An Introduction to Sage
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Title 
An Introduction to Sage

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CC Attribution 2.0 Belgium:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Release Date 
2014

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English

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Abstract 
Sage is an open source mathematical software system that is built on many components, such as Python, sympy, numpy, gap and scipy, and also brings along the power of the Python programming language. This talk will introduce cover some capabilities of Sage and enable participants to use Sage for their computation needs. Sage is an open source mathematical software system that is built on many components, such as Python, sympy, numpy, gap and scipy, and also brings along the power of the Python programming language. It greatly augments the Python programming language with a rich set of libraries that enable number theoretic computations, differential and integral calculus, combinatorics, polynomials, matrix operations, cryptographic functions, 2D/3D plotting, etc. to be performed from Sage. Sage also uses iPython, a wonderful interactive shell for Python with features such as saving session history, autocomplete etc. Sage also has a notebook interface(with an authentication system) which enables users to collaborate with each other on Sage projects. It would be impossible to cover everything about Sage. I will try to cover some applications of Sage which will be useful to a majority of people interested in using Python for mathematical computations. Below is a broad outline of the various topics I hope to cover. 1. Introduction: Modes, usage, customizing. 2. Arithmetic and builtin functions. 3. Algebra related functions. 4. Graph plotting. 5. Number theory. 6. Matrices. 7. Generating LaTeX representation of Sage code. 8. Calling Sage functions from LaTeX. 9. Writing Sage scripts. 10. Conclusion and further reading

00:00
Mathematics
Word
Exterior algebra
Computer animation
Software
Open source
Electronic mailing list
Physical system
Library (computing)
00:31
Programming language
Dialect
State of matter
Student's ttest
Mereology
Computer programming
Shareware
Radical (chemistry)
Sign (mathematics)
Mathematics
Computer animation
Personal digital assistant
Internetworking
Universe (mathematics)
Cuboid
Point cloud
Set theory
Social class
02:36
Mathematics
Computer animation
Objectoriented programming
State of matter
Student's ttest
Computer
Information security
Product (business)
03:05
Focus (optics)
Mathematics
Computer animation
Universe (mathematics)
Series (mathematics)
Quicksort
Metropolitan area network
04:06
Programming language
Computer file
State of matter
Interface (computing)
Limit (category theory)
Cartesian coordinate system
Mereology
Complete metric space
Computer animation
Website
Utility software
Contrast (vision)
Library (computing)
Physical system
05:11
Computer animation
Right angle
05:42
Graph (mathematics)
Right angle
Mereology
06:07
Functional programming
Mathematics
Exponential function
Computer animation
Different (Kate Ryan album)
State of matter
Sound effect
Declarative programming
Physical system
06:57
Logical constant
Group action
Multiplication sign
Electronic mailing list
Bit
Insertion loss
Function (mathematics)
Mereology
Numerical analysis
Mathematics
Latent heat
Computer animation
Utility software
Halbordnung
God
08:34
State of matter
Equals sign
Computer programming
Power (physics)
2 (number)
Frequency
Latent heat
Computer animation
Personal digital assistant
Number theory
Right angle
Endliche Modelltheorie
Resultant
Spacetime
10:01
Building
Divisor
Fluid mechanics
Block (periodic table)
State of matter
Planning
Cartesian coordinate system
Computer animation
Hypermedia
Number theory
Right angle
Selectivity (electronic)
Lie group
11:26
Mathematics
Computer animation
State of matter
Multiplication sign
Electronic program guide
Bit
Metropolitan area network
12:12
Performance appraisal
Functional programming
Message passing
Dependent and independent variables
Graph (mathematics)
Computer animation
State of matter
Graph (mathematics)
Universe (mathematics)
Renewal theory
Graph coloring
Set theory
13:03
Functional programming
Graph (mathematics)
Computer animation
Right angle
Office suite
13:47
Multiplication
Basis (linear algebra)
Computer animation
Operator (mathematics)
Multiplication sign
Matrix (mathematics)
Library (computing)
14:38
Category of being
Functional programming
State of matter
Matrix (mathematics)
Right angle
Utility software
Determinant
Symmetric matrix
15:13
Slide rule
Functional programming
Presentation of a group
Insertion loss
Instance (computer science)
Mereology
Frequency
Mathematics
Word
Radius
Computer animation
Objectoriented programming
Energy level
Website
Representation (politics)
Endliche Modelltheorie
Mathematician
Resultant
Physical system
16:41
Functional programming
Block (periodic table)
State of matter
File format
Decision theory
Graph (mathematics)
Electronic mailing list
Maxima and minima
Bit
Lattice (order)
Estimator
Computer animation
Personal digital assistant
Mathematical singularity
output
Quicksort
Set theory
Physical system
Library (computing)
