Expanding MatAdd or MatMul Expressions

[Curtis McCully]

I am trying to use sympy to visualize some complicated recursive functions that include matrices (albeit small 2x2 matrices). I would like to be able to expand an equation term by term. However, when I use the expand function I get the error 'MatAdd' object has no attribute 'expand'. Below is a copy of an IPython notebook illustrating what I am trying to do. Is there a way to do this? Thanks.

In [1]:

from sympy import *

init_printing()

In [16]:

I2 = Identity(2)

In [17]:

def k(i): return Symbol('kappa%i'%i)

In [62]:

def G(i): 

    if i in voids:

        g = k(i) * I2

    elif i==l:

        g = 0 * I2

    else:

        g = MatrixSymbol('Gamma%i'%i, 2,2)

    return g

In [19]:

def beta(i,j): 

    if j == s: b = 1

    else: b = Symbol('beta%i%i'%(i,j))

    return b

In [82]:

l = 5

s = 6

voids = [3,4]

In [31]:

def B(j):

    if j == 1:

        b = eye(2)

    else: 

        for i in range(1,j): 

            if i == 1: 

                sumval = beta(i,j) * G(i) * B(i)

            else: 

                sumval += simplify(beta(i,j)* G(i) * B(i))

        b = I2 - sumval

    return simplify(b)

In [45]:

B(1)

Out[45]:

[1001]

In [46]:

B(2)

Out[46]:

(−β12κ1+1)𝕀

In [81]:

B(4)

Out[81]:

𝕀+−1(β14Γ1+β24κ2(𝕀+−β12Γ1)+β34κ3(𝕀+−1(β13Γ1+β23κ2(𝕀+−β12Γ1))))

In [88]:

expand(B(4))

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-88-a23836119fe0> in <module>()
----> 1 expand(B(4))

/usr/local/astro64/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/sympy/core/function.pyc in expand(e, deep, modulus, power_base, power_exp, mul, log, multinomial, basic, **hints)
   1969     hints['multinomial'] = multinomial
   1970     hints['basic'] = basic
-> 1971     return sympify(e).expand(deep=deep, modulus=modulus, **hints)
   1972 
   1973 # These are simple wrappers around single hints.

AttributeError: 'MatAdd' object has no attribute 'expand'

[Ondřej Čertík]

Hi Curtis,

On Thu, Oct 2, 2014 at 12:31 PM, Curtis McCully <curtis...@gmail.com> wrote:
> I am trying to use sympy to visualize some complicated recursive functions
> that include matrices (albeit small 2x2 matrices). I would like to be able
> to expand an equation term by term. However, when I use the expand function
> I get the error 'MatAdd' object has no attribute 'expand'. Below is a copy
> of an IPython notebook illustrating what I am trying to do. Is there a way
> to do this? Thanks.

Would you mind posting the notebook into http://nbviewer.ipython.org/
so that we can play with it more easily?

Thanks,
Ondrej

[Curtis McCully]

Hi Ondrej,

How is this?

http://nbviewer.ipython.org/github/cmccully/multiplane_lensing/blob/master/mp.ipynb

Curtis