009)) Such huge losses dilute the incentive for development of information product. However, the losses claimed by the computer software and recorded music industries may be excessive. If piracy could be prevented, many of those who used pirated products might not switch to buying the legitimate item. Instead, they might simply not use the product. With no reduction in price, it is not likely for all the illegal users to switch to the legitimate item. (Kai-Lung et al (2003) Here in Table 1 which was conducted by Kai-Lung et al (2003), reports a very descriptive set of statistics. Consumption of music CDs per capita were a little more than one unit per year, while around 12% owned CD players. The standard deviation of personal disposable income and CD player ownership were large (Table 1) this indicted that the countries in question had different demographic characteristics and income. Worldwide MTV subscription was low per capita, but over the years has started to grow steadily. This leads us into Table 2 which reports the music CD average price and per capita consumption of pirated and legitimate CDs over a range of countries around the world. As seen in (table 2) the demand for both legitimate and pirated CDs varied across the countries with India having the lowest per capita purchase of legitimate music CDs and the United States having the highest. The consumption of pirated CDs was this time, highest in both Singapore and Hong Kong with the United Stated being the lowest. With a few exceptions (e.g., India and Japan), the average price of music CDs varied moderately across the countries. Kai-Lung et al (2003) Hui, Kai-Lung, and I.P.L. Png (2003) Piracy and the Legitimate Demand for Recorded Music, Contributions to Economic Analysis Policy. Peitz and Waelbroeck 2003 The Effect of Internet Piracy on Music Sales: Cross-Section Evidence, Review of Economic Research on Copyright Issues, 2004 Hohn, D. A., Muftic,L. R., Wolf, K. 2006. Swashbuckling Students: An Exploratory Study of Internet Piracy. Lysonski, S., Durvasula, S. 2008. Digital piracy of MP3: Consumer and ethical predispositions. Journal of Consumer Marketing. T. Ramayah, Noor Hazlina Ahmad, Lau Guek Chin, May-Chiun, Lo 2009 Testing a Causal Model of Internet Piracy Behavior Among University Students Gallup Poll. 2003. Moral Acceptability of Downloading Music for Free. Gallup Youth Survey. Freestone, O., Mitchell, W. 2004. Generation Y Attitudes towards E-ethics and Internetrelated Misbehaviours. Journal of Business Ethics

Psychodynamic Counselling Concept Essay

In this essay I mainly discuss the theory and concepts behind psychodynamic counselling, followed by brief discussions of the practice and skills involved in working as a psychodynamic counsellor, and the client’s experience of counselling. Theory/concepts Psychodynamic counselling is mainly concerned with unconscious processes; it takes for granted that humans possess a largely unconscious inner world. Freud argued that while the conscious mind is governed by logic, the unconscious mind is not, and functions in a very literal way, motivated only to experience pleasure, unable to delay gratification. Although Psychodynamic counselling works with the conscious mind, it mainly focuses on unconscious processes. We have key figures in our lives – e.g. parents, carers, and partners – are referred to as ‘objects’, and relationships with them termed ‘object relationships’. The phrase ‘object’ refers to the Freudian concept of the target, or object of the instinct. Object relationships embody not only actual relationships but also the ways that the conscious mind distorts them. The unconscious is viewed as dynamic and purposeful, having huge impact on emotions and behaviour. Psychodynamic theory posits that humans are driven by a need to remain unaware of uncomfortable truths that emerge from the unconscious, experiencing many conflicting needs and demands, e.g. between one’s own wishes and those of others. To deal with conflicts people develop ‘defences’, these include ‘repression’, a form of forgetting, ‘denial’, claiming that something is not upsetting when really it is, and ‘rationalisation’, where a story is created to account for that which feels uncomfortable. ‘Projection’ involves attributing to others characteristics unacceptable to the self, making assumptions about them based on the need to avoid threat. Psychodynamic counselling encourages the client to recognise and accept the troubling attribute, a process called ‘reintrojection’. To engage in projection a defence mechanism called, ‘splitting’, is used when one is finding it too  threatening to accept two opposing traits, such as being capable of both love and hate. It is natural to develop defences, but problems come with their overuse, e.g. using denial so often that problems are not faced. Applying defences too rigidly causes difficulties, and it’s when they start to disintegrate that individuals might seek counselling. Psychodynamic counselling holds that psychological symptoms emerge from the inner world. e.g., developmental problems or conflict may lead to anxiety or self-harm. The psychodynamic approach seeks to address these issues at their