FormRho

One step round the reduction cycle: Gauss's $\rho$ operator on an indefinite QuadraticForm — the continued-fraction step, in form coordinates.

FormRho(form)the next form in the cycle

Typed signatures

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

Domain: The modular group

Examples

Basic #

Gauss's $\rho$ on $x^2+xy-y^2$

live ↗

In$\mathrm{FormRho}(\mathrm{QuadraticForm}(1, 1, -1))$Out$\mathrm{QuadraticForm}(-1, 1, 1)$

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Examples	1

See also: FormClassNumber, FormCycle, ReduceForm