On Sat, Mar 16, 2013 at 9:02 PM, David Li <li.david...@gmail.com> wrote: > Okay, I'll start on that once I manage to get the integration algorithm to > handle most problems that a high-school/freshman college student would > encounter. (Currently it won't handle any trig integrands involving more > than a u-substitution, and does not use integration by parts.)
Actually, trig integrals (like sin^n*cos^m) are one example of integrals that are computed exactly as you learned in calculus, via the reduction formula*. So you could look into extending trigintegrate to work with this. (*) With the caveat that if the integral is reduced to a rational function via a substitution, it is computed with ratint, which works nothing like the partial fractions that you learned in calculus. For example, the integral of tan(x) is reduced to the integral of u/(1 - u**2), where u = sin(x). Aaron Meurer > > Perhaps the derivative implementation doesn't need to be in SymPy? I haven't > seen a case yet where it provides a better result (usually it is less > simplified, especially when trigonometry is involved). Actually, you could argue for that. Once you generalize it to use diff automatically, it should just be a few lines, so perhaps it should just live entirely in SymPy Gamma. It can be a good example of what you can do with SymPy without editing library code. Aaron Meurer > > On Saturday, March 16, 2013 7:57:12 PM UTC-7, Aaron Meurer wrote: >> >> This is something SymPy wants. It's even on the GSoC ideas list. >> >> I would put the integration stuff in the integration module. As I >> pointed out on the pull request, what you really have here is a new >> integration heuristic, which can (should) be "integrated" with >> integrate() itself. It is already giving better results than >> integrate() for some integrals (namely the one you posted as your >> example). >> >> The diff code I'm not sure. I guess it could go in the same file for >> now. If you derive the rules automatically, then the code will be >> short (it will only consist of special cases like Add and Mul). >> >> In general, there are a lot of things that this could be applied to >> beyond diff() and integrate(): solve(), simplify(), the core (like x + >> x => 2*x). For some, the code could naturally live very close to the >> code that currently does the work. For others, the way that the >> algorithm works and the way it works "by hand" are much different. >> >> To be clear, the symbolic manipulation should go in SymPy. The part >> about the text "now make the u substitution u = exp(x)" or the css >> formatting should go in SymPy Gamma. The SymPy objects should be easy >> to parse into those things, but they should be intended for machine >> consumption more than human consumption. >> >> Aaron Meurer >> >> On Sat, Mar 16, 2013 at 8:47 PM, David Li <li.da...@gmail.com> wrote: >> > Alright, thank you for pointing out that typo. I've fixed it. >> > >> > I have finished porting; the code is still at the same place, >> > https://github.com/sympy/sympy_gamma/pull/8. If this is something SymPy >> > would want, how best should be integrated? Which module(s) does it >> > belong in >> > and what should the API be? >> > >> > On Saturday, March 16, 2013 6:34:22 AM UTC-7, Ramana Venkata wrote: >> >> >> >> Hi David, >> >> >> >> Great work. Just wanted to point you out one small thing in >> >> >> >> http://sympy-gamma-li.appspot.com/input/?i=integrate%28exp%28x%29%20/%20%281%20%2B%20exp%282x%29%29%29 >> >> In the first step after "Let u = e^x"; "then let du = e^x ..." But I >> >> think >> >> it be some thing like this "then du = e^x dx ..." >> >> >> >> >> >> On Thursday, March 14, 2013 8:52:25 PM UTC+5:30, David Li wrote: >> >>> >> >>> Hello all, >> >>> >> >>> I have implemented a module giving steps for most derivatives and some >> >>> integrals for SymPy Gamma. However, it was suggested that at least >> >>> some of >> >>> this functionality should be added to SymPy itself. If so, what >> >>> functionality should be added and how should it be integrated into >> >>> SymPy? >> >>> >> >>> The pull request is at https://github.com/sympy/sympy_gamma/pull/8. >> >>> There >> >>> is still some work left to do, which is listed in the pull request. In >> >>> particular, integral forms involving the application of trigonometric >> >>> identities need to be implemented. >> >>> >> >>> Examples: >> >>> >> >>> Integral involving arctangent and exponentiation: >> >>> >> >>> http://sympy-gamma-li.appspot.com/input/?i=integrate%28exp%28x%29%20/%20%281%20%2B%20exp%282x%29%29%29 >> >>> Trig integral involving u-substitution: >> >>> >> >>> http://sympy-gamma-li.appspot.com/input/?i=integrate%28sin%28sin+x%29cos+x%29 >> >>> Trig derivative: >> >>> http://sympy-gamma-li.appspot.com/input/?i=diff%28cot+sin+x%29 >> >>> >> >>> Implementation: >> >>> >> >>> The module builds a tree of rules to apply, with the first rule on the >> >>> top of the tree. Examples of rules would be AddRule, ChainRule, >> >>> RewriteRule, >> >>> AlternativeRule (in case multiple methods exist), and so on. Separate >> >>> functions apply the rules and return the resulting derivative or >> >>> integral >> >>> (currently derivatives and integrals are separate functions). A set of >> >>> classes walks the tree and generates steps for the rules; there is no >> >>> translation support but multiple output formats should work (currently >> >>> only >> >>> plaintext and HTML+LaTeX are implemented). >> >>> >> >>> The code makes use of context managers, which would need to be >> >>> replaced >> >>> in order to maintain Python 2.5 compatibility. >> >>> >> >>> Thank you, >> >>> David Li >> > >> > -- >> > 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 sympy+un...@googlegroups.com. >> > To post to this group, send email to sy...@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sympy?hl=en. >> > For more options, visit https://groups.google.com/groups/opt_out. >> > >> > > > -- > 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 sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at http://groups.google.com/group/sympy?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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