Use SymEngine as a symbolic mathematics backend for SAGE

[Siddharth Bhat]

The SymPy project has another project called SymEngine, which aims to be a fast symbolic manipulation library. Perhaps we should move to use SymEngine as well, since it should be faster as it is native C++ code.

This discussion came up during a discussion on improving the performance of SageManifolds. 

[Vincent Delecroix]

See https://trac.sagemath.org/ticket/29497

Le 18/01/2021 à 14:40, Siddharth Bhat a écrit :
> The SymPy project has another project called SymEngine

> <https://github.com/symengine/symengine>, which aims to be a fast symbolic

> manipulation library. Perhaps we should move to use SymEngine as well,
> since it should be faster as it is native C++ code.
>
>
> This discussion came up during a discussion on improving the performance

> of SageManifolds <https://trac.sagemath.org/ticket/30139#comment:26>.
>

[Dima Pasechnik]

Interesting! Is there documentation about its capabilities?

On Mon, 18 Jan 2021, 13:40 Siddharth Bhat, <siddu...@gmail.com> wrote:

The SymPy project has another project called SymEngine, which aims to be a fast symbolic manipulation library. Perhaps we should move to use SymEngine as well, since it should be faster as it is native C++ code.

This discussion came up during a discussion on improving the performance of SageManifolds. 

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[Siddharth Bhat]

@vincent:  I'm very new to sage-devel. As best as I can tell, the patch has stalled? Can/should someone else pick it up? 

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[Dima Pasechnik]

On Mon, 18 Jan 2021, 14:56 Siddharth Bhat, <siddu...@gmail.com> wrote:

@vincent:  I'm very new to sage-devel. As best as I can tell, the patch has stalled? Can/should someone else pick it up? 

a patch to arb needed there has stalled

for some reason.

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[rjf]

Just a suggestion:  if you want to improve the speed of symbolic mathematics as done by Maxima, and you are no longer insisting on the use of Python, why not write in Lisp, and make Maxima faster?

[Dima Pasechnik]

On Wed, 20 Jan 2021, 01:06 rjf, <fat...@gmail.com> wrote:

Just a suggestion:  if you want to improve the speed of symbolic mathematics as done by Maxima, and you are no longer insisting on the use of Python, why not write in Lisp, and make Maxima faster?

oh well - anyway,  it is fun to watch C/C++ programmers discovering the wrath of 

https://en.m.wikipedia.org/wiki/Greenspun%27s_tenth_rule

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[kcrisman]

Just a suggestion:  if you want to improve the speed of symbolic mathematics as done by Maxima, and you are no longer insisting on the use of Python, why not write in Lisp, and make Maxima faster?

oh well - anyway,  it is fun to watch C/C++ programmers discovering the wrath of 

https://en.m.wikipedia.org/wiki/Greenspun%27s_tenth_rule

More seriously perhaps, "Python wrappers allow easy usage from Python and integration with SymPy and Sage (the symengine.py repository)" which probably is not the case even with our use of Maxima as library.

As for the substance of Richard's remark, the truth is that at least to some extent one has to go with supply, not just demand:

https://www.statista.com/statistics/793628/worldwide-developer-survey-most-used-languages/

and while I'm not sure that "HTML/CSS" is Turing-complete, at any rate if this graphic is even remotely accurate there simply aren't enough people who know Lisp (or even Scheme or Clojure or ...) well to focus on it within a scientific ecosystem already dominated by things like Python and R.  That is too bad, because if we had had that competence early in the project, I could have imagined a lot of energy on improving Maxima; but time considerations have to be part of it too, not just technical considerations of which language is "best". 

As to the question of replacing backends, there is already a ticket (which I cannot find right now, my apologies) which started the process of seeing what doctests would fail if we went to Sympy as default.  Presumably something similar could be done with this engine (I don't know if it is more for low-level symbolics or also things like integration).  However, one of the strengths of Sage is that one can check computations using several backends at a time, including with optional things like fricas (still?), and likely Maxima will still prove to be better at certain kinds of computations, so improving Maxima will still help Sage's capabilities no matter what happens.

