[HN Gopher] SageMath - Open-Source Mathematical Software System
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SageMath - Open-Source Mathematical Software System
Author : gnramires
Score : 210 points
Date : 2020-06-13 17:48 UTC (5 hours ago)
(HTM) web link (www.sagemath.org)
(TXT) w3m dump (www.sagemath.org)
| 29athrowaway wrote:
| If you are interested in trying sagemath, read the PREP
| tutorials.
|
| https://doc.sagemath.org/html/en/prep/quickstart.html
|
| These contain have examples for linear algebra, calculus, diff
| equations, statistics, etc.
|
| I use sagemath with Jupyter lab and it works pretty well. You can
| evaluate an expression and ask sage to output the LaTeX code for
| it, so you can have everything nicely formatted.
| esrh wrote:
| How good is it for machine learning? I'm currently using julia
| which I also really enjoy.
| yza wrote:
| Sage is not something that you would want to use for ML per
| say. It can, however, help you with understanding of the
| underlaying math and algorithms. It has excellent support for
| symbolic math, statistics (distributions etc.) and just about
| everything else you are going to need to study ML. I recently
| switched from Mathematica and could not be happier.
| [deleted]
| vsskanth wrote:
| I really wish I started using Sage instead of maxima directly.
| The documentation for maxima is pretty difficult to understand
| for a noob just looking to solve some non linear equations
| shuringai wrote:
| why is the existence of sagemath have any news relevance on HN?
| fish45 wrote:
| I love sage and I used it for multivar calc this year but
| unfortunately it's not as good in some aspects (mainly symbolic
| integration) as Mathematica. One of my primary motivations for
| learning math is being able to contribute
| [deleted]
| amir734jj wrote:
| I used SageMath for my master's thesis in cryptography and group
| theory. It was awesome! I highly recommended it and its
| unfortunately very underrated.
| seamyb88 wrote:
| Using it extensively for my crypto PhD. Several well-known
| cryptographers contribute to it.
|
| It's an amazing bit of kit. But I'm not without criticisms. I
| feel it could do with the kind of fresh-start overhaul that
| really isn't practical for an open-source code base of this
| nature. E.g. move python 2.6 to python3. Also, you have
| excellent multi-precision support, but many of the algorithms
| from other modules don't support precision beyond machine
| lengths.
|
| But really really good. Love it.
| williamstein wrote:
| Sagemath already switched to python3 a while ago.
| nenadst wrote:
| fyi from the website :
|
| Since version 9.0 released in January 2020, SageMath is using
| Python 3.
| gnramires wrote:
| "It builds on top of many existing open-source packages: NumPy,
| SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more.
| Access their combined power through a common, Python-based
| language or directly via interfaces or wrappers."
| Yushi212 wrote:
| v.vhackservice @ gmail . com for any of your hack service. GET
| ACCESS TO YOUR SPOUSE DEVICE AND SPY ON THEM CONVO.
| grizzles wrote:
| Is there an easy way to embed a sage notebook viewer / editor
| inside a webpage without installing a sagecell server?
| williamstein wrote:
| You can upload it to cocalc.com, then share it publicly, then
| click the embed link to get a version that is suitable for
| embedding in an iframe...
| grizzles wrote:
| It might be a good strategic move to publish a React
| component to do this for the non iframe solution enthusiasts
| out there. It would be good to see people start using
| SageMath notebooks where they otherwise might be using Katex
| or Mathjax today. It could always have an "Open/Run on
| CoCalc" link as part of it.
| williamstein wrote:
| I probably should, since the underlying renderer mentioned
| above is actually implemented using React (it takes as
| input JSON describing a notebook and renders it, entirely
| on the frontend). Also, in case it isn't clear, these days
| "Sage notebook" just means "Jupyter notebook with the
| SageMath kernel"... since "the Sage notebook" (=the
| SageMath project's predecessory to Jupyter, but written in
| 2007) is basically deprecated now in favor of the official
| Jupyter notebook project.
| mathgeek wrote:
| Previous discussions for perusal:
|
| https://news.ycombinator.com/item?id=266040 (2008)
|
| https://news.ycombinator.com/item?id=17995031 (2018)
| dang wrote:
| See also:
|
| https://news.ycombinator.com/item?id=19682126 - "Should I
| Resign from My Full Professor Job to Work Fulltime on Cocalc?"
