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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 b2 - 4ac of a quadratic form f=aX2 + bXY + cY2.
Discriminant(Q) : QuadBin -> RngIntElt
The discriminant of the quadratic forms belonging to the magma of quadratic forms Q.

IsDiscriminant(D) : RngIntElt -> BoolElt
Return true if the integer D is the discriminant of some quadratic form; false otherwise.
FundamentalDiscriminant(D) : RngIntElt -> RngIntElt
The fundamental discriminant corresponding to the integer D.
IsFundamental(D) : RngIntElt -> BoolElt
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 m2DK for m > 1 and any other such integer DK.
Conductor(Q) : QuadBin -> RngIntElt
The conductor of quadratic forms whose discriminant is that of the magma of quadratic forms Q.
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013