roots, as well as alleviating symptoms. Psychodynamic counselling is based on developmental theory, and asserts that childhood experiences affect adult personality. It is understood that episodic memory is physically unavailable to children under three, but that implicit memory and body memory function from an earlier age. Neuroscience now supports the concept that early emotional experiences influence brain development; the psychodynamic approach posits that the client-counsellor relationship is crucial to the process of change. This is considered in terms of three concepts, the first being transference: â€Å"All those impulses experienced by the patient in relation with the analyst which are not newly created by the objective analytic situation but have their source in early – indeed, the very earliest – object relations†¦Ã¢â‚¬ . The counsellor may become aware of feelings in him/herself indicating issues that the client is unable to express; this is ‘counter transference’. The ‘real relationship’ is that which is free of the previous two dynamics. Within the client-counsellor relationship, elements of the client’s inner world can be revealed and become available for healing (Howard, 2011, p.22-25) Practice/skills Psychodynamic counselling employs a number of basic skills that are common to other approaches. It shares the core values of the Rogerian approach: empathy, congruence and unconditional positive regard. The ability to listen is of course crucial. Summarising and reflecting back to the client what s/he has said are necessary skills, as well as being able to say things that the client will find difficult to hear. The following are skills specific to Psychodynamic counselling; Gaining informed consent involves informing the client of the nature, risks and benefits of counselling at the appropriate time; not so soon as to scare him/her away, but in good time. For this purpose it is advisable for the counsellor to be aware of when the assessment phase is concluding, as this is the best time to invite informed consent. The counsellor’s attention to the client is one element that facilitates change. The counsellor must alternate between close listening to the client and attention to how s/he will respond, alert to transference and counter transference. To be aware of both the conscious and unconscious elements of the client’s communication, the counsellor must practice ‘evenly suspended attention’. The counsellor must listen to unconscious communication as well as the explicit information the client is presenting. This includes being able to consider why the client is behaving and speaking as they are, linking this to issues arising in transference, and being able to raise such issues with the client. The counsellor will also make interpretations based on ‘extra transference’ – grasping connections between events, thoughts and behaviour unrelated to the client-counsellor relationship. The client’s experience Initially a client experiences the formal behaviour of the counsellor, sessions have boundaries of time, space, and confidentiality and these factors contribute to a sense of safety and predictability. The client should come to feel ‘held’ by the counselling experience, enabling him/her to feel able to explore painful issues and memories: â€Å"a safe space to lower one’s defences, be vulnerable and be held together.† Receiving a counsellor’s undivided attention contributes to this; Dibs In Search of Self illustrates an emotionally deprived child’s first experiences of undivided and non-judgemental attention, enabling him to blossom in self-discovery. A client goes through a process of developing informed consent, the transference relationship begins once enough trust is established, as it may be experienced as threatening. The client develops an attachment to the counsellor as someone who can help and care for them, and thus may become fearful both of their own needs and of being let down .The ending of the relationship can be painful for the client, and the counsellor should allow plenty of time to deal with issues around this. In conclusion, psychodynamic counselling functions to bring to awareness of the unconscious processes that govern the client’s inner life. A variety of practices are employed in order to supply a client with a sense of security as well as a source of challenge in order to facilitate positive change. References AXLINE, V. M., 1990. Dibs, In Search of Self. London: Penguin FREUD, A., 1937. The Ego and the Mechanisms of Defence. London: Hogarth HOWARD, S., 2011. Psychodynamic Counselling in a Nutshell. 2nd edition. London: Sage. HOWE, D., 1993. On Being a Client. London: Sage

Sage 50 Accounting Software Tutorial

