Axiom Computer Algebra System - Bugs: bug #10530, exquo and therefore gcd cannot...
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bug #10530: exquo and therefore gcd cannot handle UP(x, EXPR INT)
Submitter: | Martin Rubey <kratt6> | ||
Submitted: | Wed 29 Sep 2004 03:36:55 PM UTC | ||
Category: | algebra | Severity: | 3 - Normal |
Item Group: | code bug | Status: | transferred |
Privacy: | Public | Assigned to: | None |
Originator Name: | Open/Closed: | Open | |
Release: | Reproducibility: | None | |
Fixed Release: | |||
Error message: |
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Example of code trigerring the bug: | gcd((A-2^a)::UP(A, EXPR INT),(A^2-2^(2*a))::UP(A, EXPR INT)) |
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Internal cause: | In EXPR INT, 2^a and 2^(2*a) are treated as two variables without relations in EXPR INT. Therefore exquo in gcdPrimitive(p1:SUPP,p2:SUPP)$PGCD fails. |
Thu 30 Sep 2004 09:31:59 AM UTC, comment #3: |
Martin Rubey <kratt6> |
Wed 29 Sep 2004 04:20:16 PM UTC, comment #2:
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Martin Rubey <kratt6> |
Wed 29 Sep 2004 04:02:03 PM UTC, comment #1: I should have added: |
Martin Rubey <kratt6> |
Wed 29 Sep 2004 03:36:55 PM UTC, original submission:
gcd((x-2^a)::UP(x, EXPR INT), simplify((x-2^a)*(x+2^a))::UP(x, EXPR INT)) |
Martin Rubey <kratt6> |
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Follows 1 latest change.
Date | Changed by | Updated Field | Previous Value | => | Replaced by |
---|---|---|---|---|---|
2005-07-11 | billpage1 | Status | None | ![]() |
transferred |
Excuse me, I was to quick again. Here is the (hopefully correct) anaylysis:
exquo(simplify((A-2^a)*(A+2^a))::UP(A,EXPR INT),(A-2^a)::UP(A,EXPR INT))
calls exquo$SUP(EXPR INT). This implements exact division of polynomials p1 by p2 as usual. After each subtraction - done via fmecg$SUP - the result is again stored in p1. exquo terminates when p1 is the empty list - note that SUPs are stored as lists of pairs (degree, coefficient) - or the degree of p2 is larger than p1. In the latter case, exquo fails.
Thus, in our case, at one point p1 is 4^a-2^(2*a), which is zero mathematically, but axiom does not know it. In particular, p1 is not the empty list, but rather a constant polynomial...
It would be interesting to see how MuPAD or Aldor handle this.