18:24
Point (geometry)
Module (mathematics)
Latent heat
Service (economics)
Computer animation
Personal digital assistant
State of matter
View (database)
Bit
Parameter (computer programming)
Cartesian coordinate system
Library (computing)
19:41
Focus (optics)
Computer animation
20:17
Computer animation
21:46
Computer animation
Video game
Student's ttest
Graph coloring
Theory
22:31
Area
Functional programming
Group action
Open source
Sequel
State of matter
Software developer
Multiplication sign
Optimization problem
Decision theory
Water vapor
Maxima and minima
Open set
Mereology
Data mining
Word
Computer animation
Term (mathematics)
Profil (magazine)
Video game
output
Mathematical optimization
Form (programming)
Library (computing)
25:35
Radical (chemistry)
Theory of relativity
Computer animation
State of matter
Software developer
Electronic mailing list
26:11
Laptop
Collaborationism
Functional programming
Observational study
State of matter
Interface (computing)
Mathematical analysis
Axiom
Convolution
Product (business)
Mathematics
Computer animation
Software
Physicist
Graph (mathematics)
Point cloud
Right angle
Extension (kinesiology)
Set theory
Library (computing)
29:07
Slide rule
State of matter
Multiplication sign
Structural load
1 (number)
Limit (category theory)
Information technology consulting
Type theory
Mathematics
Latent heat
Causality
Different (Kate Ryan album)
Video game
Quantum
Point cloud
Right angle
Calculus
Nichtlineares Gleichungssystem
Office suite
Library (computing)
Social class
00:01
other than the 1 so it will take a list the thing is gonna stay awake
00:08
so at 11 the system sees us is actually an opensource mathematics computer software package is named to be an alternative to the big
00:18
and stuff around the Matlab made
00:21
our cities actually nothing but a collection of 5 from libraries it's the bonafide informing and was added to it so that the word attracted in this not so it
00:32
starts acting out of the city is really really nice to use the primarily because it has the part of the Python programming language and provides you with an IPython that for those of you have a that is and answer phone 5 unsettling autocompletion setting is the snippets into and copy this and so on so that's realize are using it as I'm actually values you student back in the university and I was teaching assistant with the program cost as a far 2nd set up and I'm using it extensively in my mathematics was on the past too sensitive actually it didn't work online are and it also what's this out there to you can use this 1 of them is regulated by front you can dial terminal there's something called the inaudible toward its use your nice that interface access to state so that actually let's you collaborate with other users and a set worksheets out this is the idea like a school of the University where you can now collaborating with other classes of yours was you in this that if you do extensive mathematics where you can actually use it to collaborate with other people in your team the and as such as something called now condensates math cloud coming up with his data they really so a few so was out there on the internet for anybody use are you secular is called it's a flower boxes that not all in his log no sign of pharmacology and you can use it is exactly same as using an old books but it went a lot of new features to states from the could you have a without few nm
02:29
so this might mean I am really show you a demo every it's sad imagists I work this is the end of the day so if I
02:38
don't want you understand that this is a student of U. in India I'm interested in computer security in Python that started getting into the graphic arts and lastly the same
02:48
production labs and I also used in mathematics courses are also they promise you computersecurity competition South almost the the sound using states the my objective today is to convince you that it is really cool and use use it in all of mathematics courses it is from my experience when I was in school
03:07
and university the focus of much rise was
03:10
are usually just on finding the answer in the year and this problem yeah series of steps to follow and you get the right answer but you don't get the answer and I usually don't get any money because I don't get out the usually with most important thing was I when I these USC insightful in mathematics before and after this is more than just solving the problem another thing that I ions that it's how you figure it out this is the way to get to the answer I followed the man I started using sees the lots of features that have you seen more than focus on the white hot rather than finding the X 5 uh sort of indolence that mathematics is just about finding out X it's about figuring out what and without the fault to was in cities I find these you to focus more on the problem and think for on it and it uses to completed so this is just an overview of what I hope the colonies that was this
04:09
how quickly look at all the of states and inflationary given the methodology of great look at how you can use this uses a small contrast with Python finally get up I've gotten like 5 6 applications of states and the limit what I want it and how you can contributes to I the the this is the utilizes
