[Python-ideas] Re: symbolic math in Python
On Wed, 19 May 2021 at 07:41, Martin Teichmann wrote: > > Hi list, > > as you might have noticed, I am trying to improve the syntax and semantics > for symbolic math in Python. Until now, I have to say, my ideas were not that > well received, but I learned from the discussion and maybe this time I come > up with something people like. I think that the discussion could be more productive if it started on the SymPy mailing list. Some of the things you refer to can be improved in SymPy itself without needing changes to core Python. -- Oscar ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/7LYWA23CS3SH7IJSY7CM4KBQ7DYA6T2J/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
People always come up with hacks like Ir. Robert Vanden Eynde has come up with the vertical bar hack. This is why I feel there's no need to have additional performance decrease and new syntax only to solve a little problem that occurs in some third party like sympy. ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/NCKWLCRIFHYNYC4UIAN32CK3GLIXUSGQ/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
> Oh no, not the vertical bar hack. :-( This is my first time seeing the vertical bar hack. I guess this is something that has appeared before? - DLD ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/DOLJJ57A3O5353PMGMGXPFNMZ55LIPYT/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
Oh no, not the vertical bar hack. :-( ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/B4XH4Q5PJNE65DHHIIMIZ76XSXBE4Y2T/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
> solve(x**2 == 1/2)
pip install funcoperators
>>> solve(x ** 2 |Equals| 1/2)
<<< Equals = infix(Eq)
<<< from sympy import Eq
Le mer. 19 mai 2021 à 08:40, Martin Teichmann
a écrit :
> Hi list,
>
> as you might have noticed, I am trying to improve the syntax and semantics
> for symbolic math in Python. Until now, I have to say, my ideas were not
> that well received, but I learned from the discussion and maybe this time I
> come up with something people like.
>
> To frame the problem, let us try to solve the equation x ** 2 == 1/2
> using sympy:
>
> >>> from sympy import Eq, solve, symbols, S
> >>> x = symbols("x")
> >>> solve(Eq(x**2, S(1)/2))
> [-sqrt(2)/2, sqrt(2)/2]
>
> that worked well, but actually we would like to write the last line simply
> as
>
> >>> solve(x**2 == 1/2)
>
> as you might notice, this is fully legal Python syntax. Unfortunately the
> semantics is such that sympy has no way to determine what is actually going
> on, this is why they invented all those helper functions shown above.
>
> My idea is now to start at the line above, "x = symbols('x')". I propose a
> new syntax, "symbolic x", which tells the parser that x is a symbolic
> variable, and expressions should not be executed, but handed over as such
> to the calling functions. To stay with the example, the code would look
> like this (this is fake, I did not prototype this yet):
>
> >>> from sympy import solve
> >>> symbolic x
> >>> solve(x**2 == 1/2)
> [-sqrt(2)/2, sqrt(2)/2]
>
> Now to the details. The scope that "symbolic" acts on should be the same
> as the scope of "global". Note that "symbolic x" is currently illegal
> syntax, so we would not even need to make "symbolic" a keyword.
>
> Expressions that contain a symbolic variable are not executed, but instead
> the expression should be given to the function as a tuple, so in the
> example above, solve would be given
> ('==', ('**', ('x', 2)), ('/', 1, 2)). If that looks like LISP to you,
> then you are not completely wrong. The boundaries of expressions are
> function calls, assignments, getitems and getattrs, as they can be
> overloaded much easier by other means. To give an example with gory details
> (again, this is fake):
>
> >>> symbolic x
> >>> d = {"a" : 5}
> >>> c = 7 # not symbolic!
> >>> print(c * x + d["a"])
> ('+', ('*', 7, 'x'), 5)
>
> Maybe we would want to have a new class "expressiontuple" which simply
> acts as a pretty-printer, then the last lines would become
>
> >>> print(x + d["a"])
> 7 * x + 5
>
> What sympy does with this tuple would be fully at its discretion.
