Raising fmpz_mpolys to negative fmpz powers crashes interpreter

[antieau]

The following is the output of a short session which crashes the Python interpreter. This is in version 0.7.0a5 in Python 3.12.3 on OSX Sonoma 14.1. One can raise p to flint.fmpz(2) and it correctly raises a ValueError when attempting to raise p to (-2). But, it crashes when attempting to raise p to flint.fmpz(-2).

>>> import flint
>>> ctx = flint.fmpz_mpoly_ctx.get(('x', 2), 'lex')
>>> p = ctx.from_dict({(0, 3): 2, (2, 1): 3})
>>> p ** flint.fmpz(2)
9*x0^4*x1^2 + 12*x0^2*x1^4 + 4*x1^6
>>> p ** (-2)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "flint_base.pyx", line 663, in flint.flint_base.flint_base.flint_mpoly.__pow__
ValueError: cannot raise to a negative power
>>> p ** flint.fmpz(-2)
Flint exception (General error):
    Negative power in fmpz_mpoly_pow_fmpzzsh: abort      python

[oscarbenjamin]

Thanks for testing and reporting this. The expected behaviour here should be like for univariate polynomials:

In [1]: import flint

In [2]: x = flint.fmpz_poly([0, 1])

In [3]: one = flint.fmpz_poly([1])

In [4]: x**-1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[4], line 1
----> 1 x**-1

File fmpz_poly.pyx:351, in flint.types.fmpz_poly.fmpz_poly.__pow__()

ValueError: fmpz_poly negative exponent

In [5]: 1/one
Out[5]: 1

In [6]: 1/(2*one)
---------------------------------------------------------------------------
DomainError                               Traceback (most recent call last)
Cell In[6], line 1
----> 1 1/(2*one)

File fmpz_poly.pyx:283, in flint.types.fmpz_poly.fmpz_poly.__rtruediv__()

File fmpz_poly.pyx:268, in flint.types.fmpz_poly.fmpz_poly.__truediv__()

DomainError: fmpz_poly division is not exact

In [7]: one = flint.fmpq_poly([1])

In [8]: 1/(2*one)
Out[8]: 1/2

In [9]: type(_)
Out[9]: flint.types.fmpq_poly.fmpq_poly

In other words negative powers are allowed if they are defined within the domain meaning that negative powers can be computed if the polynomial is equal to a unit in the ring of coefficients.

[oscarbenjamin]

Fixed in gh-269