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In the preceding article it is shown that algorithm EMGCD computes the matrix of polynomials M(j) = See Original U(0)=a(0)+a(1)x+...+a(n) x/n/ and U(1) = b(0)+b(1)x+...+b(m)x/m/, m/- r and deg U(j)+1 < r.
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Fast Computation of Polynomial Remainder Sequences
In the preceding article it is shown that algorithm EMGCD
computes the matrix of polynomials M(j) =
U(0)=a(0)+a(1)x+...+a(n) x/n/ and U(1) = b(0)+b(1)x+...+b(m)x/m/, m<n
are input polynomials. The function l, is defined by j=l(r), where r
is a rational number and j is the unique integer such that
deg U(j) >/- r
deg U(j)+1 < r.
This article describes algorithm PRSDC (polynomial remainder sequence
divided and conquer) which computes See Original for j - l(r) where 0 ,/- r,/-n.
Thus, by proper choice or r one can obtain two arbitrary successive terms in the
PRS sequence defined by U(0) and U(1). Algorithm EMGCD only computes M(j)
when r = n over 2.
To compute M(i) for any r we make use of a subroutine, called by PRSDC,
named PRSDC1. Algorithm PRSDC is the first fast 0(n log/2/n) algorithm to
compute any two successive terms in the PRS sequence of two polynomials U(0)
and U(1). By choosing r=0, we compute U(j+1) = 0,U(j) = gcd (U(0),U(1)). See
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