Matrix creation from a scalar fails in some cases

[vneiger]

Steps To Reproduce

Creating a matrix from a scalar (MA_ENTRIES_SCALAR flag from args.pyx), using code such as mat = matrix(ZZ, nrows, ncols, value), will unexpectedly fail in some cases. Such a call is supposed to build a diagonal matrix with value on the diagonal, and requires the matrix to be square (nrows == ncols) if value is nonzero. The issue is mainly that we cannot always successfully compare value to zero...

Consider the following example, inspired from a test in the doc for get_is_zero_unsafe in matrix0.pyx :

sage: class MyAlgebraicNumber(sage.rings.qqbar.AlgebraicNumber):
....:     def __bool__(self):
....:         raise ValueError
....:
sage: mat = matrix(1,1,MyAlgebraicNumber(1))
sage: mat
[1]
sage: mat = matrix(1,2,MyAlgebraicNumber(1))
### FAILS with ValueError ###

The failure is the same if using MyAlgebraicNumber(0).

Expected Behavior

The wanted behaviour is that such a call fails when nrows != ncols and value is not zero. The current error, for example if one does matrix(ZZ, 1, 2, 1) is TypeError("nonzero scalar matrix must be square"). If value happens to be zero, then the code just creates the zero matrix (even when nrows != ncols).

Actual Behavior

We get a value error, as below.

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [4], line 1
----> 1 mat = matrix(Integer(1),Integer(2),MyAlgebraicNumber(Integer(1)))

File ~/repositories/software/sage/src/sage/matrix/constructor.pyx:643, in sage.matrix.constructor.matrix()
    641 """
    642 immutable = kwds.pop('immutable', False)
--> 643 M = MatrixArgs(*args, **kwds).matrix()
    644 if immutable:
    645     M.set_immutable()

File ~/repositories/software/sage/src/sage/matrix/args.pyx:655, in sage.matrix.args.MatrixArgs.matrix()
    653     True
    654 """
--> 655 self.finalize()
    656
    657 cdef Matrix M

File ~/repositories/software/sage/src/sage/matrix/args.pyx:929, in sage.matrix.args.MatrixArgs.finalize()
    927 if self.typ == MA_ENTRIES_SCALAR:
    928     if self.nrows != self.ncols:
--> 929         if self.entries:
    930             raise TypeError("nonzero scalar matrix must be square")
    931         self.typ = MA_ENTRIES_ZERO

Cell In [1], line 3, in MyAlgebraicNumber.__bool__(self)
      2 def __bool__(self):
----> 3     raise ValueError

ValueError:

Additional Information

The culprit is the piece of finalize in args.pyx as highlighted in the above error message. I would suggest to correct the code so that it fails if the matrix is rectangular and value cannot be determined to be zero. So, on the above examples with both and , it would fail with a TypeError with a message such as "a scalar matrix must be square if it is nonzero or cannot be determined to be zero".

Environment

- **OS**: Ubuntu 22.04
- **Sage Version**: 10.1.beta9

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[vneiger]

Fixed via #36068