Here's what I'm doing in a SymPy session:
from sympy import *
xi1,xi2,xi3 = symbols('xi_1,xi_2,xi_3')
N1 = 1-xi1-xi2-xi3
N2 = xi3
N3 = xi1
N4 = xi2
x1,x2,x3,x4 = symbols('x_1, x_2, x_3, x_4')
x = N1*x1+N2*x2+N3*x3+N2*x4
subdict = {x1:Matrix([0.025,1.0,0.0]), x2 : Matrix([0,1,0]), x3:Matrix([0, 0.975, 0]), x4:Matrix([0,0.975,0.025])}
x.subs(subdict)
test.subs({xi1:1, xi2:0,xi3:0})
To me we are simply multiplying some scalars with some vectors then adding them up. However SymPy would disagree and throws a ginormous error for which the last line is:
TypeError: cannot add <class 'sympy.matrices.immutable.ImmutableDenseMatrix'> and <class 'sympy.core.numbers.Zero'>
Why is this a problem? Is there a workaround for what I am trying to do?