04:35
that I that it's a collection of almost 95 or libraries and price with the i tive I'm afraid we can also use an old took interface you can this from old books in in in the and get out you can be part of the I 5 and said if something fancier considered completion is the and you also have the Python programming language system can use every other Python library that's actually of and this is not a poem in adopted file so this not the and in selling is actually ECU 7 the labeled binaries from this this website and there's also be here for a one to
05:12
those willing to get everything like me is is the EPA and in fact practicing efforts to their benefits are actually on the right now once a company that you see it in those 2 and in the other district depends on all so are you
05:30
can also use like the it's it's an odd assisted in red and you can is use it in the if you try something out displayed by thing but as something more than what the experience that you can actually profile them and you can even
05:42
combined this this size statically into C. and even policy from systematically would you help us I thought then facts actually made by this is known as right now no surprise that it must fostered and you get the combined those 2 together so you can profile you code see we part of it is actually taking a lot of pain and maybe
06:02
to was to right of mood to see your even to fit the combined using 5 on the and the
06:07
bigger the advantages that I find this is facilitates expressing computationintensive applications right and
06:15
so fortunately I I use of the I have all the answers to all the questions in this light out so this before I get into this I want to do that all the answers in this lake that actually created using states I just scholar system and from from all of this is is that it has been let X I just policies command from it so you don't want the effect is the onset and insisted that increases the so I'll actually docking of states declarant FIL so a few differences with the I find felt up the single got that's the mathematical exponent function with a double and that we can be of and a single slacks actually used
06:58
to the loss of action and that was that the the label in newtons everything else is most is a modified on them and you also have to in the mathematical functions and constants and you can actually get them at any arbitrary precision you like I can either specify the British and indeed it so you can actually specify the precision bits that for a book that I yeah you have all constantly scholarly mathematics induced by the utility of D N is actually 1 that does the numerical approximation is desysopped name for the big numerical approximation of your that has signed gasses better than it you know to question really useful and mostly if that the persistence reactive right so that so it I
07:43
think this is in the main part that you can only use and this is the basic idea that's value school you see that most of it is that the day you don't have to spend time on doing this on paper I spent most of my school benefactor of the police and the fire for 5 the time to 1 another similar like to do and minus 1 minus 2 it's a time and other things so here it is likely if I place it and that is the upon intuitive fact and gives you all the factors and you downside so I them the whole in the desert as list this is just what different the studio is displayed here data again so that was the I you can also sort of orderly relations with specific value laden you the presence of God at in the so accurate that that's a list so you go right of them do any fancy
08:35
modification you want the on the userdefined out school funds in in specific cases like this cost equal sign you won't find a specific values that those are equal sort of send it into it but you can also use fine and excluding the it NEC goddesses very influential in the results returned from
08:54
this is question inside the into a comedian last later where there also view questions as an idea but this would so yes them with it is something that I started using state of the university relevant from within about this I deleted that I had no idea what it does right now back into master space number the again use it's father number these frequencies makes it must go find the use of they i've to sit and write a program unless acted so it can determine if a number is prime of I gave easily compute the more the film in the model is using more unintelligible and what that actually pretty fast this and this was this out so we can't this lake a legal right to go up to lake of power nearly 10 of 10 start of 60 days to determine whether more a fourdigit number I was at the like 2 seconds so it's really 85 a lake wide by the court IronPython really so with this is highly
10:03
optimized and so you have to work on that you get is the that the concluded and plans and anybody that means you can check if a number is apparently really fast and next friendliest but I'm finding out the factor of 1 of of these years and so on that I still don't know how do some of these in as you have seen last and so used to say that is a lie on it to make fun that so you see here that it relates to the lot of building blocks and you can use to further their whatever you working on right now that is cool with lots of interest and I'm doing what is your need to know how to the you need to really do we should have ever so as long as you know how to do it is use this and get don't what's the most important that and you see that a
