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January 30th, 2012, 07:35 AM  #1 
Joined: Jan 2012 Posts: 2 Thanks: 0  maple procedure
hi, i'm an italian student and i don't speak english very well, but i hope that you understand me. I need help with an exercise of maple. The exercise is Writing a procedure that have: INPUT: a list of polynomials OUTPUT: the gcd of this list of polynomials; the gcd must be expressed as a Q [x]linear combination to some of the elements of the list. The method that came to my mind is the following: STEP I: I find the gcd between p1(x) and p2(x) by the Bezout identity: d1(x) = a1(x) p1(x) + a2(x) p2(x) STEP II find the GCD of d1(x) and p3(x) by Bezout identity: d2(x) = b1(x) d1(x) + a3(x) p3(x) STEP III I find the GCD of d2(x) and p4(x) by Bezout identity: d3(x) = b2(x) d2 (x) + a4(x) p4 (x) Iterating the process we get to STEP n1: dn1(x) = bn2 (x) dn2 (x) + an (x) pn (x) dn1 (x) = gcd (p1 (x), ..., pn (x)) To obtain a linear combination of polynomials p1(x), ..., pn (x), i replace the first identity in the second identity: d1(x)=a1(x)p1(x)+a2(x)p2(x) d2(x)=b1(x)(a1(x)p1(x)+a2(x)p2(x))+a3(x)p3(x) (we note that this expression does not depend about d1 (x)) proceeding in this way we have that the GCD will be expressed as a linear combination of polynomials p1(x), ..., pn (x) Anyone know how to implement this method in maple? Excuse me for my broken english, but i'm italian ^^, thank you very mutch, See you soon 
February 1st, 2012, 05:51 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 13,431 Thanks: 258 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic  Re: maple procedure
Unfortunately I don't know Maple, but your procedure looks correct. I suspect you will need to use gcdex. 
February 2nd, 2012, 05:46 AM  #3  
Joined: Jan 2012 Posts: 2 Thanks: 0  Re: maple procedure Quote:
 

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