Reduced Forms

Note that in versions up to Magma V2.20, in cases where the narrow class group differs from the class group, these two functions behaved differently. In those cases, the ReducedForms and ReducedOrbits only covered half of the equivalence classes.

ReducedForms(Q) : QuadBin -> [ QuadBinElt ]

ReducedForms(D) : RngIntElt -> [ QuadBinElt ]

For {Q = QuadraticForms(D)}, this returns a sequence containing precisely one reduced form in each equivalence class of primitive forms (under the usual equivalence relation, given by IsEquivalent(f1, f2) for forms f1, f2).

When D < 0, these are simply all the primitive reduced forms in Q.

ReducedOrbits(Q) : QuadBin -> [ {@ QuadBinElt @} ]

For {Q = QuadraticForms(D)} where D is positive, this returns the ReductionOrbit of each of the ReducedForms(Q), as a sequence of indexed sets.