>
> I think that other libraries could also benefit from this proposal. As an
> example, in a numerics library (numpy? scipy?) one could improve numerical
> integration as in
>
> >>> symbolic x
> >>> integrate(sin(x), x, 0, pi)
>
> then the integrator could even compile the expression to machine code for
> faster integration.
>
> numpy could also compile expressions to machine code, making it even
> faster than it is now, as in
>
> >>> symbolic x
> >>> f = compile(5 * x + 7 * y, (x, y))
> >>> f(matrix_a, matrix_b)
>
> Let's see how well this proposal fares.
>
> Cheers
>
> Martin
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[Python-ideas] Re: symbolic math in Python
SUB
Hello everyone, what is the usual way to "like" a mail in the maillist and
subscribing to the thread ?
By sending a message it adds me to the "Participants" in the webapp which
is neat (I can then search for my messages)
I could do it in the webapp but not everybody will see it
Le mer. 19 mai 2021 à 17:02, David Lowry-Duda a
écrit :
> > To frame the problem, let us try to solve the equation x ** 2 == 1/2
> > using sympy:
> >
> > >>> from sympy import Eq, solve, symbols, S
> > >>> x = symbols("x")
> > >>> solve(Eq(x**2, S(1)/2))
> > [-sqrt(2)/2, sqrt(2)/2]
> >
> > that worked well, but actually we would like to write the last line
> simply as
> >
> > >>> solve(x**2 == 1/2)
>
> This is essentially how this would be written in sagemath (a CAS
> exposing various FOSS math software behind a unified python-based
> interface). More about sagemath can be found at https://www.sagemath.org/
>
> In sage, this would be written
>
> solve([x**2 == 1/2], x)
>
> The additional "x" is because sage also accepts things like
>
> y = var('y')
> solve([x**2 == y], x) # solve for x in terms of other variables
>
> Large amounts of sage are written in python, including essentially the
> whole symbolic mathematics stack. I'm personally content with using a
> CAS like sage when I want to manipulate mathematics and keeping symbolic
> math separate from my default python interpreter.
>
> - DLD
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[Python-ideas] Re: symbolic math in Python
> To frame the problem, let us try to solve the equation x ** 2 == 1/2
> using sympy:
>
> >>> from sympy import Eq, solve, symbols, S
> >>> x = symbols("x")
> >>> solve(Eq(x**2, S(1)/2))
> [-sqrt(2)/2, sqrt(2)/2]
>
> that worked well, but actually we would like to write the last line simply as
>
> >>> solve(x**2 == 1/2)
This is essentially how this would be written in sagemath (a CAS
exposing various FOSS math software behind a unified python-based
interface). More about sagemath can be found at https://www.sagemath.org/
In sage, this would be written
solve([x**2 == 1/2], x)
The additional "x" is because sage also accepts things like
y = var('y')
solve([x**2 == y], x) # solve for x in terms of other variables
Large amounts of sage are written in python, including essentially the
whole symbolic mathematics stack. I'm personally content with using a
CAS like sage when I want to manipulate mathematics and keeping symbolic
math separate from my default python interpreter.
