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Basic Invariants

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.

Discriminant(f) : QuadBinElt -> RngIntElt
The discriminant b^2 - 4ac of a quadratic form f=aX^2 + bXY + cY^2.
Discriminant(Q) : QuadBin -> RngIntElt
The discriminant of the quadratic forms belonging to the magma.

IsDiscriminant(D) : RngIntElt -> BoolElt
Return true if D is the discriminant of some quadratic form; false otherwise.
FundamentalDiscriminant(D) : RngIntElt -> RngIntElt
The fundamental discriminant corresponding to D.
IsFundamentalDiscriminant(D) : RngIntElt -> BoolElt
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.
Conductor(Q) : QuadBin -> RngIntElt
The conductor of quadratic forms whose discriminant is that of Q.

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