Large exponents overflow to negative in polydict ring

[sagetrac-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

Component: commutative algebra

Author: Willem Jan Palenstijn

Reviewer: Sebastian Pancratz

Merged: sage-4.3.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/6428

[sagetrac-broune]

Description changed:

--- 
+++ 
@@ -1,16 +1,20 @@
 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<sup>(2</sup>31-1)
+sage: a^(2^31-1)
 a^2147483647
 
-sage: a<sup>(2</sup>31)
+sage: a^(2^31)
 a^-2147483648
 
-sage: a<sup>(2</sup>32)
+sage: a^(2^32)
 1
 
+```
+

[sagetrac-broune]

comment:1

Fixed layout.

[williamstein]

comment:3

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

[williamstein]

comment:4

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}

[williamstein]

Attachment: trac_6428.patch.gz

[sagetrac-broune]

comment:6

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

[williamstein]

comment:7

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.

[williamstein]

comment:8

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)