How to solve easy matrix equations thanks to sympy in python?

Question

Can you tell me why

import sympy as sym
import numpy as np

a=np.eye(3)*3
eq = sym.Eq(a*y,0)
sym.solve(eq, y)

Eror code is:
---------------------------------------------------------------------------
SympifyError                              Traceback (most recent call last)
<ipython-input-100-13919806323c> in <module>()
      4 a=np.eye(3)*3
      5 print(a)
----> 6 eq = sym.Eq(a*y,0)
      7 sym.solve(eq, y)

2 frames
/usr/local/lib/python3.7/dist-packages/sympy/core/sympify.py in sympify(a, locals, convert_xor, strict, rational, evaluate)
    432 
    433     if strict:
--> 434         raise SympifyError(a)
    435 
    436     if iterable(a):

SympifyError: SympifyError: array([[3.0*y, 0, 0],
       [0, 3.0*y, 0],
       [0, 0, 3.0*y]], dtype=object)

Doesn't work but

import sympy as sym
eq = sym.Eq(x**3 + 3*x**2 + 3*x + 1,0)
sym.solve(eq, x)

Works properly. And how can I solve easy matrix equations with similar code like up.

Of course both codes are my excises to understand this library

You should be very careful about mixing numpy and sympy like that. Use `a = sym.eye(3) * 3` instead. But I still don't see how you're supposed to make sense of `sym.Eq(a*y, 0)` unless the 0 is supposed to mean a zero matrix of size equal to the lhs of the equation. — Reti43, Oct 13 '21 at 11:25
In recent https://stackoverflow.com/questions/69533045/solve-attributeerror-immutabledensendimarray-object-has-no-attribute-as-ind I looked another attempt at use numpy and sympy — hpaulj, Oct 13 '21 at 14:47
See also [SymPy `solve` fails to solve Matrix equation A*x = b](https://stackoverflow.com/questions/54010664/sympy-solve-fails-to-solve-matrix-equation-ax-b-when-symbols-are-replaced-b) — JohanC, Oct 13 '21 at 18:49

hpaulj · Answer 1 · 2021-10-13T20:33:23.550

In [101]: a = np.eye(3)*3

In [103]: a*y
Out[103]: 
array([[3.0*y, 0, 0],
       [0, 3.0*y, 0],
       [0, 0, 3.0*y]], dtype=object)

It can be made into a sympy.Array:

In [104]: Array(a*y)
Out[104]: 
⎡3.0⋅y    0      0  ⎤
⎢                   ⎥
⎢  0    3.0⋅y    0  ⎥
⎢                   ⎥
⎣  0      0    3.0⋅y⎦

and Eq works, though it's unnecessary, since an expression is equal 0 (in solve) by default):

In [105]: Eq(_, 0)
Out[105]: 
⎡3.0⋅y    0      0  ⎤    
⎢                   ⎥    
⎢  0    3.0⋅y    0  ⎥ = 0
⎢                   ⎥    
⎣  0      0    3.0⋅y⎦

But apply solve to this results in the same error as the one I addressed previously:

In [106]: solve(Array(a*y))
---------------------------------------------------------------------------
...

AttributeError: 'ImmutableDenseNDimArray' object has no attribute 'as_independent'

solve(a*y) produces the same error.

SOLVE: AttributeError: 'ImmutableDenseNDimArray' object has no attribute 'as_independent'

That [105] array is not the same as: x**3 + 3*x**2 + 3*x + 1. Why did you expect it to work?

Also why did you use np.eye. sympy has an eye

In [128]: eq =  eye(3)*3*y
In [129]: eq
Out[129]: 
⎡3⋅y   0    0 ⎤
⎢             ⎥
⎢ 0   3⋅y   0 ⎥
⎢             ⎥
⎣ 0    0   3⋅y⎦
In [130]: Eq(eq,0)
Out[130]: False
In [131]: solve(eq,y)
Out[131]: {y: 0}

I only have a superficial understanding of what solve can use, but the difference in type might well be the key:

In [132]: type(eq)
Out[132]: sympy.matrices.dense.MutableDenseMatrix
In [133]: type(Out[104])
Out[133]: sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray
In [134]: Matrix(a*y)
Out[134]: 
⎡3.0⋅y    0      0  ⎤
⎢                   ⎥
⎢  0    3.0⋅y    0  ⎥
⎢                   ⎥
⎣  0      0    3.0⋅y⎦
In [135]: type(Matrix(a*y))
Out[135]: sympy.matrices.dense.MutableDenseMatrix

How to solve easy matrix equations thanks to sympy in python?

1 Answers1