CyclicGroup

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

Wolfram's own CyclicGroup, 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 LanguageCyclicGroup!↗

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

Oscarenumeratio_cyclic(cyclic_group(PermGroup, ...), ...)

Typed signatures

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

Domain: Wolfram

Examples

Basic #

A cyclic group of degree $n$ has order $n$

live ↗

In$\mathrm{GroupOrder}(\mathrm{CyclicGroup}(10))$Out$10$

live ↗

In$\mathrm{GroupElements}(\mathrm{CyclicGroup}(10))$Out$\bigl\lbrack\mathrm{GroupBasis}(\text{0}), \mathrm{GroupBasis}(\text{1}), \mathrm{GroupBasis}(\text{2}), \mathrm{GroupBasis}(\text{3}), \mathrm{GroupBasis}(\text{4}), \mathrm{GroupBasis}(\text{5}), \mathrm{GroupBasis}(\text{6}), \mathrm{GroupBasis}(\text{7}), \mathrm{GroupBasis}(\text{8}), \mathrm{GroupBasis}(\text{9})\bigr\rbrack$

Scope #

live ↗

In$\mathrm{GroupElements}(\mathrm{CyclicGroup}(1))$Out$\bigl\lbrack\mathrm{GroupBasis}(\text{0})\bigr\rbrack$

live ↗

In$\mathrm{GroupElements}(\mathrm{CyclicGroup}(2))$Out$\bigl\lbrack\mathrm{GroupBasis}(\text{0}), \mathrm{GroupBasis}(\text{1})\bigr\rbrack$

live ↗

In$\mathrm{GroupElements}(\mathrm{CyclicGroup}(3))$Out$\bigl\lbrack\mathrm{GroupBasis}(\text{0}), \mathrm{GroupBasis}(\text{1}), \mathrm{GroupBasis}(\text{2})\bigr\rbrack$

About

Examples	5
Checked against	Wolfram Language 1 agree4 differ
Crosswalk	Wolfram LanguageOscar

Implementation

mappedoscarpackages/oracle/src/mappings.ts