[kcrisman]

As to the question of replacing backends, there is already a ticket (which I cannot find right now, my apologies) which started the process of seeing what doctests would fail if we went to Sympy as default.  Presumably something similar could be done with this engine (I don't know if it is more for low-level symbolics or also things like integration).  

In particular, the (very minimal) documentation (really an API is all) makes it seems more a replacement for things like Ginac (already in C++), not Maxima et al.  I don't know if that would provide a noticeable speedup per se, though the SageManifolds ticket mentioned parallelization so perhaps it is better suited for that?

[rjf]

I think you have to figure that there is a difference in productivity of people who just learned Python in high school and would really like to write a computer algebra system

versus people who know more mathematics, are comfortable spending 2 weeks learning lisp, spending ?? (weeks? months?) studying the state of the art in

computer algebra systems as evolved over 60 years, and want to contribute to advancing the art (rather than re-programming the easy stuff). 

 I am under the impression that learning python is a reasonable stepping stone to learning lisp.

As far as checking results for various systems,  there is a category of CAS bugs that are syistem independent.

That is, they occur in many systems!  Sometimes they depend on secretly dividing by zero, or doing something

that is invalid at a singularity.  So "Maple and Mathematica and ...  all agree" does not mean they are right!

I think my essential point previously is that rewriting easy stuff (in a different language) typically fails to push the frontier.

[parisse]

As the author of a CAS, I can state that you need much more than 2 weeks to learn a programming language to make a CAS, and much much more if you want to be fast. Life is short, therefore choose your programming language carefully! I don't regret my choice for C (+ C++ STL and operator redefinition) made 20 years ago, because C can interact with a lot of languages (including compilation to Javascript). If I had to choose today, I would perhaps choose Julia. Not Python, it's much too slow. I don't know for Lisp speed, but it's not a language I would choose anyway, I like to write e.g. a+b*c when I do algebraic computations in my source code.

[kcrisman]

I think you have to figure that there is a difference in productivity of people who just learned Python in high school and would really like to write a computer algebra system

I'm not referring to that, obviously.

[Dima Pasechnik]

On Wed, Jan 20, 2021 at 7:13 PM parisse <bernard...@ujf-grenoble.fr> wrote:
>
> As the author of a CAS, I can state that you need much more than 2 weeks to learn a programming language to make a CAS, and much much more if you want to be fast. Life is short, therefore choose your programming language carefully! I don't regret my choice for C (+ C++ STL and operator redefinition) made 20 years ago, because C can interact with a lot of languages (including compilation to Javascript). If I had to choose today, I would perhaps choose Julia. Not Python, it's much too slow. I don't know for Lisp speed, but it's not a language I would choose anyway, I like to write e.g. a+b*c when I do algebraic computations in my source code.

There are macro packages for infix maths in Common Lisp, so this by no
means should be a deal-breaker for anyone.

Needless to say, C++ has its own can of worms, which anyone who tried
to used it might easily produce, as a reason to stay
away from it.