- DLD
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[Python-ideas] Re: symbolic math in Python
On Wed, May 19, 2021 at 8:14 AM Ricky Teachey wrote: > It's a neat idea but I agree with the others that as proposed, it's > probably too focused on turning python into a better mathematics tool, > rather than turning python into a better programming language. > > That being said, from a more generalist standpoint I wonder if it would be > useful in many connects other than symbolic math to have a way to "get to" > and work with the actual written code in a module from inside that same > module. Essentially to parse actual lines of code, not strings containing > code, into an AST, and work with it. > >> >> You can essentially do this using import hooks as I have mentioned many times on this list. A good example of what one can accomplish by transforming and AST is given by MacroPy: https://macropy3.readthedocs.io/en/latest/ I also gave various examples of using import hooks to modify Python's syntax using https://github.com/aroberge/ideas which I wrote to facilitate such experimentation -- although I consider this more of a toy than anything resembling a professional and robust package. André Roberge ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/FYXX7EMPLJ23CCIGDVFNNPP2NPDNJCS6/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
I'm +1 on the idea but -1 on the proposed syntax. Yes it would be kind of nice *but* it's not how Python arithmetic or grammar works. And why should Python have that functionality? AFAICT Python doesn't have a module in stdlib for symbolic math. This looks like a feature request to third party modules that support symbolic math like sympy. People usually doesn't use symbolic math in Python but those who do know the drawbacks and have already come up with hacks to overcome those. ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/NBBNTKTXTUXR2CQEQ5JQ3G3X2NICPLXA/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
It's a neat idea but I agree with the others that as proposed, it's probably too focused on turning python into a better mathematics tool, rather than turning python into a better programming language. That being said, from a more generalist standpoint I wonder if it would be useful in many connects other than symbolic math to have a way to "get to" and work with the actual written code in a module from inside that same module. Essentially to parse actual lines of code, not strings containing code, into an AST, and work with it. The "poison the well" approach is an interesting idea from that standpoint. On Wed, May 19, 2021, 6:32 AM Jonathan Fine wrote: > Martin wrote: > > as you might have noticed, I am trying to improve the syntax and semantics >> for symbolic math in Python. Until now, I have to say, my ideas were not >> that well received, but I learned from the discussion and maybe this time I >> come up with something people like. >> > > For about 10 years I've used PARI/gp for computer algebra, mainly for > integer linear algebra and polynomials. One day I might use its number > theory features. > http://pari.math.u-bordeaux.fr/ > > Lately it's acquired good Python bindings, and most likely for my next > project I'll start using them. > https://pari.math.u-bordeaux.fr/Events/PARI2019/talks/jeroen.html > https://pypi.org/project/cypari2/ > https://cypari2.readthedocs.io/en/latest/ > > Regarding semantics, I'm very happy to go along with PARI/gp. This is in > part because of its deep roots in computational number theory and the > community it has around it. > > See also: Integer Factorization Software: PARI/GP, Mathematica, and SymPy > > https://dzone.com/articles/integer-factorization-software-parigp-mathematica > > Regarding syntax, I'd be pleased to see a paritools package that makes it > easier to use the cypari2 bindings for common purposes. This perhaps could > become part of sympy. It's also worth looking at sage. > https://doc.sagemath.org/html/en/reference/libs/sage/libs/pari.html > > This is what I would like. Other people will most likely have different > wishes for improving symbolic math in Python. > > -- > Jonathan > > > ___ > Python-ideas mailing list -- python-ideas@python.org > To unsubscribe send an email to python-ideas-le...@python.org > https://mail.python.org/mailman3/lists/python-ideas.python.org/ > Message archived at > https://mail.python.org/archives/list/python-ideas@python.org/message/EOOMLHOIY66OM453SAKQKAPFVXYE5MLY/ > Code of Conduct: http://python.org/psf/codeofconduct/ > ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/SOUCZBMP4UZIEJJ32RXU3ABHBD46ES3H/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
Martin wrote: as you might have noticed, I am trying to improve the syntax and semantics > for symbolic math in Python. Until now, I have to say, my ideas were not > that well received, but I learned from the discussion and maybe this time I > come up with something people like. > For about 10 years I've used PARI/gp for computer algebra, mainly for integer linear algebra and polynomials. One day I might use its number theory features. http://pari.math.u-bordeaux.fr/ Lately it's acquired good Python bindings, and most likely for my next project I'll start using them. https://pari.math.u-bordeaux.fr/Events/PARI2019/talks/jeroen.html https://pypi.org/project/cypari2/ https://cypari2.readthedocs.io/en/latest/ Regarding semantics, I'm very happy to go along with PARI/gp. This is in part because of its deep roots in computational number theory and the community it has around it. See also: Integer Factorization Software: PARI/GP, Mathematica, and SymPy https://dzone.com/articles/integer-factorization-software-parigp-mathematica Regarding syntax, I'd be pleased to see a paritools package that makes it easier to use the cypari2 bindings for common purposes. This perhaps could become part of sympy. It's also worth looking at sage. https://doc.sagemath.org/html/en/reference/libs/sage/libs/pari.html This is what I would like. Other people will most likely have different wishes for improving symbolic math in Python. -- Jonathan ___ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/EOOMLHOIY66OM453SAKQKAPFVXYE5MLY/ Code of Conduct: http://python.org/psf/codeofconduct/
[Python-ideas] Re: symbolic math in Python
On Wed, 19 May 2021 at 07:41, Martin Teichmann
wrote:
> that worked well, but actually we would like to write the last line simply as
>
> >>> solve(x**2 == 1/2)
>
> as you might notice, this is fully legal Python syntax. Unfortunately the
> semantics is such that sympy has no way to determine what is actually going
> on, this is why they invented all those helper functions shown above.
