The class group of a nonmaximal quadratic order R of discriminant m^2 D_K, are related to the class group of the maximal order O_K of fundamental discriminant D_K by an exact sequence.
1 -> ((O_K/mO_K)^ * /O_K^ * (Z/mZ)^ * ) -> Cl(O) -> Cl(O_K) -> 1
Similar maps exist between quadratic orders O_1 and O_2 in a field K, with conductors m_1 and m_2, respectively, such that m_1 | m_2. 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.
The quotient homomorphism from the class group of Q to the class group of fundamental discriminant.
Given two structures of quadratic forms Q_1 and Q_2, such that the discriminant of Q_2 equals a square times the discriminant of Q_1, the quotient homomorphism from Q_1 to Q_2 is returned as a map object.
The ! operator applies the quotient homomorphism for automatic coercion of forms of discriminant m^2D into the structure of forms of discriminant D.[Next][Prev] [Right] [Left] [Up] [Index] [Root]