10:48
small city in the arborescent administering the use of media started to off pain not consist on this that I really say already new states I decided using it may thinking of different than ISIS plywood to on with it again of different and I find that this use the funds into it gets to the analogous to the answer selection next muscle easier especially during the fluid mechanics or something like that that you really need to use all of these on any of there's a lot of applications for benefits and kind of not familiar with that but it makes it so much more easier to you so you don't need to spend
11:28
time finding out that this this fear because they get to the late at the end ritalin out so in fact you also have supported Fatah differently then became a solid defensive positions and add them because I don't know how and when a man your in awarded it is pretty easy to get started in they actually have a guide for those who already know mathematics University of Southern states and this community included 1 so the
12:04
but I so far gasses standing there are lots of people do it I play around with this quite a bit that is a lot of fun he actually plot duty and 3 D
12:14
graph and what is the origin of the users and we have an on messages that the renewal of this is going to it so the but maybe at the end of so this plot is actually uploaded using the deck of the state's plugging protect ideas say plot this function the so that the function that it is is a good set of 0 0 really useful so you can actually do a lot of things to this you can adjust size change the color you can even plot my the responses in the graph later than
12:48
here is the plot of land lots together you can fit the color for them you can set the skin considering evaluation in it so the alkali offloading is something I used to go after the backtoschool anywhere in the university so you have this
13:05
mission was easy adherence and and that a bad right so this can never get the graph to be really good but you have to take seriously if it makes you extremely useful you gave out another function that you can functions as you want so long as you can identify themselves and that offices located in it I
13:26
actually have at the the plot it looks intestinal gas the celestial actually not in the in this in 2 we do in the so in the the US of it you can actually interact with that rotated around them see from any and you want as accidentally using here minus the Solomonic allow
13:48
manipulation library and resource that but they do outside of the united as a lot of things that you can play along with the of I see the intuitive idea that's
14:02
mostly what got out cellular rise some of
14:08
those that have been using these for quite some time now and I am last semester courses most in all of it is that you now and learning you know that I use it I asked you know my basis I ask you a little in to the matrix multiplication it to a long buried is and again the debugging and local it was going on and I thought this is tested automatically is of that if you so this is actually to read this as the interest of sorting when you can do all the operations that you 1 the it added
14:41
subtracted on the right in here you 1 X 1 and it was a half the other functions that define the determinant of a state and again tech properties of a metric that says this is the the matrix is singular is a symmetric matrix is skewsymmetric union but it an Israeli to find out a lot of support it because I have masses of recent
15:02
things I finally use iPhone also these they using the other company that distance being and utilities there is good know this is so you see this in every
15:15
Member Emeritus assessment very many this I don't think you can get any simpler of this of the similarities in if the other mathematics of the 2 so if you always use it in that we should not have it that the 1st thing foreigners and the new model that anything else that all a gift 1 so
15:39
that it is something that is not people 1st mathematicians who like system part and in fact you can actually generate the letter representation of any object that you want so this year period to let the cough that relevant and you that only get the level the percentage of that and say step is so that they used to create most of this pessimism along the beam of illicit got initiates come and I want and even for loss functions that I would like they are all the results in the earlier slides that actually is those under the age of command and the gossip modern exist about the press and this is later that I make up so you can a splitsecond losses the example that i from the document instance if that wasn't the word on the website so is clear these lakes any radius some difficulties intersecting canonistic my slides we also can embed scored in the middle of the pack presentation and you can choose if you want to display it makes the AUC is block and within that the functions and a few really was on
