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FormClasses ​

Every class of indefinite forms of discriminant DD: its reduced forms, partitioned into ρ\rho-cycles.

FormClasses(D)the classes, each a listed cycle
Typed signatures
TypePackageApplies
(integer) -> listmodularalways

Domain: The modular group

Examples

Basic #

One class: a single ρ\rho-cycle of two forms

live ↗
InFormClasses(5)\mathrm{FormClasses}(5)Out[[QuadraticForm(−1,1,1),QuadraticForm(1,1,−1)]]\bigl\lbrack\bigl\lbrack\mathrm{QuadraticForm}(-1, 1, 1), \mathrm{QuadraticForm}(1, 1, -1)\bigr\rbrack\bigr\rbrack

Two classes

live ↗
InFormClasses(12)\mathrm{FormClasses}(12)Out[[QuadraticForm(−2,2,1),QuadraticForm(1,2,−2)],[QuadraticForm(−1,2,2),QuadraticForm(2,2,−1)]]\bigl\lbrack\bigl\lbrack\mathrm{QuadraticForm}(-2, 2, 1), \mathrm{QuadraticForm}(1, 2, -2)\bigr\rbrack, \bigl\lbrack\mathrm{QuadraticForm}(-1, 2, 2), \mathrm{QuadraticForm}(2, 2, -1)\bigr\rbrack\bigr\rbrack
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Examples2

See also: FormClassNumber, ReducedForms