Large exponents overflow to negative in polydict ring

[broune]

Large exponents overflow to negative in polydict ring:

sage: from sage.rings.polynomial.multi_polynomial_ring import \
...       MPolynomialRing_polydict
sage: ring = MPolynomialRing_polydict(ZZ, 3, ['a','b','c'], "lex")
sage: a = ring.gens()[0]

sage: a^(2^31-1)
a^2147483647

sage: a^(2^31)
a^-2147483648

sage: a^(2^32)
1

[broune]

Fixed layout.

[was]

This is still a bug. Ick!

sage: R.<y,z> =Frac(QQ['x'])[]
sage: y^(2^32)
1
sage: y^(2^32-1)
y^-1
sage: y^(2^31)
y^-2147483648

[was]

Here is better input to replicate what is at the core of the problem:

sage: a = sage.rings.polynomial.polydict.PolyDict({(2147483647r,):1r})
sage: a*a
PolyDict with representation {(-2,): 1}

[broune]

This patch simply reports an error if this happens. I thought the polydict ring was supposed to allow arbitrary precision exponents.

[was]

This patch simply reports an error if this happens. I thought the polydict ring was supposed to allow arbitrary precision exponents.

Since in the entire Cython implementation of polydict, the exponents are represented internally as C ints there is no way it is supposed to represent arbitrary precision exponents. One could write something that does arbitrary exponents, but that ETuple stuff simply isn't such a thing.

[was]

By the way, for basic arithmetic, the symbolic ring supports arbitrary exponents.

sage: var('y')
y
sage: y^(2^32)
y^4294967296
sage: y^(2^50)
y^1125899906842624
sage: y^(2^50+y)
y^(y + 1125899906842624)

[wjp]

I added a new patch (to be applied instead of the old one) that also handles negative exponents. (The previous patch broke LaurentPolynomials?).

[spancratz]

This now passes all doctests.

[mvngu]

Merged  6428_ETuple_overflow.patch.