FormAutomorph

The automorph: the hyperbolic matrix generating an indefinite QuadraticForm's stabiliser in $\mathrm{SL}(2,\mathbb{Z})$, built from the fundamental PellSolution of its discriminant.

FormAutomorph(form)the stabiliser's generator

Typed signatures

Type	Package	Applies
(expression<QuadraticForm>) -> expression<ModularMatrix>	modular	always

Domain: The modular group

Examples

Basic #

Built from the fundamental solution $(3,1)$ of $t^2-5u^2=4$

live ↗

In$\mathrm{FormAutomorph}(\mathrm{QuadraticForm}(1, 1, -1))$Out$\mathrm{ModularMatrix}(1, 1, 1, 2)$

About

Examples	1

See also: QuadraticForm, FormClassNumber, PellSolution