Symbolic integration

New to Julia
,
1

Is there any recommend package to compute the integration of following？
image

2

SymPy?

3

Is there any other package other than SymPy.jl that could do symbolic integration?

4

Try with Reduce.jl

5

I read the docs of Reduce.jl but it does not mention symbolic integration.

6

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

7

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).

8

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.

9

MTK, not yet. I have some cool ideas but right now they are ideas

10

What is required for integration?

11

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.

12

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)

13

open an issue