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-rw-r--r--divers/sageries/resolvante-c4-dans-d415
1 files changed, 15 insertions, 0 deletions
diff --git a/divers/sageries/resolvante-c4-dans-d4 b/divers/sageries/resolvante-c4-dans-d4
new file mode 100644
index 0000000..5e7cfa4
--- /dev/null
+++ b/divers/sageries/resolvante-c4-dans-d4
@@ -0,0 +1,15 @@
+R.<z1,z2,z3,z4,p,a1,a2,a3,a4> = PolynomialRing(QQ,9,order='lex(4),lex(1),deglex(4)')
+asym1 = -(z1+z2+z3+z4)
+asym2 = +(z1*z2+z1*z3+z1*z4+z2*z3+z2*z4+z3*z4)
+asym3 = -(z1*z2*z3+z1*z2*z4+z1*z3*z4+z2*z3*z4)
+asym4 = +(z1*z2*z3*z4)
+Isym = R.ideal([a1-asym1, a2-asym2, a3-asym3, a4-asym4])
+pexpr = z1*z3+z2*z4
+Ip = R.ideal([p-pexpr])
+fexpr = z1*z2^2+z2*z3^2+z3*z4^2+z4*z1^2
+fexprConj = fexpr.subs({z1:z3,z3:z1})
+coef0 = fexpr*fexprConj
+coef1 = -(fexpr+fexprConj)
+B = (Isym+Ip).groebner_basis()
+coef1.reduce(B)
+coef0.reduce(B)