Hi Aaron,
Thanks for your explanation.
How does SymPy evaluates integrals like,
*>>integrate((a + b*u)**m, x) when u = c + dx (*i.e. Integration by
substitution)
I couldn't find such an example can give one?
Abdullah Javed Nesar
On Sunday, March 5, 2017 at 11:58:20 AM UTC+5:30, Aaron Meurer wrote:
>
> The SymPy assumptions system lets you define x = Symbol('x',
> positive=True) (and query like x.is_positive). The pattern matcher
> will need to be able to set and define restrictions like this. Also
> note that expand_log() and logcombine() already expand and combine
> logarithms and check the domain restrictions.
>
> Another thing is that the integrator should return a Piecewise
> whenever possible. For example, the current integrator:
>
> In [6]: integrate(x**n, x)
> Out[6]:
> ⎧log(x) for n = -1
> ⎪
> ⎪ n + 1
> ⎨x
> ⎪────── otherwise
> ⎪n + 1
> ⎩
>
> This way we get results that are mathematically correct, even when
> assumptions aren't set.
>
> Aaron Meurer
>
> On Thu, Mar 2, 2017 at 8:56 AM, Abdullah Javed Nesar
> <[email protected] <javascript:>> wrote:
> > Hi Ondřej,
> >
> > I am willing to work on Rubi Integrator this summer. I went through the
> > issues you raised for this project and this idea really sounds cool. It
> > would be great to segregate the different methods of integration into a
> > decision tree which would hence improve its performance.
> >
> > Before implementing Rule-based integrator we need to implement fast
> pattern
> > matching/replacement for the set of 10,000 rules so we need to plan out
> an
> > efficient decision tree for it.
> >
> > log(x*y) -> log(x) + log(y); x > 0, y > 0
> >
> >
> > In the above example how do we exactly move on with domain restrictions
> > (i.e. x, y).
> >
> > On Wednesday, March 1, 2017 at 8:39:41 PM UTC+5:30, Ondřej Čertík wrote:
> >>
> >> Hi,
> >>
> >> Here is a project that I would love to see happen:
> >>
> >> https://github.com/sympy/sympy/issues/12233
> >>
> >> I am available to mentor it, and I think quite a few people are
> >> excited about it and such a system/framework (i.e. set of rules for
> >> patter matching + compiler to generate a fast if/then/else decision
> >> tree) would have applications beyond just integration, but integration
> >> would already be super useful. As you can browse on Rubi web page, the
> >> integrator's capabilities are very impressive, i.e. the rule based
> >> system Rubi 4.9 can do more integrals than Mathematica, and is about
> >> as fast, due to the large number of rules, and the if/then/else
> >> decision tree Rubi 5 promises an order of magnitude (or more) speedup,
> >> but it's still in development.
> >>
> >> The project is big in scope, so there could even be multiple projects.
> >> If anybody is interested in this, please get in touch, and try to
> >> propose a good plan.
> >>
> >> Ondrej
> >
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