The problem with this method is that looking at all combinations becomes *very* inefficient for Muls with many terms. For example:
In [41]: %timeit integrate2(diff(x*sqrt(sin(x))), x) 1 2 1 2 1 2 1 2 1 loops, best of 3: 5.2 s per loop At the end of the day, you'll get even worse performance than the currently used heurisch, with a much lower success rate. That isn't to say that it isn't possible to make it more efficient, though. For computing symbolic integration by parts, I think some logic in the ODE module can be used, in particular, the exact ODE solver. For example: In [34]: print dsolve(diff(f(x)*x), simplify=False, hint='1st_exact') x*f(x) == C1 It's possible to recognize exact equations of any order, though solvers for them have not been implemented yet. But in general, if you are trying to integrate an expression with a symbolic f(x), converting it to a problem for dsolve() will give you better luck than integrate() (but of course, we really should "integrate" the two). Aaron Meurer On Thu, Jul 12, 2012 at 5:05 PM, pallab <pallabb...@gmail.com> wrote: > <code> > from sympy import * > import itertools as it > import operator as op > > def byparts(expr,x,depth=1): > print depth > hintarr=[] > if expr.is_Mul: > for part in it.combinations(expr.args,depth): > part=reduce(op.mul,part) > rest=simplify(expr/part) > part_int=integrate(part,x) > #print part_int,rest > hint=simplify(part_int*diff(rest,x)) > integral=rest*part_int > hintarr=hintarr+[(hint,integral)] > > hintarr=hintarr+[(x*diff(expr,x),x*expr)] > return(dict(hintarr)) > > def integrate2(expr,x,depth=1): > if expr.is_Add: > for part in expr.args: > rest=simplify(expr-part) > > for depth in range(1,len(part.args)+1): > byparts_dict=byparts(part,x,depth) > #print rest, list(byparts_dict) > if rest in byparts_dict: > return(byparts_dict[rest]) > <\code> > > > On Wednesday, July 11, 2012 1:23:01 PM UTC-4, pallab wrote: >> >> simple by parts integral can not be done: >> >> integrate(diff(x*f(x),x),x) >> >> >> also can not do simple integral like: >> >> integrate(diff(x*sqrt(sin(x)),x),x) >> >> >> best, >> >> Pallab >> > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To view this discussion on the web visit > https://groups.google.com/d/msg/sympy/-/kqWwCQXDF1YJ. > > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
