diff options
Diffstat (limited to 'src/algebra/prs.spad.pamphlet')
| -rw-r--r-- | src/algebra/prs.spad.pamphlet | 15 |
1 files changed, 5 insertions, 10 deletions
diff --git a/src/algebra/prs.spad.pamphlet b/src/algebra/prs.spad.pamphlet index 14a68daf..e117eb99 100644 --- a/src/algebra/prs.spad.pamphlet +++ b/src/algebra/prs.spad.pamphlet @@ -326,31 +326,27 @@ PseudoRemainderSequence(R, polR) : Specification == Implementation where Lazard(x : R, y : R, n : NNI) : R == zero?(n) => error("Lazard$PRS : n = 0") --- one?(n) => x - (n = 1) => x + one?(n) => x a : NNI := 1 while n >= (b := 2*a) repeat a := b c : R := x n := (n - a)::NNI repeat -- c = x**i / y**(i-1), i=n_0 quo a, a=2**? --- one?(a) => return c - (a = 1) => return c + one?(a) => return c a := a quo 2 c := ((c * c) exquo y)::R if n >= a then ( c := ((c * x) exquo y)::R ; n := (n - a)::NNI ) Lazard2(F : polR, x : R, y : R, n : NNI) : polR == zero?(n) => error("Lazard2$PRS : n = 0") --- one?(n) => F - (n = 1) => F + one?(n) => F x := Lazard(x, y, (n-1)::NNI) return ((x * F) exquo y)::polR Lazard3(V : Vector(polR), x : R, y : R, n : NNI) : Vector(polR) == -- computes x**(n-1) * V / y**(n-1) zero?(n) => error("Lazard2$prs : n = 0") --- one?(n) => V - (n = 1) => V + one?(n) => V x := Lazard(x, y, (n-1)::NNI) return ((x * V) exquo y) @@ -382,8 +378,7 @@ PseudoRemainderSequence(R, polR) : Specification == Implementation where (P, Q) := (VP.1, VQ.1) (lcP, c) := (LC(P), LC(Q)) e : NNI := degree(Q) --- if one?(delta := degree(P) - e) then -- algo_new - if ((delta := degree(P) - e) = 1) then -- algo_new + if one?(delta := degree(P) - e) then -- algo_new VP := c * VP - coefficient(P, e) * VQ VP := VP exquo lcP VP := c * (VP - X * VQ) + coefficient(Q, (e-1)::NNI) * VQ |