Sage Tutorial Release 5. 3 The Sage Development Team September 10, 2012 CONTENTS 1 Introduction 1. 1 Installation 1. 2 Ways to Use Sage . . 1. 3 Longterm Goals for Sage . . 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 Assignment, Equality, and Arithmetic 2. Getting Help . 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 Parents, Conversion and Coercion . . 2. 11 Finite Groups, Abelian Groups . 2. 12 Number Theory . . 2. 13 Some More Advanced Mathematics 3 The Interactive Shell 3. 1 Your Sage Session . . 3. 2 Logging Input and Output . 3. 3 Paste Ignores Prompts 3. 4 Timing Commands . . 3. 5 Other IPython tricks . 3. 6 Errors and Exceptions 3. 7 Reverse Search and Tab Completion . . 3. 8 Integrated Help System . 3. 9 Saving and Loading Individual Objects 3. 10 Savi ng and Loading Complete Sessions 3. 11 The Notebook Interface . . 4 Interfaces 4. 1 GP/PARI 4. 2 GAP . . 4. 3 Singular . 4. 4 Maxima i 5 Sage, LaTeX and Friends 5. 1 Overview . . 5. 2 Basic Use . . 5. 3 Customizing LaTeX Generation . . 5. 4 Customizing LaTeX Processing . . 5. 5 An Example: Combinatorial Graphs with tkz-graph . 5. 6 A Fully Capable TeX Installation . 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 99 101 103 105 6 Programming 6. 1 Loading and Attaching Sage ? les 6. 2 Creating Compiled Code . 6. 3 Standalone Python/Sage Scripts . 6. 4 Data Types 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 SageTeX 8 . . Afterword 8. 1 Why Python? . . 8. I would like to contribute somehow. How can I? . 8. 3 How do I reference Sage? . 9 Appendix 9. 1 Arithmetical binary operator precedence . . 10 Bibliography 1 1 Indices and tables Bibliography Index ii Sage Tutorial, Release 5. 3 Sage is free, open-source math software that supports research and teaching in algebra, geometry, number theory, cryptography, numerical computation, and related areas. Both the Sage development model and the technology in Sage itself are distinguished by an extremely strong emphasis on openness, community, cooperation, and collaboration: we are building the car, not reinventing the wheel. The overall goal of Sage is to create a viable, free, open-source alternative to Maple, Mathematica, Magma, and MATLAB. This tutorial is the best way to become familiar with Sage in only a few hours. You can read it in HTML or PDF versions, or from the Sage notebook (click Help, then click Tutorial to interactively work through the tutorial from within Sage). This work is licensed under a Creative Commons Attribution-Share Alike 3. 0 License. CONTENTS 1 Sage Tutorial, Release 5. 3 2 CONTENTS CHAPTER ONE INTRODUCTION This tutorial should take at most 3-4 hours to fully work through. You can read it in HTML or PDF versions, or from the Sage notebook click Help, then click Tutorial to interactively work through the tutorial from within Sage. Though much of Sage is implemented using Python, no Python background is needed to read this tutorial. You will want to learn Python (a very fun language! ) at some point, and there are many excellent free resources for doing so including [PyT] and [Dive]. If you just want to quickly try out Sage, this tutorial is the place to start. For example: sage: 2 + 2 4 sage: factor(-2007) -1 * 3^2 * 223 sage: A = matrix(4,4, range(16)); A [ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11] [12 13 14 15] sage: factor(A. charpoly()) x^2 * (x^2 – 30*x – 80) sage: m = matrix(ZZ,2, range(4)) sage: m[0,0] = m[0,0] – 3 sage: m [-3 1] [ 2 3] sage: E = EllipticCurve([1,2,3,4,5]); sage: E Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Field sage: E. anlist(10) [0, 1, 1, 0, -1, -3, 0, -1, -3, -3, -3] sage: E. ank() 1 sage: k = 1/(sqrt(3)*I + 3/4 + sqrt(73)*5/9); k 1/(I*sqrt(3) + 5/9*sqrt(73) + 3/4) sage: N(k) 0. 165495678130644 – 0. 0521492082074256*I sage: N(k,30) # 30 â€Å"bits† 0. 16549568 – 0. 052149208*I sage: latex(k) frac{1}{i , sqrt{3} + frac{5}{9} , sqrt{73} + frac{3}{4}} 3 Sage Tutorial, Release 5. 3 1. 1 Installation If you do not have Sage installed on a computer and just want to try s ome commands, use online at http://www. sagenb. org. See the Sage Installation Guide in the documentation section of the main Sage webpage [SA] for instructions on installing Sage on your computer. Here we merely make a few comments. 1. The Sage download ? le comes with â€Å"batteries included†. In other words, although Sage uses Python, IPython, PARI, GAP, Singular, Maxima, NTL, GMP, and so on, you do not need to install them separately as they are included with the Sage distribution. However, to use certain Sage features, e. g. , Macaulay or KASH, you must install the relevant optional package or at least have the relevant programs installed on your computer already. Macaulay and KASH are Sage packages (for a list of available optional packages, type sage -optional, or browse the â€Å"Download† page on the Sage website). . The pre-compiled binary version of Sage (found on the Sage web site) may be easier and quicker to install than the source code version. Just unpack the ? le and run sage. 3. If you’d like to use the SageTeX package (which allows you to embed the results of Sage computations into a LaTeX ? le), you will need to make SageTeX known to yo ur TeX distribution. To do this, see the section â€Å"Make SageTeX known to TeX† in the Sage installation guide (this link should take you to a local copy of the installation guide). It’s quite easy; you just need to set an environment variable or copy a single ? e to a directory that TeX will search. The documentation for using SageTeX is located in $SAGE_ROOT/local/share/texmf/tex/generic/sagetex/, where â€Å"$SAGE_ROOT† refers to the directory where you installed Sage – for example, /opt/sage-4. 