It's almost possible to do this right now. Using the compiler and ast
module, you can write a version of solve that works like
>>> solve("x**2 == 1/2")
You have to quote the argument, and yes that probably means your
editor/IDE won't help you as much with the expression syntax, but
otherwise this could be made to work exactly as you want with no
language changes.
People don't often do this, so presumably there's a reason people
don't like having to quote "stuff that's basically Python code". But
it *is* technically possible.
> My idea is now to start at the line above, "x = symbols('x')". I propose a
> new syntax, "symbolic x", which tells the parser that x is a symbolic
> variable, and expressions should not be executed, but handed over as such to
> the calling functions. To stay with the example, the code would look like
> this (this is fake, I did not prototype this yet):
>
> >>> from sympy import solve
> >>> symbolic x
> >>> solve(x**2 == 1/2)
> [-sqrt(2)/2, sqrt(2)/2]
>
> Now to the details.
Before you get to details of implementation, you should explain:
1. Why sympy doesn't have a solve("x**2 == 1/2") function taking a
string like I described above? Why isn't that a good solution here?
2. Why new syntax is any more likely to be useful for sympy than a
string-based function.
The barrier for language changes, and in particular new syntax, is
high (as you've discovered). So proposals need to be pretty thorough
in examining ways to solve a problem within the existing language
before proposing a new language feature. Particularly if the feature
is focused on improving things just for a subset of the Python user
base.
You really should look at the history of the matrix multiplication
operator in Python - start with PEP 465,
https://www.python.org/dev/peps/pep-0465/, but look back at the
history of all the proposals that *didn't* work leading up to that -
to get a feel for how much work it needs to get a feature focused on
the needs of a specialist community into the core language. And as
others have pointed out, symbolic maths and sympy is nowhere near as
big an audience as the numeric community.
Paul
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[Python-ideas] Re: symbolic math in Python
On Wed, 19 May 2021 at 07:41, Martin Teichmann
wrote:
> Hi list,
>
> To frame the problem, let us try to solve the equation x ** 2 == 1/2
> using sympy:
>
> >>> from sympy import Eq, solve, symbols, S
> >>> x = symbols("x")
> >>> solve(Eq(x**2, S(1)/2))
> [-sqrt(2)/2, sqrt(2)/2]
>
> that worked well, but actually we would like to write the last line simply
> as
>
> >>> solve(x**2 == 1/2)
>
> as you might notice, this is fully legal Python syntax. Unfortunately the
> semantics is such that sympy has no way to determine what is actually going
> on, this is why they invented all those helper functions shown above.
