Inverting symbolic matrix from NumPy complex array raises MACSYMA-QUIT error #42608

Steps To Reproduce

import numpy as np

a = np.zeros((5, 5), dtype="complex")
np.fill_diagonal(a, 1)

x = var("x")

b = x * a
c = matrix(b)

c.inverse()

Expected Behavior

The inverse should be returned successfully.

[1/x   0    0    0    0]
[0   1/x    0    0    0]
[0     0  1/x    0    0]
[0     0    0  1/x    0]
[0     0    0    0  1/x]

Actual Behavior

Instead, Sage raises

RuntimeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined.

During handling of the above exception, another exception occurred:

TypeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined.

Paste the complete traceback here.

Additional Information

Working Alternative

Converting the NumPy array to a Sage matrix before symbolic multiplication avoids the problem.

import numpy as np

a = np.zeros((5, 5), dtype="complex")
np.fill_diagonal(a, 1)

x = var("x")

b = matrix(a)
c = x * b

c.inverse()

Output

[1/x   0    0    0    0]
[0   1/x    0    0    0]
[0     0  1/x    0    0]
[0     0    0  1/x    0]
[0     0    0    0  1/x]

Observations

The only difference is the order of operations.

Fails

matrix(x * numpy_array)

Works

x * matrix(numpy_array)

This suggests the failure occurs while converting a symbolic NumPy complex array into a Sage matrix.

Possible Cause

NumPy represents the imaginary unit using Python's 1j, whereas Sage represents it as I.

When a symbolic NumPy complex array is converted into a Sage matrix, Maxima appears unable to interpret the mixed representation correctly, eventually leading to the MACSYMA-QUIT error during symbolic inversion.

Environment

• OS: Ubuntu 22.04
• Sage Version: 9.2 – 10.10.beta6
• Python: 3.x

Related Discussion

https://ask.sagemath.org/question/56850/issue-with-inversion-of-complex-symbolic-array-initialized