2. 1. 1. 2 Ways to Use Sage You can use Sage in several ways. †¢ Notebook graphical interface: see the section on the Notebook in the reference manual and The Notebook Interface below, †¢ Interactive command line: see The Interactive Shell, †¢ Programs: By writing interpreted 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 Sag e library (see Standalone Python/Sage Scripts). 1. 3 Longterm Goals for Sage †¢ Useful: Sage’s intended audience is mathematics students (from high school to graduate school), teachers, and research mathematicians. The aim is to provide software that can be used to explore and experiment with mathematical constructions in algebra, geometry, number theory, calculus, numerical computation, etc. Sage helps make it easier to interactively experiment with mathematical objects. Ef? cient: Be fast. Sage uses highly-optimized mature software like GMP, PARI, GAP, and NTL, and so is very fast at certain operations. †¢ Free and open source: The source code must be freely available and readable, so users can understand what the system is really doing and more easily extend it. Just as mathematicians gain a deeper understanding of a theorem by carefully reading or at least skimming the proof, people who do computations should be able to understand how the calculations work by re ading documented source code. If you use Sage to do computations 4 Chapter 1. Introduction Sage Tutorial, Release 5. 3 in a paper you publish, you can rest assured that your readers will always have free access to Sage and all its source code, and you are even allowed to archive and re-distribute the version of Sage you used. †¢ Easy to compile: Sage should be easy to compile from source for Linux, OS X and Windows users. This provides more ? exibility for users to modify the system. †¢ Cooperation: Provide robust interfaces to most other computer algebra systems, including PARI, GAP, Singular, Maxima, KASH, Magma, Maple, and Mathematica. Sage is meant to unify and extend existing math software. †¢ Well documented: Tutorial, programming guide, reference manual, and how-to, with numerous examples and discussion of background mathematics. †¢ Extensible: Be able to de? ne new data types or derive from built-in types, and use code written in a range of languages. †¢ User friendly: It should be easy to understand what functionality is provided for a given object and to view documentation and source code. Also attain a high level of user support. 1. 3. Longterm Goals for Sage 5 Sage Tutorial, Release 5. 3 6 Chapter 1. Introduction CHAPTER TWO A GUIDED TOUR This section is a guided tour of some of what is available in Sage. For many more examples, see â€Å"Sage Constructions†, which is intended to answer the general question â€Å"How do I construct ? †. See also the â€Å"Sage Reference Manual†, which has thousands more examples. Also note that you can 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 evaluate any input cell. You can even edit the input before pressing shift-enter. On some Macs you might have to press shift-return rather than shift-enter. ) 2. 1 Assignment, Equality, and Arithmetic With some minor exceptions, Sage uses the Python programming language, so most introductory books on Python will help you to learn Sage. Sage uses = for assignment. It uses ==, =, < and > for comparison: sage: sage: 5 sage: True sage: False sage: True sage: True a = 5 a 2 == 2 2 == 3 2 < 3 a == 5 Sage provides all of the basic mathematical operations: age: 8 sage: 8 sage: 1 sage: 5/2 sage: 2 sage: True 2**3 2^3 10 % 3 10/4 10//4 # for integer arguments, // returns the integer quotient # # # ** means exponent ^ is a synonym for ** (unlike in Python) for integer arguments, % means mod, i. e. , remainder 4 * (10 // 4) + 10 % 4 == 10 7 Sage Tutorial, Release 5. 3 sage: 3^2*4 + 2%5 38 The computation of an expression like 3^2*4 + 2%5 depends on the order in which the operations are applied; this is speci? ed in the â€Å"operator precedence table† in Arithmetical binary operator precedence. Sage also provides many familiar mathematical functions; here are just a few examples: sage: sqrt(3. ) 1. 84390889145858 sage: sin(5. 135) -0. 912021158525540 sage: 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 function n or the method n (and both of these have a longer name, numerical_approx, and the function N is the same as n)). These take optional arguments prec, which is the requested number of bits of precision, and digits, which is the requested number of decimal digits of precision; the default is 53 bits of precision. sage: exp(2) e^2 sage: n(exp(2)) 7. 8905609893065 sage: sqrt(pi). numerical_approx() 1. 77245385090552 sage: sin(10). n(digits=5) -0. 54402 sage: N(sin(10),digits=10) -0. 5440211109 sage: numerical_approx(pi, prec=200) 3. 