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January 30th, 2012, 07:35 AM   #1
 
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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
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February 1st, 2012, 05:51 AM   #2
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Re: maple procedure

Unfortunately I don't know Maple, but your procedure looks correct.

I suspect you will need to use gcdex.
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February 2nd, 2012, 05:46 AM   #3
 
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Re: maple procedure

Quote:
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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