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| author | David A. Madore <david+git@madore.org> | 2012-04-05 16:19:50 (GMT) |
|---|---|---|
| committer | David A. Madore <david+git@madore.org> | 2012-04-05 16:19:50 (GMT) |
| commit | 88d0c083cfaeb70a62eda27b3e2850b9ece99110 (patch) | |
| tree | 69d569b0c0d7f4c2ca60f0b75d5ee2f75e16da5c /divers | |
| parent | d0f8d4a92d6eab284eb333d4e89f525c13295d12 (diff) | |
| download | galois-88d0c083cfaeb70a62eda27b3e2850b9ece99110.zip galois-88d0c083cfaeb70a62eda27b3e2850b9ece99110.tar.gz galois-88d0c083cfaeb70a62eda27b3e2850b9ece99110.tar.bz2 | |
[radicaux] Changement de base pour l'expression de cos(2π/19).
Diffstat (limited to 'divers')
| -rw-r--r-- | divers/sageries/racine-19e-de-1 | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/divers/sageries/racine-19e-de-1 b/divers/sageries/racine-19e-de-1 index b9aa12c..35e6b07 100644 --- a/divers/sageries/racine-19e-de-1 +++ b/divers/sageries/racine-19e-de-1 @@ -6,13 +6,13 @@ powtab = [NN(18/gcd(i,18)) for i in range(18)] atab = [alpha[i]^powtab[i] for i in range(18)] atab_on_zeta_basis = [(QQ^6)((zeta.coordinates_in_terms_of_powers())(x)) for x in atab] sqrtm3 = 2*zeta^3-1 -nice_basis = [1, sqrtm3, zeta, zeta^-1, -sqrtm3*zeta^5, sqrtm3*zeta^-5] +nice_basis = [1, sqrtm3, zeta^2, zeta^-2, zeta, zeta^-1] m = Matrix(QQ, 6, 6, [(QQ^6)((zeta.coordinates_in_terms_of_powers())(x)) for x in nice_basis]) atab_on_nice_basis = [v * m.inverse() for v in atab_on_zeta_basis] zetab = [ZZ(floor(arg(CC(N(alpha[i])/N(atab[i]^(1/powtab[i]))))/arg(zeta)+0.5)) for i in range(18)] btab = [zeta^zetab[i] for i in range(18)] btab_on_zeta_basis = [(QQ^6)((zeta.coordinates_in_terms_of_powers())(x)) for x in btab] btab_on_nice_basis = [v * m.inverse() for v in btab_on_zeta_basis] -symbolic_basis = [1, sqrt(-3), ((1/2)*(1+sqrt(-3)))^(1/3), ((1/2)*(1-sqrt(-3)))^(1/3), ((1/2)*(9+3*sqrt(-3)))^(1/3), ((1/2)*(9-3*sqrt(-3)))^(1/3)] +symbolic_basis = [1, sqrt(-3), ((1/2)*(-1+sqrt(-3)))^(1/3), ((1/2)*(-1-sqrt(-3)))^(1/3), ((1/2)*(1+sqrt(-3)))^(1/3), ((1/2)*(1-sqrt(-3)))^(1/3)] symbolic_omega = sum([sum([btab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(6)])*(sum([atab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(6)]))^(1/powtab[i]) for i in range(18)])/18 symbolic_cos = sum([sum([btab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(6)])*(sum([atab_on_nice_basis[i][j]*symbolic_basis[j] for j in range(6)]))^(1/powtab[i]) for i in range(0,18,2)])/18 |