14 15926535897932384626433832795028841971693993751058209749 Python is dynamically typed, so the value referred to by each variable has a type associated with it, but a given variable may hold values of any Python type within a given scope: sage: sage: The C programming language, which is statically typed, is much different; a variable declared to hold an int can only hold an int in its scope. A potential 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) # string representation 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 Getting Help Sage has extensive built-in documentation, accessible by typing the name of a function or a constant (for example), followed by a question mark: sage: tan? Type: Definition: 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? Type: Definition: log2( [noargspec] ) Docstring: The natural logarithm of the real number 2. EXAMPLES: sage: log2 log2 sage: float(log2) 0. 69314718055994529 sage: RR(log2) 0. 693147180559945 sage: R = RealField(200); R Real Field 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. 18123221829928249948761381864650311423330609774776013488056 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 File: Type: D efinition: Docstring: sage/local/lib/python2. 5/site-packages/sage/games/sudoku. py sudoku(A) Solve the 9Ãâ€"9 Sudoku puzzle defined 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 3] Sage also provides ‘Tab completion’: type the ? rst few letters of a function and then hit the tab key. For example, if you type ta followed by TAB, Sage will print 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 command and a colon after 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 three 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 specify the types of any of the input arguments. You can specify multiple inputs, each of which may have an optional defaul t 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 can also explicitly specify one or either of the inputs when calling the function; if you specify the inputs explicitly, you can 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 exactly. For example, the following is a syntax error because the return statement is not indented the same amount as the other lines above it. sage: def even(n): v = [] for i in range(3,n): if i % 2 == 0: v. append(i) return v Syntax Error: return v If you ? x the indentation, the function works: 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 = b^2; c 64 If 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 x^2 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 while g is a callable symbolic 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: x^2 sage: g(x). derivative() plot(g(x), 0, 2) 3. Use a pre-de? ed Sage ‘calculus function’. These can be plotted, 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) instead 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 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 character modulo 12 of conductor 1 mapping 7 |–> 1, 5 |–> 1, Dirichlet character modulo 12 of conductor 4 mapping 7 |–> -1, 5 |–> 1, Dirichlet character modulo 12 of conductor 3 mapping 7 |–> 1, 5 |–> -1, Dirichlet character modulo 12 of conductor 12 mapping 7 |–> -1, 5 |–> -1] sage: G. gens() (Dirichlet character modulo 12 of conductor 4 mapping 7 |–> -1, 5 |–> 1, Dirichlet character modulo 12 of conductor 3 mapping 7 |–> 1, 5 |–> -1) sage: len(G) 4 Having created the group, we next create an element and compute with it. age: G = DirichletGroup(21) sage: chi = G. 1; c hi 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 corresponding to the factorization of the modulus. sage: chi. alois_orbit() [Dirichlet character modulo 21 of conductor 7 mapping 8 |–> 1, 10 |–> zeta6, 2. 13. Some More Advanced Mathematics 45 Sage Tutorial, Release 5. 3 Dirichlet character modulo 21 of conductor 7 mapping 8 |–> 1, 10 |–> -zeta6 + 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 char acters of modulus 3 over Cyclotomic Field of order degree 2, of Dirichlet characters of modulus 7 over Cyclotomic Field 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(x^2+1) G = DirichletGroup(20,K) G of Dirichlet characters of modulus 20 over Number Field in i with defining polynomial x^2 + 1 We next 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 choice of root of unity by the third argument to DirichletGroup below. age: x = polygen(QQ, ’x’) sage: K = NumberField(x^4 + 1, ’a’); a = K. 0 sage: b = K. gen(); a == b True sage: K Number Field in a with defining polynomial x^4 + 1 sage: G = DirichletGroup(5, K, a); G Group of Dirichlet characters of modulus 5 over Number Field in a with defining polynomial x^4 + 1 sage: chi = G. 0; chi Dirichlet character modulo 5 of conductor 5 mapping 2 |–> a^2 sage: [(chi^i)(2) for i in range(4)] [1, a^2, -1, -a^2] Here NumberField(x^4 + 1, ’a’) tells Sage to use the symbol â€Å"a† in printing what K is (a Number Field in a with de? ning polynomial x4 + 1). The name â€Å"a† is undeclared at this point. Once a = K. 0 (or equivalently a = K. gen()) is evaluated, the symbol â€Å"a† represents a root of the generating polynomial x4 + 1. 46 Chapter 2. A Guided Tour Sage Tutorial, Release 5. 3 2. 13. 