IsReducedForm

Whether an indefinite QuadraticForm satisfies Gauss's reduction condition, $|\sqrt D - 2|a|| < b < \sqrt D$.

IsReducedForm(form)Gauss's reduction condition

Typed signatures

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

Domain: The modular group

Examples

Basic #

Satisfies Gauss's condition for $D=5$

live ↗

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

Fails the condition for $D=25$

live ↗

In$\mathrm{IsReducedForm}(\mathrm{QuadraticForm}(1, 3, -4))$Out$\mathrm{False}$

About

Examples	2

See also: QuadraticForm, ReduceForm, FormClassNumber