FormClasses

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

FormClasses(D)the classes, each a listed cycle

Typed signatures

Type	Package	Applies
(integer) -> list	modular	always

Domain: The modular group

Examples

Basic #

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

live ↗

In$\mathrm{FormClasses}(5)$Out$\bigl\lbrack\bigl\lbrack\mathrm{QuadraticForm}(-1, 1, 1), \mathrm{QuadraticForm}(1, 1, -1)\bigr\rbrack\bigr\rbrack$

Two classes

live ↗

In$\mathrm{FormClasses}(12)$Out$\bigl\lbrack\bigl\lbrack\mathrm{QuadraticForm}(-2, 2, 1), \mathrm{QuadraticForm}(1, 2, -2)\bigr\rbrack, \bigl\lbrack\mathrm{QuadraticForm}(-1, 2, 2), \mathrm{QuadraticForm}(2, 2, -1)\bigr\rbrack\bigr\rbrack$

About

Examples	2

See also: FormClassNumber, ReducedForms