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author committer David A. Madore 2011-06-22 18:23:12 +0200 David A. Madore 2011-06-22 18:23:12 +0200 befb691798a765506066c0f589056d6b0b5b5a31 (patch) f4fd46c808f85dbc6bdb3e3dadad3321a93ccba7 /divers 60b9d8e60bbc32319871bcf41eb4629cc6396d46 (diff) galois-befb691798a765506066c0f589056d6b0b5b5a31.tar.gzgalois-befb691798a765506066c0f589056d6b0b5b5a31.tar.bz2galois-befb691798a765506066c0f589056d6b0b5b5a31.zip
[calculs] Résolvante sextique d'un polynôme de degré 5 (pour tester si le groupe de Galois est inclus dans M_20).
Bon, il va falloir arrêter le concours de gros polynômes explicites, à la fin, quand même.
Diffstat (limited to 'divers')
-rw-r--r--divers/sageries/resolvante-m2013
1 files changed, 13 insertions, 0 deletions
 diff --git a/divers/sageries/resolvante-m20 b/divers/sageries/resolvante-m20new file mode 100644index 0000000..15e18c0--- /dev/null+++ b/divers/sageries/resolvante-m20@@ -0,0 +1,13 @@+e = SymmetricFunctionAlgebra(QQ, basis='elementary')+R. = PolynomialRing(QQ,11,order='lex(1),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)+asym4 = +e([4]).expand(5).subs(x0=z1,x1=z2,x2=z3,x3=z4,x4=z5)+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])+p = 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)+tmp = (x-p)*(x-p).subs({z4:z5,z5:z4})+res = tmp*tmp.subs({z1:z2,z2:z3,z3:z1})*tmp.subs({z1:z3,z2:z1,z3:z2})+B = Isym.groebner_basis()+res0 = res.reduce(B)