How to manipulate expressions in matrices using sympy?

I'm writing a library, and I can construct expressions using objects from my library. For example, x and y are instances from my library, and I can construct expressions like:

# below is a simplified version of my class 
class MySymbol(object):
    import random
    _random_value = random.randint(1,4)

    def __init__(self, value):
        self.value = value

    def __add__(self, symbol):
        return MySymbol(self.value + symbol.value)

    def __mul__(self, symbol):
        return MySymbol(self.value * symbol.value)

    def __repr__(self):
        return str(self.value)

    def _get_random_value(self):
        return self._random_value

x,y = sympy.symbols('x y')


x = MySymbol(9)
y = MySymbol(3)

import sympy
A = sympy.Matrix([[x,y],[x,y]])
B = sympy.Matrix([[x+y,x*y]])

This is also true for matrix operations. The sympy.Matrix class converts these elements to sympy.core.numbers.Integer , when I want them to maintain their type MySymbol :

BA=B*A
print type(BA[0,0])
print type(x*x+y*x+x*x*y) # first element of matrix in *symbolic* form

<class 'sympy.core.numbers.Integer'>
<class '__main__.MySymbol'>

Now, because BA[0,0] is not of type MySymbol anymore, I cannot call the methods I want on it:

BA[0,0]._get_random_value()  # DOES NOT WORK 
>> AttributeError: 'Integer' object has no attribute '_get_random_value'


expression = x*x+y*x+x*x*y
expression._get_random_value()   # THIS DOES WORK
>> 4

How do I take advantage of matrix multiplication from sympy.Matrix , but yet still allow the elements of the matrix to retain their class type of MySymbol ? and still allow all of their methods (such as _get_random_value() ) to be accessible?

---

You need to subclass from a SymPy class to use it within SymPy. Depending on what your class is doing will tell you what class to subclass, but the most typical superclass is Expr . See my answer to a very similar question here.

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