| - 2019
|
| https://news.ycombinator.com/item?id=19485166 - "Computational
| Mathematics with SageMath" - 2019
|
| https://news.ycombinator.com/item?id=11883987 - "The Origins of
| SageMath" - 2016
|
| https://news.ycombinator.com/item?id=11078220 - "Open source is
| now ready to compete with Mathematica for use in the classroom"
| - 2016
|
| https://news.ycombinator.com/item?id=10175563 - "The Simons
| Foundation and Open Source Software" - 2015
|
| https://news.ycombinator.com/item?id=10147401 - "React, Flux,
| RethinkDB and SageMathCloud - Summer 2015 Update" - 2015
|
| https://news.ycombinator.com/item?id=2088871 - "SageMath:
| Python-based Mathematics. Rock it." - 2011 - a little bit of
| editorializing there...
|
| https://news.ycombinator.com/item?id=983423 - "Conception,
| birth and developement of a Free math software (Sage)" -
| ditto...
|
| https://news.ycombinator.com/item?id=179416 - "Sage: Can There
| be a Viable Free Open Source Alternative to Magma, Maple,
| Mathematica, and Matlab?" - 2008
|
| Any others?
| noir_lord wrote:
| Saved my bacon about 5-6 years ago, the company we where going to
| depend on to do a whole bunch of complex calculations related to
| solar insolation discontinued their API but didn't tell anyone, I
| found out when I rang up to get a price.
|
| So suddenly I was in the situation of dealing with maths that was
| harder than anything I'd done at school years and years ago.
|
| In the end I transliterated the equations into sage, checked the
| results carefully and then wrote the PHP to do the same
| calculations using a large set of tests against the official
| stuff, stressful two weeks but sage was useful as hell.
| heavyset_go wrote:
| I highly suggest using this package if you're in school or
| otherwise learning higher level math. Being able to
| programmatically interact and manipulate abstractions over the
| mathematical concepts you're learning is an enriching experience,
| and it can help you check your answers to your homework. It's
| also a Python module so you can learn a skill that transfers well
| to other domains compared to, say, Mathematica.
| bollu wrote:
| I'm a huge fan of SAGE! I keep using it to discover new math. I
| generally play with the associate Sage module of any algebraic
| structure to get a real feel for what is going on. Some examples
| of:
|
| 1. Grobner basis: http://bollu.github.io/#computing-equivalent-
| gate-sets-using...
|
| 2. Commutators of subgroups: http://bollu.github.io/#5age-code-
| to-play-around-with-commut...
|
| 3. Graph/group theory:
| https://github.com/bollu/bollu.github.io/blob/2f88c28efc54fb...
| Alkhwarizmi wrote:
| I LOVE your blog man! Keep it up
| abdullahkhalids wrote:
| Completely off topic question. Can Grobner basis techniques be
| used to solve a set of quadratic inequalities?
| enriquto wrote:
| > Can Grobner basis techniques be used to solve a set of
| quadratic inequalities?
|
| One application of Grobner bases is to solve systems of
| polynomial equations [0], and characterize their solutions.
| In many circumstances it is not however the best method, for
| example if you are content with a numerical solution you can
| use other techniques.
|
| Notice that this concerns equations, not inequalities. After
| a cursory search, I cannot find any "big" reference for
| solving polynomial inequalities using Grobner bases. There is
| this [1], still, not sure how serious it is.
|
| [0] https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis#Solution
| s_o...
|
| [1] https://arxiv.org/abs/1603.01183
| thechao wrote:
| Not ... really? I usually compare the Grobner basis to
| generalized matrix decomposition in the sense of solving
| systems of linear equations. If you're solving systems of
| quadratic equations, you should look into interior barrier
| solving methods, which generalize the simplex method.
| generationP wrote:
| Grobner bases appear in the standard reference on real
| algebraic geometry ( https://perso.univ-rennes1.fr/marie-
| francoise.roy/bpr-ed2-po... ), so the answer may well be
| "yes", but don't ask me for the details. (All I can tell is
| that quadratic systems are no easier than degree-n systems in
| general -- there's a known trick how any system can be
| reduced to degree 2 by introduced extra variables.)
| skeeks wrote:
| We used SageMath in cryptography lessons at university. Very
| useful stuff and easy to get!
