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: 


Example of code trigerring the bug:  gcd((A2^a)::UP(A, EXPR INT),(A^22^(2*a))::UP(A, EXPR INT)) 

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:

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((x2^a)::UP(x, EXPR INT), simplify((x2^a)*(x+2^a))::UP(x, EXPR INT)) 
Martin Rubey <kratt6> 
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Date  Changed by  Updated Field  Previous Value  =>  Replaced by 

20050711  billpage1  Status  None  transferred 
Excuse me, I was to quick again. Here is the (hopefully correct) anaylysis:
exquo(simplify((A2^a)*(A+2^a))::UP(A,EXPR INT),(A2^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^a2^(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.