GroupIsAbelian

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

Mapped through to oscar for the oracle; not yet written up here.

GroupIsAbelian(...)Mapped through to oscar for the oracle; not yet written up here.

SageMathenumeratio_is_abelian(...)Oscaris_abelian((...).G)

Typed signatures

Type	Package	Applies
(expression<CyclicGroup> | expression<DihedralGroup> | expression<GroupDirectProduct>) -> boolean	groupalgebra	always

Domain: Oracle

Examples

Basic #

live ↗

In$\mathrm{GroupIsAbelian}(\mathrm{CyclicGroup}(6))$Out$\mathrm{True}$

$D_3$ is not abelian

live ↗

In$\mathrm{GroupIsAbelian}(\mathrm{DihedralGroup}(3))$Out$\mathrm{False}$

About

Examples	2
Checked against	Wolfram Language 2 agreeSageMath 2 agree
Crosswalk	SageMathOscar

Implementation

mappedoscarpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedwolframpackages/oracle/src/mappings.ts

Wolfram has no abelian test for a permutation group; a group is abelian when its generators commute, which PermutationProduct decides on canonical Cycles.