4 Modular Forms Sage can do some computations related to modular forms, including dimensions, computing spaces of modular symbols, Hecke operators, and decompositions. There are several functions available for computing dimensions of spaces of modular forms. For example, sage: dimension_cusp_forms(Gamma0(11),2) 1 sage: dimension_cusp_forms(Gamma0(1),12) 1 sage: dimension_cusp_forms(Gamma1(389),2) 6112 Next we illustrate computation of Hecke operators on a space of modular symbols of level 1 and weight 12. sage: M = ModularSymbols(1,12) sage: M. basis() ([X^8*Y^2,(0,0)], [X^9*Y,(0,0)], [X^10,(0,0)]) sage: t2 = M. T(2) sage: t2 Hecke operator T_2 on Modular Symbols space of dimension 3 for Gamma_0(1) of weight 12 with sign 0 over Rational Field sage: t2. matrix() [ -24 0 0] [ 0 -24 0] [4860 0 2049] sage: f = t2. charpoly(’x’); f x^3 – 2001*x^2 – 97776*x – 1180224 sage: factor(f) (x – 2049) * (x + 24)^2 sage: M. T(11). charpoly(’x’). factor() (x – 285311670612) * (x – 534612)^2 We 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 Rational Field sage: ModularSymbols(Gamma1(11),2) Modular Symbols space of dimension 11 for Gamma_1(11) of weight 2 with sign 0 and over Rational Field Let’s compute some characteristic polynomials and q-expansions. sage: M = ModularSymbols(Gamma1(11),2) sage: M. T(2). charpoly(’x’) x^11 – 8*x^10 + 20*x^9 + 10*x^8 – 145*x^7 + 229*x^6 + 58*x^5 – 360*x^4 + 70*x^3 – 515*x^2 + 1804*x – 1452 sage: M. T(2). charpoly(’x’). actor() (x – 3) * (x + 2)^2 * (x^4 – 7*x^3 + 19*x^2 – 23*x + 11) * (x^4 – 2*x^3 + 4*x^2 + 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*q^2 – q^3 + 2*q^4 + q^5 + 2*q^6 – 2*q^7 – 2*q^9 + O(q^10) ] 2. 13. Some More A dvanced Mathematics 47 Sage Tutorial, Release 5. 3 We can even compute spaces of modular symbols with character. sage: G = DirichletGroup(13) sage: e = G. 0^2 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_submodule(); 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)*q^2 + (2*zeta6 – 2)*q^3 + zeta6*q^4 + (-2*zeta6 + 1)*q^5 + (-2*zeta6 + 4)*q^6 + (2*zeta6 – 1)*q^8 – zeta6*q^9 + O(q^10) ] Here is another 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 Modular 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 denote the usual 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 command. This starts a customized version of the IPython shell, and imports many functions and classes, so they are ready to use from the command prompt. Further customization is possible by editing the $SAGE_ROOT/ipythonrc ? le. Upon starting Sage, you get output 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 (CPU time 0m0. 00s, Wall time 0m0. 89s) The wall time is the time that elapsed on the clock hanging from your wall. This is relevant, since CPU time 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 f rom $HOME/. sage/tmp. ) 3. 1 Your Sage Session The session is the sequence of input and output from when you start Sage until you quit. Sage logs all Sage input, via IPython. In fact, if you’re using the interactive shell (not the notebook interface), then at any point you may type %history (or %hist) to get a listing of all input lines typed so far. You can type ? at the Sage prompt to ? nd out more about IPython, e. g. â€Å"IPython offers numbered prompts with input and output caching. All input is saved and can be retrieved as variables (besides the usual arrow key recall). The following GLOBAL variables always exist (so don’t overwrite them! )†: _: previous 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 = 2^2 * 5^2 sage: kronecker_symbol(3,5) 51 Sage Tutorial, Release 5. 3 _2 = -1 sage: %hist #This only works from the interacti ve shell, not the notebook. : factor(100) 2: kronecker_symbol(3,5) 3: %hist sage: _oh _4 = {1: 2^2 * 5^2, 2: -1} sage: _i1 _5 = ’factor(ZZ(100)) ’ sage: eval(_i1) _6 = 2^2 * 5^2 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 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 Macro ‘em‘ created. To execute, type its name (without quotes). sage: E Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Field sage: E = 5 sage: M = None sage: em Executing Macro sage: E Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 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 listing of the current directory. The PATH has the Sage bin directory at the front, so if you run gp, gap, singular, maxima, etc. you get the versions included with Sage. sage: ! gp Reading 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 saving 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 future session (by simply reloading the log ? le). [email  protected]:~$ 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 Mode : backup Output logging : False Timestamping : False State : active sage: E = EllipticCurve([1,2,3,4,5]). minimal_model() sage: F = QQ^3 sage: x,y = QQ[’x,y’]. gens() sage: G = E. gens() sage: Exiting SAGE (CPU time 0m0. 61s, Wall time 0m50. 39s). [email  protected]:~$ sage ———————————————————————| SAGE Version 3. 0. 2, Release Date: 2008-05-24 | | Type notebook() for the GUI, and license() for information. | ———————————————————————sage: load â€Å"setup† Loading log file one line at a time Finished replaying log file sage: E Elliptic Curve defined by y^2 + x*y = x^3 – x^2 + 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 â€Å"settings†, then â€Å"history †, then â€Å"set unlimited†. When you are ready to save your session, select â€Å"edit† then â€Å"save history as † and type in a name to save the text of your session to your computer. After saving this ? le, you could 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 Suppose 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 de fault the Sage parser strips any leading >>> or sage: prompt before passing it to Python. For example, sage: 2^10 1024 sage: sage: sage: 2^10 1024 sage: >>> 2^10 1024 3. 