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Class Group Coercions

The class group of a nonmaximal quadratic order R of discriminant m2 DK, are related to the class group of the maximal order OK of fundamental discriminant DK by an exact sequence.

1 -> ((OK/mOK)^ * /OK^ * (Z/mZ)^ * ) -> Cl(O) -> Cl(OK) -> 1

Similar maps exist between quadratic orders O1 and O2 in a field K, with conductors m1 and m2, respectively, such that m1 | m2. The corresponding maps on quadratic forms are implemented on quadratic forms. The homomorphism is returned as a map object, or can be called directly via the coercion operator.

FundamentalQuotient(Q) : QuadBin -> Map
The quotient homomorphism from the class group of Q to the class group of fundamental discriminant.
QuotientMap(Q1, Q2) : QuadBin, QuadBin -> Map
Given two structures of quadratic forms Q1 and Q2, such that the discriminant of Q2 equals a square times the discriminant of Q1, the quotient homomorphism from Q1 to Q2 is returned as a map object.
Q ! f : QuadBin, QuadBinElt -> QuadBinElt
The ! operator applies the quotient homomorphism for automatic coercion of forms f of discriminant m2D into the structure Q of forms of discriminant D.
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013