FormAction

The image of a QuadraticForm under the modular group's action: substituting $(x,y)\mapsto(px+qy,rx+sy)$ for a matrix $\begin{pmatrix}p&q\\r&s\end{pmatrix}$. The discriminant is invariant, which is why classes live inside one discriminant.

FormAction(form, matrix)the form after the substitution

Typed signatures

Type	Package	Applies
(expression<QuadraticForm>, expression<ModularMatrix> | list | string) -> expression<QuadraticForm>	modular	always

Domain: The modular group

Examples

Basic #

Substituting $x\mapsto x+y$ in $x^2+xy-y^2$; the discriminant stays $5$

live ↗

In$\mathrm{FormAction}(\mathrm{QuadraticForm}(1, 1, -1), \mathrm{ModularMatrix}(1, 1, 0, 1))$Out$\mathrm{QuadraticForm}(1, 3, 1)$

About

Examples	1

See also: QuadraticForm, FormClassNumber