DihedralGroup

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

Wolfram's own DihedralGroup, mapped through for the transpiler and the oracle but not yet written up here.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageDihedralGroup!↗

DihedralGroup(...)Wolfram's own DihedralGroup, mapped through for the transpiler and the oracle but not yet written up here.

SageMathenumeratio_dihedral(...)Oscarenumeratio_dihedral(dihedral_group(PermGroup, 2 * ...), ...)

Typed signatures

Type	Package	Applies
(integer) -> expression<DihedralGroup>	groupalgebra	always

Domain: Wolfram

Examples

Basic #

The dihedral group of the 10-gon has order $2n=20$

live ↗

In$\mathrm{GroupOrder}(\mathrm{DihedralGroup}(10))$Out$20$

live ↗

In$\mathrm{GroupElements}(\mathrm{DihedralGroup}(4))$Out$\bigl\lbrack\mathrm{GroupBasis}(\text{0}), \mathrm{GroupBasis}(\text{1}), \mathrm{GroupBasis}(\text{2}), \mathrm{GroupBasis}(\text{3}), \mathrm{GroupBasis}(\text{s0}), \mathrm{GroupBasis}(\text{s1}), \mathrm{GroupBasis}(\text{s2}), \mathrm{GroupBasis}(\text{s3})\bigr\rbrack$

About

Examples	2
Checked against	Wolfram Language 1 agree1 differSageMath 2 agree
Crosswalk	Wolfram LanguageSageMathOscar

Implementation

mappedoscarpackages/oracle/src/mappings.ts

Our DihedralGroup(n) is the symmetries of an n-gon; Oscar and GAP index dihedral groups by order, so it is dihedral_group(2n) there.

mappedsagepackages/oracle/src/mappings.ts

Sage's DihedralGroup(n) is the symmetries of an n-gon, order 2n on n points, as ours is. Elements are labeled k for a rotation and sk for a reflection.