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author committer David A. Madore 2011-11-25 18:05:31 +0100 David A. Madore 2011-11-25 18:05:31 +0100 67b5d565ff54baf8c5cf2ed136efc8e0ba87717c (patch) 3a685da2ce86dc4eb31fca0c0be5b99b9968eaff /divers/sageries 13edc3ed9beb69c0da42c6ffff303ccc2627ee66 (diff) galois-67b5d565ff54baf8c5cf2ed136efc8e0ba87717c.tar.gzgalois-67b5d565ff54baf8c5cf2ed136efc8e0ba87717c.tar.bz2galois-67b5d565ff54baf8c5cf2ed136efc8e0ba87717c.zip
Plus de sageries.
Diffstat (limited to 'divers/sageries')
-rw-r--r--divers/sageries/resolvante-d5-dans-m2023
1 files changed, 13 insertions, 10 deletions
 diff --git a/divers/sageries/resolvante-d5-dans-m20 b/divers/sageries/resolvante-d5-dans-m20index 7c7f956..2d15b9f 100644--- a/divers/sageries/resolvante-d5-dans-m20+++ b/divers/sageries/resolvante-d5-dans-m20@@ -49,9 +49,9 @@ Iq = R.ideal([q-qexpr]) B = (Isym+Iq).groebner_basis() pexpr.reduce(B) -### Encore une tentative...+### Essayons avec de l'algèbre linéaire e = SymmetricFunctionAlgebra(QQ, basis='elementary')-R. = PolynomialRing(QQ,11,order='lex(1),lex(5),deglex(5)')+R. = PolynomialRing(QQ,10,order='lex(5),deglex(5)') asym1 = -e([1]).expand(5).subs(x0=z1,x1=z2,x2=z3,x3=z4,x4=z5) asym2 = +e([2]).expand(5).subs(x0=z1,x1=z2,x2=z3,x3=z4,x4=z5) asym3 = -e([3]).expand(5).subs(x0=z1,x1=z2,x2=z3,x3=z4,x4=z5)@@ -60,12 +60,15 @@ asym5 = -e([5]).expand(5).subs(x0=z1,x1=z2,x2=z3,x3=z4,x4=z5) Isym = R.ideal([a1-asym1, a2-asym2, a3-asym3, a4-asym4, a5-asym5]) pexpr = z1^2*(z2*z5 + z3*z4) + z2^2*(z1*z3 + z4*z5) + z3^2*(z1*z5 + z2*z4) + z4^2*(z1*z2 + z3*z5) + z5^2*(z1*z4 + z2*z3) qexpr = z1*z2 + z2*z3 + z3*z4 + z4*z5 + z1*z5-tmp = (x-pexpr)*(x-pexpr).subs({z4:z5,z5:z4})-presful = tmp*tmp.subs({z1:z2,z2:z3,z3:z1})*tmp.subs({z1:z3,z2:z1,z3:z2})-tmp0 = (x-qexpr)*(x-qexpr).subs({z1:z2,z2:z4,z4:z3,z3:z1})-tmp = tmp0*tmp0.subs({z4:z5,z5:z4})-qresful = tmp*tmp.subs({z1:z2,z2:z3,z3:z1})*tmp.subs({z1:z3,z2:z1,z3:z2})+dexpr = (z1-z2)*(z1-z3)*(z1-z4)*(z2-z3)*(z2-z4)*(z3-z4) B = Isym.groebner_basis()-pres = presful.reduce(B)-qres = qresful.reduce(B)-# Mais que faire ensuite ?+def debase(r):+ return [r.coefficient({z1:0,z2:i2,z3:i3,z4:i4,z5:i5}) for i2 in range(2) for i3 in range(3) for i4 in range(4) for i5 in range(5)]++qtab = [debase((qexpr^i).reduce(B)) for i in range(12)]+pdtab = [debase((pexpr^i*dexpr^j).reduce(B)) for i in range(6) for j in range(2)]+qmat = matrix(R, 12, 120, qtab)+pdmat = matrix(R, 12, 120, pdtab)+cols = [0, 10, 105, 84, 109, 119, 57, 91, 111, 90, 110, 15]+qsubmat = qmat[range(12),cols]+pdsubmat = pdmat[range(12),cols]