Why doesn't Sympy produce a numerical output?

Question

I am using sympy to solve a system of equations Ax=B and finding the matrix x . x is a 3 by 3 matrix, A and B are 3 by 4 matrices. The results are not numbers, but in the form of symbols. How can I obtain a numeric result?

Code:

import sympy as sp

X = sp.Matrix([[1,2,3,4],
               [5,6,7,8],
               [1,1,1,1]])

x = sp.Matrix([[5,6,7,8],
               [1,2,3,4],
               [1,1,1,1]])

a,b,c,d,e,f,g,h = sp.symbols('a,b,c,d,e,f,g,h')

M = sp.Matrix([[a,b,c],
               [d,e,f],
               [g,h,1]])

eq = solve(x-M.multiply(X),(a,b,c,d,e,f,g,h))
print(eq)

Output:

{a: c/4, b: 1 - c/4, d: f/4 + 1, e: -f/4, g: 0, h: 0}

Answer 1

The output of solve seems to indicate that there are infinity many solutions, and that you can use c and f as free parameters. To see your full matrix, and choosing some values for c and f , you could use:

M.subs(eq).subs({c:1, f:2}).evalf()

Result:

Matrix([
[0.25, 0.75, 1.0],
[ 1.5, -0.5, 2.0],
[   0,    0, 1.0]])

Here subs(eq) fill in the solution. subs({c:44, f:28}) fills in some values for c and f . evalf() creates a numerical result; this is needed when the expressions would contain fractions, square roots or other functions without evaluation.

For a more general approach, one could try to substitute all unassigned symbols with zero:

Ms = M.subs(eq)
Ms.subs({fr:0 for fr in Ms.free_symbols}).evalf()

Result:

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