diff --git a/lmfdb/number_fields/code.yaml b/lmfdb/number_fields/code.yaml index 739461e07c..b1c6dd243c 100644 --- a/lmfdb/number_fields/code.yaml +++ b/lmfdb/number_fields/code.yaml @@ -65,10 +65,13 @@ discriminant: oscar: OK = ring_of_integers(K); discriminant(OK) rd: + comment: Root discriminant sage: (K.disc().abs())^(1./K.degree()) pari: abs(K.disc)^(1/poldegree(K.pol)) magma: Abs(Discriminant(OK))^(1/Degree(K)); - oscar: (1.0 * dK)^(1/degree(K)) + oscar: | + OK = ring_of_integers(K); + (1.0 * abs(discriminant(OK)))^(1/degree(K)) automorphisms: comment: Autmorphisms @@ -81,7 +84,7 @@ ramified_primes: sage: K.disc().support() pari: factor(abs(K.disc))[,1]~ magma: PrimeDivisors(Discriminant(OK)); - oscar: prime_divisors(discriminant((OK))) + oscar: prime_divisors(discriminant(OK)) integral_basis: comment: Integral basis @@ -161,7 +164,7 @@ class_number_formula: 2^r1 * (2*Pi(RR))^r2 * RK * hK / (wK * Sqrt(RR!Abs(DK))); oscar: | # self-contained Oscar code snippet to compute the analytic class number formula - Qx, x = PolynomialRing(QQ); K, a = NumberField(%s); + Qx, x = polynomial_ring(QQ); K, a = number_field(%s); OK = ring_of_integers(K); DK = discriminant(OK); UK, fUK = unit_group(OK); clK, fclK = class_group(OK); r1,r2 = signature(K); RK = regulator(K); RR = parent(RK); @@ -173,12 +176,15 @@ galois_group: sage: K.galois_group(type='pari') pari: polgalois(K.pol) magma: G = GaloisGroup(K); - oscar: G, Gtx = galois_group(K); G, transitive_group_identification(G) + oscar: | + G, Gtx = galois_group(K); + degree(K) > 1 ? (G, transitive_group_identification(G)) : (G, nothing) + intermediate_fields: comment: Intermediate fields sage: K.subfields()[1:-1] - pari: L = nfsubfields(K); L[2..length(b)] + pari: L = nfsubfields(K); L[2..length(L)] magma: L := Subfields(K); L[2..#L]; oscar: subfields(K)[2:end-1] @@ -216,3 +222,5 @@ snippet_test: - oscar - gp url: NumberField/2.0.4.1/download/{lang} + +