>
> Le mercredi 20 janvier 2021 à 19:47:01 UTC+1, rjf a écrit :
>>
>> I think you have to figure that there is a difference in productivity of people who just learned Python in high school and would really like to write a computer algebra system
>> versus people who know more mathematics, are comfortable spending 2 weeks learning lisp, spending ?? (weeks? months?) studying the state of the art in
>> computer algebra systems as evolved over 60 years, and want to contribute to advancing the art (rather than re-programming the easy stuff).
>> I am under the impression that learning python is a reasonable stepping stone to learning lisp.
>>
>> As far as checking results for various systems, there is a category of CAS bugs that are syistem independent.
>> That is, they occur in many systems! Sometimes they depend on secretly dividing by zero, or doing something
>> that is invalid at a singularity. So "Maple and Mathematica and ... all agree" does not mean they are right!
>>
>> I think my essential point previously is that rewriting easy stuff (in a different language) typically fails to push the frontier.
>>
>>
>>
>> On Wednesday, January 20, 2021 at 5:54:51 AM UTC-8 kcrisman wrote:
>>>>
>>>>
>>>> As to the question of replacing backends, there is already a ticket (which I cannot find right now, my apologies) which started the process of seeing what doctests would fail if we went to Sympy as default. Presumably something similar could be done with this engine (I don't know if it is more for low-level symbolics or also things like integration).
>>>
>>>
>>> In particular, the (very minimal) documentation (really an API is all) makes it seems more a replacement for things like Ginac (already in C++), not Maxima et al. I don't know if that would provide a noticeable speedup per se, though the SageManifolds ticket mentioned parallelization so perhaps it is better suited for that?
>

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[parisse]

Well, searching for "lisp infix notation" is not very convincing (unless I missed something?), compared to built-in infix support. You might prefer Lisp to C/C++, it's your choice, but I don't see any objective reason that one should stay away from C/C++. And Giac is a proof that one can actually write a CAS in C/C++, that compares very well with the Lisp-based CAS Maxima.

[Dima Pasechnik]

On Thu, Jan 21, 2021 at 8:04 PM parisse <bernard...@ujf-grenoble.fr> wrote:
>
> Well, searching for "lisp infix notation" is not very convincing (unless I missed something?), compared to built-in infix support. You might prefer Lisp to C/C++, it's your choice, but I don't see any objective reason that one should stay away from C/C++. And Giac is a proof that one can actually write a CAS in C/C++, that compares very well with the Lisp-based CAS Maxima.

Maxima is ~40 years old with a bit of work done since then, but the
core is that old, as far as I know:
https://en.wikipedia.org/wiki/Macsyma

As for staying away from C++, most people who might be trying to do
something with supposedly state of the art library like boost,
would run away screaming, closely followed by 100 screens of error messages :-)
Or, now mostly gone (?), iterator_traits (my closest encounter with
C++, contributing to CGAL, 20 years ago, where these had to be
generated by a script for some classes, otherwise compilers kept
crashing...)

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[Thierry Dumont]

There was a message from B. Paisse some days ago, about C (++) and Julia
for CAS.

May be this https://arxiv.org/pdf/1705.06134v1.pdf
is interesting.

t.d.

[parisse]

I (almost) do not code C++ myself, probably 99% of my code is C-style, but I'm using a C++ compiler, that way I can link to the C++ standard template library and benefit of features like operator overload. Doing so, I do not have screens of error messages.

[rjf]

Just a note to point out that infix  like a+b*c  in a conventional programming language

is not helpful if a,b,c  are symbolic expressions..  Writing it as  add(a, mul(b,c)) is not

a big deal,  nor is writing it in lisp  (add a (mul b c)).  Of course you need to write programs

add and mul,  but you have to do that regardless.  Languages that are primarily oriented

to provide arithmetic on fixed-length integers or double-float numbers, mostly have to be

covered over by macros etc to do computer algebra.  Languages like FORTRAN, Algol, C.

You could look at RLISP used for Reduce, if you want to see a version of lisp with "syntactic sugar"

to look "infix" ish. And that is used for a computer algebra system, Reduce.

 There is something of a tradition, to hand to someone, perhaps someone

who prefers infix, a project to "Write a scanner/parser/code generator  for an infix language

of your design [ or pick one, say Pascal]" in Lisp.

 I've done this with programming language/compiler

undergraduate classes at Berkeley for decades, with probably thousands of students.

It takes 10 weeks, assuming you know no lisp, nothing about lexical analysis,

nothing about parsing, nothing about intermediate code generation. and maybe

nothing about Pascal.

At the completion of the project, most students prefer Lisp's parenthesized prefix.

They also understand Pascal better, having written an interpreter and compiler for it.

