The way I'd do this is: - Write down all possible ways to rewrite expressions. These could be patterns which are unified against the expression, or just functions which are applied to an expression. - Have a system which goes through all subexpressions and applies these until it finds what it is looking for. - Since this gets combinatorially large fast, have some way to "hint" which methods are better to try and in what order.
I think the second part already exists, somewhere in the strategies module. Matthew Rocklin would be able to answer the best. But I think this is a very hard problem as it is, because although what I described is simple, without any limitations, it gets combinatorially impossible. For example, an addition of n terms has 2**n sub-expressions of just taking all possible combinations of terms to make smaller additions (that doesn't even count the subexpressions of the terms themselves). That also doesn't consider that you might want to consider something like x + x as a "subexpression" of 3*x. For the s1 = x + y example, you can let x = s1 - y and substitute this in the expression, and simplify it to get s1**2. Aaron Meurer On Sat, Aug 23, 2014 at 11:45 AM, F. B. <[email protected]> wrote: > I think your problem is a bit general, and it requires a combination of > tools. > > On Saturday, August 23, 2014 1:38:36 AM UTC+2, Ondřej Čertík wrote: >> >> Some examples: >> >> e = x^2+2*x*y+*y*^2 >> s1 = x+y >> > > Maybe this could be done using a solver, the condition *e-s1* being true > for all *x, y*? > > Mathematica has this: > http://reference.wolfram.com/language/ref/SolveAlways.html > > Is there anything like that in SymPy? > > >> e = c*Integral(x**2, (x, a, b)) >> s1 = Integral(sin(y)**2, (y, asin(a), asin(b))) >> # I hope I substituted correctly >> >> > Maybe this could be tackled by > > - a structural unification yielding all incompatible subtrees pairs > (in this case: [(x**2, sin(y)**2), (a, asin(a)), (b, asin(b)], > - relabeling the vars from the e expression: [(x_e**2, sin(y)**2), > (a_e, asin(a)), (b_e, asin(b)] > - matching all pairs but something similar to Mathematica's > SolveAlways or some other clever usage of a solver. > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/9166b421-24f9-45eb-918c-c697b2e2e451%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/9166b421-24f9-45eb-918c-c697b2e2e451%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6KRnedGTM9RqpViPQiOa4KSdfcHBVQpVyg4GGwJ4YinSA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
