Structures of binary quadratic forms are defined in terms of a discriminant, and membership in a structure determined by this invariant. To aid in the construction of forms, additional elementary functions are provided to test integer inputs to determine if they define valid discriminants of quadratic forms.
The discriminant b^2 - 4ac of a quadratic form f=aX^2 + bXY + cY^2.
The discriminant of the quadratic forms belonging to the magma.
Return true if D is the discriminant of some quadratic form; false otherwise.
The fundamental discriminant corresponding to D.
Return true if D is an integer other than 0 or 1 congruent to 0 or 1 modulo 4, which is not of the form m^2D_K for m > 1 and any other such integer D_K.
The conductor of quadratic forms whose discriminant is that of Q.[Next][Prev] [Right] [Left] [Up] [Index] [Root]