Often they choose to use Lisp for other projects, given a choice.

Most criticisms of Lisp come from people who have never used it, and it shows.

Complaints about too many parentheses. No, there are just exactly enough, and

your editor helps.  Or indentation (hi Pythonistas). Editors indent for you, exactly right.

Not webby enough (see cl-http or other packages).

Too slow (uh, faster than Python, some excellent optimizing compilers for Lisp).

Too hard to learn.   Think about how much time you spent in learning your current

favorite language on the precedence of operators. Or what the operators meant.

Or what happens when integers "overflow".

Consider learning Lisp.

Parts of Macsyma/Maxima are more like 60 years old. Almost as old as Lisp (circa 1959).

James Slagle's 1961 PhD on symbolic integration (SAI'NT) includes a substantial section explaining Lisp,

which was quite new at the time .

[parisse]

rjf, I wonder why you say that " infix  like a+b*c  in a conventional programming language is not helpful if a,b,c  are symbolic expressions". Of course it is, otherwise CAS would not use infix notation in their user interfaces. Parts of my source code are much easier to write and read with infix notations than with prefix notation. This is perhaps not true in other application areas, but CAS is about programming math algorithms. It's not a question of parentheses match, of course a programming editor will help you match them. But what do you prefer to read/write:

* det=a*d-b*c

* store(det,sub(mul(a,d),mul(b,c)))

Or

* delta=b*b-4*a*c

* store(delta,sub(mul(b,b),mul(4,mul(a,c)))))

[Vincent Delecroix]

Shouldn't it be

(- (* a d) (* b c))

and

(- (* b b) (* 4 a c)))

[Michael Orlitzky]

On Mon, 2021-01-25 at 12:08 +0100, Vincent Delecroix wrote:
> Shouldn't it be
>
> (- (* a d) (* b c))
>
> and
>
> (- (* b b) (* 4 a c)))
>
>

The unary "negate" operation and the binary "subtract" operation are
usually distinguished by context, i.e. by whether prefix or infix
notation is used. Unless you do some tricks (like calling one "sub"),
the above would likely be parsed as an attempt to call "negate" with
two arguments, which is a syntax error.

[Dima Pasechnik]

On Sunday, January 24, 2021 at 9:17:14 PM UTC rjf wrote:

Just a note to point out that infix  like a+b*c  in a conventional programming language

is not helpful if a,b,c  are symbolic expressions..  Writing it as  add(a, mul(b,c)) is not

a big deal,  nor is writing it in lisp  (add a (mul b c)).  Of course you need to write programs

add and mul,  but you have to do that regardless.  Languages that are primarily oriented

to provide arithmetic on fixed-length integers or double-float numbers, mostly have to be

covered over by macros etc to do computer algebra.  Languages like FORTRAN, Algol, C.

You could look at RLISP used for Reduce, if you want to see a version of lisp with "syntactic sugar"

to look "infix" ish. And that is used for a computer algebra system, Reduce.

 There is something of a tradition, to hand to someone, perhaps someone

who prefers infix, a project to "Write a scanner/parser/code generator  for an infix language

of your design [ or pick one, say Pascal]" in Lisp.

 I've done this with programming language/compiler

undergraduate classes at Berkeley for decades, with probably thousands of students.

It takes 10 weeks, assuming you know no lisp, nothing about lexical analysis,

nothing about parsing, nothing about intermediate code generation. and maybe

nothing about Pascal.

At the completion of the project, most students prefer Lisp's parenthesized prefix.

They also understand Pascal better, having written an interpreter and compiler for it.

Mind you, the initial versions of an alive and kicking computational group theory system GAP was mostly written by maths

students in RWTH Aachen 25-30 years ago. 

One could ask why human-years of relatively good quality LISP coders coding time were wasted doing the same

lab projects, and not something more creative, like impoving Maxima code. :P

LISP enthousiasts, including many US academics, have mostly themselves to blame for  the present sorry state of 

computer algebra in LISP...