#11856: Raise an overflow error if the exponent of a multivariate polynomial
flows
over
-------------------------------------------------+--------------------------
Reporter: SimonKing | Owner: malb
Type: defect | Status:
positive_review
Priority: critical | Milestone: sage-4.7.2
Component: commutative algebra | Keywords: exponent
overflow
Work_issues: 32bit doctests | Upstream: N/A
Reviewer: Martin Albrecht, Alexander Dreyer | Author: Simon King
Merged: | Dependencies:
-------------------------------------------------+--------------------------
Old description:
> The following happens at least since sage-4.6.2 and was detected in #4539
> by a new doctest:
> {{{
> sage: P.<x,y> = QQ[]
> sage: y^2^30
> y^1073741824
> sage: P.<x,y,z> = QQ[]
> sage: y^2^30
> 0
> }}}
>
> According to Hans, the maximal exponent of a variable in a monomial does
> depend on the number of variables in the ring. There is no function that
> returns that maximal exponent, but it is stored in the `bitmask`
> attribute of a ring. The Singular interpreter actually only tests whether
> the ''total'' degree is below what is provided by bitmask; in theory,
> ''any'' exponent (not only the totall degree) can go up to that bound.
>
> Here is the corresponding code in Singular's `iparith.cc`:
> {{{
> static BOOLEAN jjTIMES_P(leftv res, leftv u, leftv v)
> {
> poly a;
> poly b;
> int dummy;
> if (v->next==NULL)
> {
> a=(poly)u->CopyD(POLY_CMD); // works also for VECTOR_CMD
> if (u->next==NULL)
> {
> b=(poly)v->CopyD(POLY_CMD); // works also for VECTOR_CMD
> if ((a!=NULL) && (b!=NULL)
> &&
> (pTotaldegree(a)+pTotaldegree(b)>si_max((long)rVar(currRing),(long)currRing->bitmask)))
> {
> Werror("OVERFLOW in mult(d=%ld, d=%ld, max=%ld)",
> pTotaldegree(a),pTotaldegree(b),currRing->bitmask);
> pDelete(&a);
> pDelete(&b);
> return TRUE;
> ...
> }}}
New description:
The following happens at least since sage-4.6.2 and was detected in #4539
by a new doctest:
{{{
sage: P.<x,y> = QQ[]
sage: y^2^30
y^1073741824
sage: P.<x,y,z> = QQ[]
sage: y^2^30
0
}}}
According to Hans, the maximal exponent of a variable in a monomial does
depend on the number of variables in the ring. There is no function that
returns that maximal exponent, but it is stored in the `bitmask` attribute
of a ring. The Singular interpreter actually only tests whether the
''total'' degree is below what is provided by bitmask; in theory, ''any''
exponent (not only the totall degree) can go up to that bound.
Here is the corresponding code in Singular's `iparith.cc`:
{{{
static BOOLEAN jjTIMES_P(leftv res, leftv u, leftv v)
{
poly a;
poly b;
int dummy;
if (v->next==NULL)
{
a=(poly)u->CopyD(POLY_CMD); // works also for VECTOR_CMD
if (u->next==NULL)
{
b=(poly)v->CopyD(POLY_CMD); // works also for VECTOR_CMD
if ((a!=NULL) && (b!=NULL)
&&
(pTotaldegree(a)+pTotaldegree(b)>si_max((long)rVar(currRing),(long)currRing->bitmask)))
{
Werror("OVERFLOW in mult(d=%ld, d=%ld, max=%ld)",
pTotaldegree(a),pTotaldegree(b),currRing->bitmask);
pDelete(&a);
pDelete(&b);
return TRUE;
...
}}}
Apply
* [attachment:trac11856_exponent_overflow.patch]
* [attachment:trac11856_fix_docs_32bit.patch Reviewer patch]
--
Comment(by SimonKing):
Let's try to sort things out:
The patch that Alexander posted at #4539 should better be a reviewer patch
here. Thus, I copied his patch, added a commit message, and posted it here
under a new name reflecting the ticket number. The positive review can be
kept (I hope we agree on that), and:
Apply trac11856_exponent_overflow.patch trac11856_fix_docs_32bit.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11856#comment:17>
Sage <http://www.sagemath.org>
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