16:42
the list can be declared a a nice mathematical formatting say states that upon that and it's really nice and the let document you know on this they just this this silent and you can access those if was at a meeting in the block in here in the States for and in the letter government so that makes it the seriously standard states programming with that on a lot of so I into a lot of other medicines that the use that for it by sitting there and how you can also use it to fit solid assessment indirectly added in the nation western region the question the of that sort Italian estimates so triangular then they can let it finish that of the status after this is a set of about below our are you do this since it's out this a lot of intricacies you get the stadium does lay out of our it actually interface with all the mathematical system the singular maxima in fact could you functions depending on the kind of input that it gets a taxi to associate slavery to actually use underlying so I say 1st modern would might probably GP will enable us to be important to is something that is a bit more optimal for that size its assistance on decision making for you those and place
18:04
to find the optimal way of finding the answer and you can of course all related and interact with each of these libraries statically so AUC on that in is the yes yes they also all right right hand and
18:24
this where yes it is actually there are it actually gets fight to those who through a
18:29
little bit work so you have all the other modules AntiVenom but I could go with support our CADCAE years and the years so I use it mostly for the public the mostly Odyssey actually our most of them I don't know I'm not going to use the could dress that's most of them I find that I can implement the parameters myself but in most cases I have to remind myself because of a specific body with Salinger's where those libraries is that it's by the book the thing is by writing spike of GOBP in large social and of course you can add your on to the library's to so you can choose about on if it exists at service and so you have to derive something on sewing it I now have a course in of this and that and finding it really was would you and it's because I've never learned in other reform and finding that focusing on states that's me I focus more our important and adults this still a computational makes it easy for Of course this advanced applications almost everything that I spoke about right now besides point of view to produce forward and you can get to it was
19:45
the care of that and
19:54
to this is the 1st is that it means that the columns of the the focus of that event and get a
20:20
the good for that good so
20:28
this and
20:32
and I mean
20:38
and the spirit of the to
21:47
but I was so this was
21:52
the theory at the end so and the so you can actually you
22:11
in life with it the new ones that that that you insulin and allow the last thing in college students is the colors later to get the nice thing with things have of this yes was worth and using others
22:33
that the other thing I'd like to be the question that so who is the person to water as a way life you have lot of the OK so the question was our policy is compared to other mathematical of with and Weiss and on asphalt them so I haven't used any of the permeated to start that again I will use any of the others this the 1st thing I found was this a friend of mine said now uses of development in the state of as the countries and their father this pipeline monitoring so I asked why is not popular this year that I have no idea how because I think 1 of the biggest reasons is no we know the life of the life that using it is because somebody is still there were states that I will know what is my mother my professors don't know what the everyday and they ask us to elect a matter of this is a function in matlab if you you get the look at life is something as opensource so maximizing the expensive and the religious hands on Matlab and is the reason I members the same have nobody uses the next thing like is that of so hold that it is in terms of optimization problems school you want like a are like userdefined is that the proposed optimization the homeowners and so on and I had estimates and that there are so this is actually say that he's finally a part time so that can get through the slope so you can ask profile is it's good and see that the problem exactly is again a move that would to see and make a really after even the but and you can make a modular phonetically college out so that's the best optimization that you can do they could not see where otherwise most of the functions that only the answers are pretty optimal I in fact was somewhat constants accuses minded libraries depending on the input means they fit in with a really smart ID brought to the and it's really lies in mind I want EPA to something else like singular maximum I don't remember a function with this definitely from that make the decision based on the input so our and you can also combine it into using CI so that you get the sequel or directly that makes it even more fast Denis so this is a 3 D plot that since it in this form which have the same area I sit in life I think that if you put thought NetSquared with the
