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Subsections
For any integer D congruent to 0 or 1 modulo 4, it is possible
to create the parent structure of binary quadratic forms of discriminant
D.
QuadraticForms(D) : RngIntElt -> QuadBin
Create the structure of integral binary quadratic forms of discriminant
D.
Binary quadratic forms may be created by coercing a triple [a, b, c] of
integer coefficients into the parent structure of forms of discriminant
D = b2 - 4ac. Other constructors are provided for constructing the
group identity, prime forms, or allowing the omission of third element
c of the sequence.
Q ! 1 : QuadBin, RngIntElt -> QuadBinElt
Create the principal form in the structure Q of binary quadratic forms
of discriminant D. The principal form is either X2 - D/4Y2 if
D mod 4 is 0 and X2 + XY + (D - 1)/4Y2 if it is 1. The principal
form is a reduced form representing the identity element of the class
group of Q.
elt< Q | a, b, c> : QuadBin, RngIntElt, RngIntElt, RngIntElt -> QuadBinElt
elt< Q | a, b> : QuadBin, RngIntElt, RngIntElt -> QuadBinElt
Returns the binary quadratic form aX2 + bXY + cY2 in the magma
of forms Q of discriminant D. Here c is determined by the
solution of the equality D = b2 - 4ac; if no integer c exists
satisfying this, an error will occur.
If p is a split prime or a ramified prime not dividing the conductor
of the magma of quadratic forms Q, returns a quadratic form pX2 + bXY + cY2 in Q.
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