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 January 30th, 2012, 06:35 AM #1 Newbie   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 n-1: dn-1(x) = bn-2 (x) dn-2 (x) + an (x) pn (x) dn-1 (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, 04:51 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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, 04:46 AM   #3
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Re: maple procedure

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 Originally Posted by CRGreathouse Unfortunately I don't know Maple, but your procedure looks correct. I suspect you will need to use gcdex.
I can not use the predefined functions, Unfortunately few people know about maple, however I would be fine also an implementation in MATLAB, thank you very much for the response

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