4 Timing Commands If you place the %time command at the beginning 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 exponentiation operation in several ways. The timings below will probably be much different on your computer, or even between different versions of Sage. First, native Python: sage: %time a = int(1938)^int(99484) CPU times: user 0. 66 s, sys: 0. 00 s, total: 0. 66 s Wall time: 0. 66 This means that 0. 66 seconds total were taken, and the â€Å"Wall time†, i. e. , the amount of time that elapsed on your wall clock, is also 0. 66 seconds. If your computer is heavily loaded 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 = 1938^99484 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 = 1938^99484 c = pari(1938)^pari(99484) 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 i n CPU seconds The walltime command behaves just like the cputime command, except that it measures wall time. We can also compute the above 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 difference between the wall time and the CPU time then this may indicate a performance issue worth looking into. sage: time 1938^99484; CPU times: user 0. 01 s, sys: 0. 00 s, total: Wall time: 0. 01 sage: gp(0) 0 sage: time g = gp(’1938^99484’) CPU times: user 0. 00 s, sys: 0. 00 s, total: Wall time: 0. 04 sage: maxima(0) 0 sage: time g = maxima(’1938^99484’) CPU times: user 0. 00 s, sys: 0. 00 s, total: Wall time: 0. 0 sage: kash(0) 0 sage: time g = kash(’1938^99484’) CPU times: user 0. 00 s, sys: 0. 00 s, total: Wall time: 0. 04 sage: mathematica(0) 0 sage: time g = mathematica(’1938^99484’) CPU times: user 0. 00 s, sys: 0. 00 s, total: Wall time: 0. 03 sage: maple(0) 0 sage: time g = maple(’1938^99484’) CPU times: user 0. 00 s, sys: 0. 00 s, total: Wall time: 0. 11 sage: gap(0) 0 sage: time g = gap. eval(’1938^99484;;’) 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 machine 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 IPython’s commands and features. You can read the full IPython documentation. Meanwhile, here are some fun tricks – these are called â€Å"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 doesn’t work well with S age’s automatic testing facility. If you type this in yourself, it should work as written. This is of course most useful 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: jobs[0]. result # the actual answer, not tested 40 Note that jobs run in the background don’t 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 commands which don’t require the preparser. †¢ You can use %edit (or %ed or ed) to open an editor, if you want to type in some complex code. Before 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 magic commands is available online. 3. 6 Errors and Exceptions When something goes wrong, you will usually see a Python â€Å"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 â€Å"†, line 1 ZZ(3)_2 ^ SyntaxError: invalid syntax 6 Chapter 3. The Interactive Shell Sage Tutorial, Release 5. 3 sage: EllipticCurve([0,infinity]) ———————————————— Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€œTraceback (most recent call last): TypeError: Unable to coerce Infinity () to Rational The interactive debugger is sometimes useful for understanding what went wrong. You can toggle it on 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 stack. 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> ? Documented commands (type help ): ======================================== EOF break commands debug h a bt condition disable help alias c cont down ignore args cl continue enable j b clear d exit jump 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) t o 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 = QQ^3 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 indicated. sage: V. i[tab key] V. is_ambient V. is_dense V. is_full V. is_sparse If you wonder what a particular function does, e. g. , the coordinates function, type V. coordinates? for help or V. coordinates for the source code, as explained 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 = QQ^3 sage: V. coordinates? Type: instancemethod Base Class: String Form: Namespace: Interactive File: /home/was/s/local/lib/python2. /site-packages/sage/modules/f ree_module. py Definition: V. coordinates(self, v) Docstring: Write v in terms 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 t he type of the object, the ? le in which it is de? ned, and a useful description of the function with examples that you can paste into your current session. Almost 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 spirit of the open source nature of Sage is that if f is a Python function, then typing f displays the source code that de? nes f. For example, sage: V = QQ^3 sage: V. coordinates Type: instancemethod Source: def coordinates(self, v): â€Å"†Ã¢â‚¬  Write $v$ in terms of the basis for self. â€Å"†Ã¢â‚¬  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 = QQ^3 sage: V. coordinate_vector def coordinate_vector(self, v): return