Is there any recommend package to compute the integration of following？
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Is there any other package other than SymPy.jl that could do symbolic integration?
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I read the docs of Reduce.jl but it does not mention symbolic integration.
Better check the tutorials and books section of reduce itself
I only briefly used Reduce, and never the Julia interface package. So I’m afraid I can’t give you more help.
Good luck
Does ModelingToolkit or SymbolicUtilities have symbolic integration, otherwise I would look at SymEngine, then SymPy. (Maxima and Reduce are neat, but they have issues when using Weave, and I don’t think, that LISP is much faster than Python).
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SymPy is your best option, although it can have problems. Maxima is good, but better in it’s GUI. Reduce has a lot of problems. Modelling Tookit is the best option for derivatives, but it can’t do integration at this time. I’ll be sure to keep you posted on this. @ChrisRackauckas is in charge of ModelingToolkit, so he can tell you more.
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MTK, not yet. I have some cool ideas but right now they are ideas
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What is required for integration?
Just someone to do it. There is a symbolic integration now:
https://docs.sciml.ai/SymbolicNumericIntegration/dev/
We should get more standard methods too though.
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I get a strange result
using Symbolics
using SymbolicNumericIntegration
E(x)=(x^(3/2)/a^2)*exp(-(x/(2*a^2))) # the function provided
F(X)=integrate(E(x^2),(x,0,Inf);symbolic=true , detailed=false)
print(F(x))
gives me
\begin{equation}
- \infty e^{\frac{-\infty}{2 a^{2}}} + 2.0 a^{2} - 2.0 a^{2} e^{\frac{-\infty}{2 a^{2}}}
\end{equation}
sorry it’s in Tex, I can’t load a screenshot, but it’s not 2a^2 (I used a for theta)
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