If I define the following equation
import sympy as sp
x00, x01, x02 = sp.symbols('x_{00} x_{01} x_{02}')
x10, x11, x12 = sp.symbols('x_{10} x_{11} x_{12}')
x20, x21, x22 = sp.symbols('x_{20} x_{21} x_{22}')
px0, px1, px2 = sp.symbols('p_{x0} p_{x1} p_{x2}')
py0, py1, py2 = sp.symbols('p_{y0} p_{y1} p_{y2}')
Z = sp.Matrix([ [x00, x01, x02],
[x10, x11, x12],
[x20, x21, x22]])
px = sp.Matrix([px0, px1, px2])
py = sp.Matrix([py0, py1, py2])
expr = (py.T * Z * px)[0, 0]
print(expr.coeff(x00))
print(expr.coeff(px0))
I get the output
0
p_{y0}*x_{00} + p_{y1}*x_{10} + p_{y2}*x_{20}
Why is sympy returning the correct output for px0 but not for x00?
You need to expand before calling coeff:
In [20]: x, y, z = symbols('x, y, z')
In [12]: expr = x*(y + z)
In [13]: expr
Out[13]: x⋅(y + z)
In [14]: expr.coeff(x)
Out[14]: y + z
In [15]: expr.coeff(y) # y does not appear at top level
Out[15]: 0
In [16]: expr.expand() # Now y and z are at top level
Out[16]: x⋅y + x⋅z
In [17]: expr.expand().coeff(x)
Out[17]: y + z
In [18]: expr.expand().coeff(y)
Out[18]: x
In [19]: expr.expand().coeff(z)
Out[19]: x