>
Numpy override __eq__ liberally to allow this kind of behaviour (though not
root searching, but returning ndarray instead of a boolean for == so things
remain matrices. As a toy example to show that it is definitely possible to
let the x "poison the well":
```
class Symbolic:
def __init__(self, expression):
self.expression = expression
def __pow__(self, power):
return Symbolic(f"{self.expression} ** {power}")
def __eq__(self, other):
return Symbolic(f"{self.expression} == {other}")
def __truediv__(self, other):
return Symbolic(f"{self.expression} / {other}")
def __str__(self):
return self.expression
def __repr__(self):
return f"{self.__class__}({self.expression})"
x = Symbolic("x")
print(x ** 2 == 1 / 2)
print(x ** 2 == Symbolic(1) / 2)
```
Which gives output:
```
x ** 2 == 0.5
x ** 2 == 1 / 2
```
Now, it hasn't done root solving, but it could (or return an object that
could), so to say that "Unfortunately the semantics is such that sympy has
no way to determine what is actually going on" is an unsound foundation for
your idea.
>
> My idea is now to start at the line above, "x = symbols('x')". I propose a
> new syntax, "symbolic x", which tells the parser that x is a symbolic
> variable, and expressions should not be executed, but handed over as such
> to the calling functions.
>
So... what you're suggesting can basically already be done, though as I did
above, might require some additional "poisoning" so that all roots are
poisoned, just like when there was the thread about float literals (e.g. 1F
/ 3 to become Float(1, 3)).
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[Python-ideas] symbolic math in Python
Hi list,
as you might have noticed, I am trying to improve the syntax and semantics for
symbolic math in Python. Until now, I have to say, my ideas were not that well
received, but I learned from the discussion and maybe this time I come up with
something people like.
To frame the problem, let us try to solve the equation x ** 2 == 1/2 using
sympy:
>>> from sympy import Eq, solve, symbols, S
>>> x = symbols("x")
>>> solve(Eq(x**2, S(1)/2))
[-sqrt(2)/2, sqrt(2)/2]
that worked well, but actually we would like to write the last line simply as
>>> solve(x**2 == 1/2)
as you might notice, this is fully legal Python syntax. Unfortunately the
semantics is such that sympy has no way to determine what is actually going on,
this is why they invented all those helper functions shown above.
My idea is now to start at the line above, "x = symbols('x')". I propose a new
syntax, "symbolic x", which tells the parser that x is a symbolic variable, and
expressions should not be executed, but handed over as such to the calling
functions. To stay with the example, the code would look like this (this is
fake, I did not prototype this yet):
>>> from sympy import solve
>>> symbolic x
>>> solve(x**2 == 1/2)
[-sqrt(2)/2, sqrt(2)/2]
Now to the details. The scope that "symbolic" acts on should be the same as the
scope of "global". Note that "symbolic x" is currently illegal syntax, so we
would not even need to make "symbolic" a keyword.
Expressions that contain a symbolic variable are not executed, but instead the
expression should be given to the function as a tuple, so in the example above,
solve would be given
('==', ('**', ('x', 2)), ('/', 1, 2)). If that looks like LISP to you, then you
are not completely wrong. The boundaries of expressions are function calls,
assignments, getitems and getattrs, as they can be overloaded much easier by
other means. To give an example with gory details (again, this is fake):
>>> symbolic x
>>> d = {"a" : 5}
>>> c = 7 # not symbolic!
>>> print(c * x + d["a"])
('+', ('*', 7, 'x'), 5)
Maybe we would want to have a new class "expressiontuple" which simply acts as
a pretty-printer, then the last lines would become
>>> print(x + d["a"])
7 * x + 5
What sympy does with this tuple would be fully at its discretion.
I think that other libraries could also benefit from this proposal. As an
example, in a numerics library (numpy? scipy?) one could improve numerical
integration as in
>>> symbolic x
>>> integrate(sin(x), x, 0, pi)
then the integrator could even compile the expression to machine code for
faster integration.
numpy could also compile expressions to machine code, making it even faster
than it is now, as in
>>> symbolic x
>>> f = compile(5 * x + 7 * y, (x, y))
>>> f(matrix_a, matrix_b)
Let's see how well this proposal fares.
Cheers
Martin
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