Matrix with expressions as elements

[Carlos Bouthelier Madre]

Hi, I have just started using sympy and I don't really know how to make this work. I've got functions that should return a matrix (I don't know if that is possible) whose elements are expressions of symbolic variables.  

This is my code, I've made a logical analysis of it (in pseudo-code) and it should do what I want to, the issue is that I am neither used to sympy variables nor to python syntaxis, so I would really appreciate your help. 

from sympy import *

from sympy import cos

from sympy.tensor.array import Array

from sympy import I, Matrix, symbols

from sympy import init_printing

from sympy import init_session

from IPython.display import display, Math, Latex

var('Tita1 Tita2 Tita3 Tita4 Tita5 Tita6 Beta eps', real=True)

def delta(n):

    f='Tita'+str(n)

    return sqrt(cos(f)*cos(f)*eps*eps+1)

def EF(i):

    return Matrix([[0,0],[0,2*delta(i)]])

ID=Matrix([[1,0],[0,1]])

def ExtDim(X,n):

    if n==1:

        return X

    else:

        return kron(ExtDim(X,n-1),ID)

def n_energy(n):

    if n==1:

        return EF(n)

    else:

        return kron(ID,n_energy(n-1))+ExtDim(EF(n),n) #This should be a matrix

Thanks in advance!

[Aaron Meurer]

Matrices can have expressions as elements. What does the code do when you run it? It doesn't run for me because kron is not defined.

Aaron Meurer

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[Carlos Bouthelier Madre]

Thanks for your message, Aaron!

I restarted my computer and it worked, not having changed a thing, so.... problem solved!

I have another problem though,  I have a function f(x) which I know has no primitive, but I want to define its integral from 0 to 2*pi, would python know what integrate(f(x),(x,0,2*pi)) means? Or, conversely, would it keep trying to get a primitive expression "indefinitely"? (I think this is what is happening) If so, does anybody know if there is another way to do this?

In fact , what I have is f(x1,x2,...xi,xi+1,....xn,Beta) and I want to define the integral of that function in the xi variables from i=1 to n iteratively (n is a value, like 10) from i=1 to N, obtaining an expression exclusively on Beta (I say this just in case it makes harder the use of an hypothetic method that could solve my problem )

Thanks in advance!!

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[Aaron Meurer]

If you use Integral() instead of integrate() it will keep the integral unevaluated. Otherwise, it will try to compute it, and if it cannot compute a closed-form expression, it will return an Integral object.

Aaron Meurer

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[Carlos Bouthelier Madre]

All right! Thanks again.

If later I would like to plot that integral(f(xi,Beta)*dxi) with Beta in the X axis, would it work?

[Aaron Meurer]

It should work, yes. plot() will evaluate the integral numerically.

Aaron Meurer

On Wed, May 3, 2017 at 4:58 PM, Carlos Bouthelier Madre <carlosbo...@gmail.com> wrote:

All right! Thanks again.

If later I would like to plot that integral(f(xi,Beta)*dxi) with Beta in the X axis, would it work?

El miércoles, 3 de mayo de 2017, 0:17:41 (UTC+2), Aaron Meurer escribió:

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