> On Feb 8, 10:38 pm, ObsessiveMathsFreak
> <obsessivemathsfr...@gmail.com> wrote:
> > I have a certain integration result which Sage is currently unaware
> > of. I need a way to make sage aware of it in some fashion, via
> > substitution or anything else.
> >
> > For example, sage currently cannot perform the following integral
> >
> > sage: var(' k t')
> > sage: integrate(sqrt(1-k^2*sin(t)^2),t,0,pi/2)
> > integrate(sqrt(-k^2*sin(t)^2+1),t,0,pi/2)
> >
> > In fact, the integral defines the elliptice function E(k).
> >
> > Is there any way of substituting the unknown integral above for a
> > function like E(k) in sage? Can sage be programmed to recognise
> > such substitutions automatically?
If you find a reliable way to detect these expressions using the
pattern matching functionality, then you can define a function similar
to sage.symbolic.integration.external.maxima_integrator and add it to
the self.integrators list defined by IndefiniteIntegral and
DefiniteIntegral in sage/symbolic/integration/integral.py.
For pattern matching, this might be useful:
sage: var('a,b,c,t')
(a, b, c, t)
sage: ex = a*b^2*sin(t)^2 + c
sage: ex
a*b^2*sin(t)^2 + c
sage: w0 = SR.wild()
sage: ex.find(w0*sin(t)^2)
[a*b^2*sin(t)^2]
Cheers,
Burcin
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