| lvh wrote:
| Sage is wonderful. It has a huge number of uses but I mostly use
| it for cryptography. Sage has the best (certainly open source)
| support I know of for a myriad of things like group theory and
| elliptic curves. Here's a short example for how easy it is to
| play around with a tiny elliptic curve: sage: p
| = 19; p.is_prime() True sage: K = GF(p); K
| Finite Field of size 19 sage: E = EllipticCurve(K, [5,
| 9]); E Elliptic Curve defined by y^2 = x^3 + 5*x + 9 over
| Finite Field of size 19 sage: E.count_points(),
| E.order(), E.gens() (19, 19, [(4 : 6 : 1)])
|
| There are far too many things to name that sage can do, but the
| CLI has a great autocomplete. Here's an example: let's say you
| have ECDH with point compression, and you specify only an x
| coordinate. Point compression limits the effectiveness of invalid
| curve attacks, where an attacker gives you a maliciously picked
| Diffie-Hellman value that isn't actually on the curve you're
| supposed to be on. However, if the x coordinate doesn't map to a
| point on the curve, it's necessarily on its "nontrivial quadratic
| twist". Sage makes this easy to play with because sage makes
| pretty much everything easy to play with: sage:
| E.lift_x(6, all=True) [] sage: E.quadratic_twist()
| Elliptic Curve defined by y^2 = x^3 + 6*x + 13 over Finite Field
| of size 19 sage: E.quadratic_twist().lift_x(6, all=True)
| [(6 : 6 : 1), (6 : 13 : 1)]
|
| If you want to do a full-on invalid curve attack, the easiest way
| to do that is with Sage. You look up how the explicit formulas
| work in the EFD[efd], you write a ladder, you figure out how to
| create other elliptic curves for which the short Weierstrass
| doubling formulas still work (which parameter doesn't appear in
| the formula?), and then just let sage generate every possible
| curve and see which ones have the poor cryptographic properties
| you're after.
|
| There's a reason the introduction to Cryptopals Set 8[set8] sends
| with the words:
|
| > By the time you're done, you will have written an ad hoc,
| informally-specified, bug-ridden, slow implementation of one
| percent of SageMath.
|
| As much as I'm a Clojure fanboy none of the Java libraries come
| even close. Unfortunately, sage is mildly annoying to use/install
| as a Python library (that would help interop significantly).
|
| [efd]: https://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
|
| [set8]: https://cryptopals.com/sets/8
| amw-zero wrote:
| How does it compare to Mathematica?
| chaoxu wrote:
| I've contributed some code to matroid optimization. The people
| working on it are very knowledgable, often professors at
| universities donating their time. I definitely learned a lot
| through implementing some algorithms from the 70s.
| haberman wrote:
| As someone who needs math software somewhat infrequently, I had
| assumed that SageMath was a sort of de facto standard for people
| using Python with math. I was surprised to see that Google Colab
| doesn't support Sage in its notebooks.
|
| I asked a coworker about it, someone who had previously worked on
| Sage. It sounds like some parts of the community are now favoring
| using lighter-weight libraries directly (like SymPy for symbolic
| math).
|
| I discovered that Sage is not pure Python: Sage is translated to
| Python before running, which is how it can support syntax like
| "f(x) = x + 1" to define a function (whereas in pure Python you
| would need to use "def".
| watwatinthewat wrote:
| Graduate educational background in math here and working in
| software engineering and machine learning. Like your coworker
| said, I do my work in Python and libraries like
| Sympy/pandas/numpy, not Sage. Sage never made more sense than
| Python since Python covers everything I need to do, including
| what Sage does that I need.
|
| I've never met anyone who uses Sage and work at large research
| center. If your college background is math, you used Matlab in
| school. If your background is in computer science, you go with
| Python or another programming language. Sage seems like the
| middle ground between those two, but who is that?
|
| The cases posted here seem to be like yours where there is
| occasional need for workers or students whose employer or
| school doesn't or won't supply a Matlab license. Matlab is in
| most college math departments and offers keys directly to
| students for like $50-100, so there are few of those cases. An
| employer with math researchers isn't going blink at the $2k for
| a perpetual license, so anyone doing the work regularly gets
| Matlab who wants it.
|
| I do think Sage is good software and it is important to have a
| free alternative to Matlab. The audience is pretty limited,
| though.
| boothby wrote:
| > An employer with math researchers isn't going blink at the
| $2k for a perpetual license, so anyone doing the work
| regularly gets Matlab who wants it.
|
| Not all employers can splash for matlab. You might be right
| about a simple license, but in my experience most matlab
| developers rely on toolkits which ratchet that price up
| through the roof.
|
| For one example, somebody I worked with rewrote the parfor
| functionality as a c extension, because we couldn't justify
| the expense of that addon for every seat. Not a _great_ use
| of that math researcher 's time, but it got the job done, I
| guess.
|
| I and a couple others at my company showed that Python /
| Cython could be meet and beat matlab's performance, and we
| built up an open source stack that our customers love and
| contribute to -- good luck doing that with matlab.
|
| Our physicists found that the only feature they needed of
| matlab was its plotting functionality -- so they rewrote that
| in their native lisp and moved on with their lives.
