Hi,
I propose that pynac be included in Sage.
Pynac is a rewrite of Ginac to seamlessly use native Python objects instead
of CLN -- for inclusion in Sage. Pynac is a C++ library plus extensive
Cython bindings. Pynac is about 30K lines, is very well documented and
commented, and as C++ code goes is extremely readable.
VOTE:
[ ] Yes, include Pynac in Sage
[ ] No, do not (please explain)
[ ] Hmm, I have questions (please ask).
MANY MORE DETAILS:
The idea to rewrite Ginac so it can manipulate native Python objects
directly appears to be new, and hasn't been tried before.
After thinking through all the options in detail, having experimented
with gfurnish's symbolics approach, watching how sympycore and sympy
have developed, and seeing what is possible using Maxima and Axiom,
I think Burcin's proposal to use a rewritten Ginac as the core symbolics
library for Sage is by far the best, given the goal of having a very solid
nearly-bug-free-well-documented-robust-fast symbolic system in literally
weeks from when we start. Absolutely all other approaches result in
something that either doesn't scale speedwise, is buggy, is slow, or
will take a long time to finish. I'm so convinced that Burcin is right
about the Ginac approach that I've invested most of my time during
the last two weeks in this.
The new Pynac:
(1) doesn't depend at all on (the heavy) CLN library,
(2) can manipulate Python objects instead of CLN classes,
(3) has Cython bindings that replicate roughly 50% (?) of the
functionality of the current Sage calculus, and at the same time
works with many more data types in Sage (e.g., interval arithmetic)
unlike the current calculus code which only works with types
that Maxima supports. Currently the new code is 100% independent
of the Maxima-base calculus code in sage, and in many cases
much faster and potentially more powerful.
To try it out:
(a) if you have an account on sage.math, just run the system-wide sage.
(b) To install yourself into sage-3.1.1, see
http://sage.math.washington.edu/home/was/pynac/
In particular, do
sage -i http://sage.math.washington.edu/home/was/pynac/pynac-0.1.spkg
The above build should take between 2 and 6 minutes depending on how fast
your computer is. On one of my test machines with export MAKE="make -j4"
it takes 45 seconds realtime to build.
Then do:
sage: hg_sage.pull()
sage:
hg_sage.apply('http://sage.math.washington.edu/home/was/pynac/pynac.hg')
sage: hg_sage.merge() # possibly not needed
sage: hg_sage.ci() # possibly not needed
and exit and do:
sage -br
You can create symbolic expression in the new symbolic ring
by doing e.g.,
sage: var('x,y,z',ns=1)
(x, y, z)
sage: f = (x+y+sin(z)^x)^3
sage: f.expand()
3*sin(z)^x*x^2 + 3*sin(z)^x*y^2 + 3*(sin(z)^x)^2*x + ...[snip]
sage: f.[tab]
An example with interval coefficients:
sage: f = x^3 + x^RIF(1) + y*RIF(pi)
sage: f
x^3 + x^(1.0000000000000000?) + (3.141592653589794?)*y
sage: expand(f^2).diff(y)
(6.283185307179587?)*x^3 + (6.283185307179587?)*x + (19.73920880217872?)*y
Arithmetic with relations is fully supported, including squaring both
sides:
sage: f = (x^3 + x - 2/3 + y < x^3)
sage: f^2
(x^3 + x + y - 2/3)^2 < x^6
sage: f - x^3
x + y - 2/3 < 0
Arithmetic with formal functions -- something that Burcin was originally
very concerned about -- is well supported. Here's an example illustrating
applying a differential operator and extracting off coefficients of
it, a feature
that somebody recently wanted but the current Sage calculus didn't have:
sage: from sage.symbolic.function import function
sage: r, kappa = var('r,kappa', ns=1)
sage: psi = function('psi', 1)(r)
sage: g = 1/r^2*(2*r*psi.diff(r,1) + r^2*psi.diff(r,2)); g
(2*psi(1,r)*r + psi(2,r)*r^2)*r^(-2)
sage: g.coeff(psi.diff(r,2))
1
sage: g.coeff(psi.diff(r,1))
2*r^(-1)
See the directory SAGE_ROOT/devel/sage/sage/symbolic for nearly 500 lines of
input examples or point your browser here:
http://sage.math.washington.edu/home/was/d/sage/symbolic/
Let me know if you have any questions.
There are still a lot of questions that I didn't answer above. Including:
(a) who will do the actual work? (mainly Burcin at this point)
(b) what will the new design look like? How much
will change from the current symbolic calculus interface?
In particular, how are we ensuring that the many requests
from users in recent threads are addressed in this redesign?
(See http://wiki.sagemath.org/symbench)
(c) how does all this relate to the coercion model?
(That will help with, e.g., a symbolic complex number type.)
(d) what's the time frame for completely replacing the current calculus code?
(Two months?)
(e) how does this relate to sympy?
(I dont' know.
Sympy does several things Ginac doesn't, such as symbolic
integration and
sophisticated limits. I would like to find a way to somehow
reuse that code directly,
especially since sympy is in sage already, and is already often better
than using Sage's current maxima + pexpect symbolic manipulation.
On the other hand, Burcin is I think driven mostly by his Ph.D. thesis
research, and has told me he will only write GPL'd code, which means
it can't go into Sympy.)
(f) How did you rewrite ginac to work with Python objects?
(This basically involved creating
a hybrid Cython/C++ wrapper of Python's object system; this same technique
could be used to change Pari/Gap/Singular, etc. so they could
also manipulate
any Sage arithmetic data types, e.g., intervals, finite field
elements, flint
polynomials, etc. I'm not sure why nobody has done this before with Sage.)
(g) Are you proposing forking Ginac? (Ans: No, definitely not. We'll just
merge in their changes when they make new releases. It's a mature old
project, hence quite stable, so this should be easy, especially given the
high quality of their work.)
I think with polish and proper refereeing, the code Burcin and I have
already written should be included in Sage, so that others can start using it
and developing it further.
-- William
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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