25:26
words what groups of are you aware of these seats user groups of the conferences help New World seat open
25:35
so terminal comes from since all I don't know if I think there was conference like few years ago that was even before I started using state quiet in this book among conference in Europe and the so the need regularly visited a active I channel animating list uh as I mentioned suspect that they have a lot of relation is that most interested dĂ©veloppement the thing in the development of the use of Russia but their reliance is on a moving ceremony to now that I have and I have
26:14
the x for the community much so that actually so but ask him so but this
26:21
is called the the so unlike like this is about the book and I was elected are wondering if I if it is and then as to the mind and there's a downside of using them to my performance is used on maybe and is used up so I think the order with the axiom of analysis and with the Norwood can also get that but I you can execute a workbook of cheap that's how about the normal while because our I have used or is because setting up a award book so that the collaborative a people is that actually physicists seeing the use of when use more book as CDC but setting up being a scientist is undocumented and that's that's not of the convolutional was and is actually make easier set of an old so but I think you probably never using season at low because that's going to be the future states all the notebook more and those already that online he can just use it collaborated with any other user so I want to commend cloud over the 1 the the to the of love the all that that on and make all of the the the library can assume all users will follow the same steps of the question was how is this is covered with the other mathematical software like matlab made are I like this to the extent of it out so I don't have access to any of those so but from more than that and then there production making the interface to the other libraries is not the biggest through this last right now but I think it was to with the subclass and maybe even the year before the Spanish I don't think anybody worked on it below so if there's somebody was inherited idling they're actually use American those various but I'm I'm not familiar with them as such so I don't know how good it is yeah a lot and other things could choose so was please the mobile interface to but the interfaces OK with the ritual of the talk show it up yes I would be interested to see the look that this think the the I think you did detecting final about the cost the know what my emaciated again a study design the donor typing normal function it gets out
29:09
up and the twisted soda the back and bring out with so that it can connected to this over because then you can use type in the URL you get pretty items when the back question yes have In is disaster I didn't the yeah I can't do it I don't really have a question on your comment on their place of Matlab love and Mathematica at don't want to get in then it up so I can't say anything specific but there are ways to get them for free OK OK if you I mean I do and I decided to learn the worst is of using it as far as the forward so thai stuck yes all yet symbolic feet sitting things like consulting also flying equations are writing it and features ferrets symbolic uh and work like consulting equations also the falling them all of the fact then is that there slide and then solving quantum only this insight few so I I don't know how you would ah various earlier this on 1 of the reasons and different and it myself but I already did was it extends to on how complex it can go officers in blue ones that at his wealth in what I've seen in my curriculum developed works by but for the actor's things that you see in real life and how would it is that that I have not done it before but I'm pretty sure that it was at but similar to 1 another so and I could could in any other questions time you know this of our ideas through the right to left to 2 hours so I decided not linger how you get the contribute states of 1 of the best things that you can do this by today's there's somebody that that's not but also at the at the top with that what the out that it will I know Python because it might be you our spending actually extended with a lot of other libraries that makes it a lot easier to use a lot of fun but more importantly in the US and it's the beginning of this debate relational so if you're interested in helping with that if the limit then you help us out and that only the more important thing is there's a lot of with mathematics that I'm not completely supported instead of cause if you in mathematics and you know seriously when I actually this so it to you so if you're really interested in any of those I you can go only gone by community about and how about and that that's what the awardwinning and doing the best that was by editing right now and of course I think actually few these courses in mathematics you know somebody would courses in mathematics and the reason we use this method load UCL this calculus class actually uses is that cloud right now so you can actually get a lot more people use it and spread it out thank you very much for a but