|
| Today, we only need a few seats for some researchers with
| seniority. I can't say how much we're saving, obviously, but
| we eliminated a significant cost in two departments' budgets
| and our finance folks are quite pleased.
|
| My regret in this is that I used to be a Sage developer, but
| I've only got so much sway at the company and GPL'd code is a
| no-go.
| williamstein wrote:
| Sage is primarily written and developed to support pure
| mathematics research, and you're describing applied/numerical
| mathematics. They are completely different things. Look at
| the chapters and sections in the Sage reference manual to
| begin to get a sense of what Sage is about:
| https://doc.sagemath.org/html/en/reference/index.html Sage
| has basically no overlap at all with Matlab in terms of new
| interesting code, but does have around a million lines of new
| code written by over 600 people:
| https://trac.sagemath.org/#AccountNamesMappedtoRealNames That
| code is mostly about the world of pure mathematics research,
| which has almost nothing to do with Matlab.
| watwatinthewat wrote:
| My background is pure math; sorry if that wasn't clear.
| Even in that environment I have not seen someone use Sage
| over Matlab.
| sdenton4 wrote:
| In my experience, the math community is a very lumpy
| peanut butter... People use matlab, mathematica or sage
| depending largely on what was easily available and usable
| when they were in grad school, and or what their
| colleagues and collaborators were using. So some areas
| end up with lots of Matlab plugins, and other freedom-
| loving folks work in sage, slowly winning others to the
| cause with the promise of open source.
| williamstein wrote:
| - The total available functionality of Matlab is
| __dramatically __different than that of SageMath. It 's
| apples to oranges. I've never once even heard of a single
| research in arithmetic geometry (my area) using Matlab
| for research. For example, look at the top google hit for
| matlab and "elliptic curve": https://www.mathworks.com/ma
| tlabcentral/answers/282367-may-i... Compare that with
| what you find for Sage: https://doc.sagemath.org/html/en/
| constructions/elliptic_curv...
|
| - Research mathematicians often use Sage not just because
| they are "freedom-loving folks", but because their
| research fundamentally demands that they can see, modify
| and extend the source code of the software they are using
| to do computations, and in many cases this simply isn't
| possible with commercial options.
| krastanov wrote:
| I very strongly disagree with your suggestion. Matlab is
| mostly for numerical work (e.g. what NumPy/SciPy/R/Octave are
| usually used for). Almost universally, this is __not
| __research mathematics (although it is certainly useful for
| many cutting edge engineering research topics and plenty of
| applied math work).
|
| Sage can deal with these tasks as well as Matlab, simply by
| virtue of having interfaces to NumPy/SciPy/Octave/others, but
| this is not where Sage shines. Sage is indispensable for
| research math (some examples I understand: group theory,
| cryptography, abstract algebras; but there are many others
| that are far beyond my level of math education).
|
| In short, I think you are misrepresenting or missing who Sage
| is really useful for. Matlab simply does not have these
| features. The competitors would be Mathematica/Maple/Magma.
| nxpnsv wrote:
| Applied math can still be research and often is.
| krastanov wrote:
| You are right. Bad phrasing on my part. Research applied
| math and research "pure" math even overlap, and the
| distinction is fuzzy. I do try to distinguish them from
| engineering research.
| krastanov wrote:
| Be careful with your last statement: Sage is actually
| accessible as a python library with purely python syntax, but
| it also has an interface that supports weirder syntax like the
| one you mentioned.
| sgdpk wrote:
| Do you know how to install the library in a Python
| environment?
| williamstein wrote:
| In one sense, what you want is possible but not currently
| supported, though people are working on it
| (https://trac.sagemath.org/ticket/29705 is a good start).
| In another sense, the SageMath install _is_ just a Python
| environment. When you install Sage (from source or a
| binary) you are install a Python environment, similar to
| Anaconda. You can then type "sage -sh" to setup the
| environment, then install packages (pip3 install), or run a
| Python interpreter (by typing "python3") and do "import
| sage.all" to get the full sage library as a normal Python
| library. You could write a Python program and use any of
| Sage in them by importing "sage.all" in your Python
| program.
|
| The reason Sage is currently distributed this way is
| similar to the reason Anaconda exists, which is that
| Python's package manager isn't (or wasn't in 2005 when I
| started this!) meant to build something as complicated as
| Sage, which has about 100 complicated dependencies. I
| really hope this eventually changes someday and people can
| type "pip install sagemath" and get something useful.
|
| Oh, I think for several Linux distributions there are
| SageMath packages that just build Sage into the standard
| system-wide Python. So if you're using Linux, the problem
| may already be solved for you.
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