self. ambient_vector_space()(v) The coordinate_vector function coerces its input into the ambient space, which has the effect of computing the vector of coef? cients of v in terms of V . The space V is already ambient since it’s just Q3 . There is also a coordinate_vector function for subspaces, and it’s different. We create a subspace and see: sage: V = QQ^3; W = V. span_of_basis([V. 0, V. 1]) sage: W. coordinate_vector def coordinate_vector(self, v): â€Å"†Ã¢â‚¬  â€Å"†Ã¢â‚¬  # 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 given 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 clutter up your session, unlike the output of function_name? som etimes does. It’s particularly helpful 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 doesn’t 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; it’s 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-r–r– 1 was was 153500 2006-01-28 19:23 E. sobj ~/tmp$ sage [ ] sage: E = load(’E’) sage: v = E. anlist(100000) # instant! (In Pytho n, 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 â€Å"invalid†. In GAP, though many objects print in a form from which they can be reconstructed, many don’t, so reconstructing from their print representation 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 longer 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’) 2 Saved 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 isn’t 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 can’t 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 you’re 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 you’ve 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 you’ve already de? ned in your current session; instead, the two 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 [ email  protected]:~/tmp$ ls -l misc. sobj -rw-r–r– 1 was was 2979 2006-01-28 19:47 misc. sobj Finally 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 again 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 y^2 + y = x^3 – x^2 – 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 server’s state ? les are stored in $HOME/. sage/sage\_notebook. Other options include: sage: notebook(â€Å"directory†) which starts a new notebook server using ? les in the given dir ectory, 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 â€Å"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 ev erything 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 Notebook: ———————| | | | | 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 â€Å"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 convenient program launcher, similar to the Linux bash shell. 2. gap. interact(): This is a convenient way to interact with a running GAP instance that may be â€Å"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 two very distinct interfaces that you can use in Sage: †¢ gp – the â€Å"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 behind 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 won’t be freed). Then the value of that variable is displayed. In the 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 you’re 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, won’t 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 silently and automatically double the stack size and retry that input line. Thus your computation won’t crash if you didn’t correctly anticipate the amount of memory that would be needed. This is a nice trick the usual GP interpreter doesn’t seem to provide. Regarding the PARI C library interface, it immediately 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 impose 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 sophisticated 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) Every PARI object is of type py_pari. gen. The PARI type of the underlying object 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 th at 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: f[:5] [1, -1, 0, 4, 3] 4. 2 GAP Sage comes with GAP 4. 4. 10 for computational discrete mathematics, especially group theory. Here’s an example of GAP’s 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 sage: 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-GPL’d 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 plane curve, and factorizations, 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 : ordering dp // : names x y // block 2 : ordering C sage: f = singular(’9*y^8 – 9*x^2*y^7 – 18*x^3*y^6 – 18*x^5*y^6 + 9*x^6*y^4 + 18*x^7*y^5 + 36*x^8*y^4 + 9*x^10*y^4 – 18*x^11*y^2 – 9*x^12*y^3 – 18*x^13*y^2 + 9*x^16’) Now that we have de? ned f , we print it and factor. sage: f 9*x^16-18*x^13*y^2-9*x^12*y^3+9*x^10*y^4-18*x^11*y^2+36*x^8*y^4+18*x^7*y^5-18*x^5*y^6+9*x^6*y^4-18*x^ sage: f. parent() Singular sage: F = f. factorize(); F [1]: _[1]=9 _[2]=x^6-2*x^3*y^2-x^2*y^3+y^4 _[3]=-x^5+y^2 [2]: 1,1,2 sage: F[1][2] x^6-2*x^3*y^2-x^2*y^3+y^4 As 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 = QQ[’x, y’]. gens() f = 9*y^8 – 9*x^2*y^7 – 18*x^3*y^6 – 18*x^5*y^6 + 9*x^6*y^4 + 18*x^7*y^5 + 36*x^8*y^4 + 9*x^10*y^4 – 18*x^11*y^2 – 9*x^12*y^3 – 18*x^13*y^2 + 9*x^16 factor(f) (-x^5 + y^2)^2 * (x^6 – 2*x^3*y^2 – x^2*y^3 + y^4) 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