# Difference between revisions of "ApCoCoA-1:NCo.SetRelations"

From ApCoCoAWiki

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</short_description> | </short_description> | ||

<syntax> | <syntax> | ||

− | NCo.SetRelations( | + | NCo.SetRelations(R:LIST) |

</syntax> | </syntax> | ||

<description> | <description> | ||

Before calling the function, please set ring environment alphabet (or set of indeterminates) <tt>X</tt> through the functions <ref>NCo.SetX</ref>. For more information, please check the relevant functions. | Before calling the function, please set ring environment alphabet (or set of indeterminates) <tt>X</tt> through the functions <ref>NCo.SetX</ref>. For more information, please check the relevant functions. | ||

<itemize> | <itemize> | ||

− | <item>@param <em> | + | <item>@param <em>R:</em> a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in <tt><X></tt>. Each word is represented as a STRING. For example, the word <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the relation <tt>(yx, xy)</tt> is represented as [<quotes>yx</quotes>, <quotes>xy</quotes>], and the set of relations <tt>{(yx, xy),(zx,xz),(zy,yz)}</tt> is represented as [[<quotes>yx</quotes>, <quotes>xy</quotes>],[<quotes>zx</quotes>, <quotes>xz</quotes>],[<quotes>zy</quotes>, <quotes>yz</quotes>]].</item> |

</itemize> | </itemize> | ||

<example> | <example> | ||

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------------------------------- | ------------------------------- | ||

NCo.SetX(<quotes>abc</quotes>); | NCo.SetX(<quotes>abc</quotes>); | ||

− | + | R:=[[<quotes>ba</quotes>,<quotes>ab</quotes>], [<quotes>ca</quotes>,<quotes>ac</quotes>], [<quotes>cb</quotes>,<quotes>bc</quotes>]]; --ba=ab, ca=ac, cb=bc | |

− | NCo.SetRelations( | + | NCo.SetRelations(R); |

NCo.RingEnv(); | NCo.RingEnv(); | ||

Coefficient ring : Q | Coefficient ring : Q |

## Revision as of 16:13, 6 May 2013

## NCo.SetRelations

Set relations for a finitely presented monoid ring.

### Syntax

NCo.SetRelations(R:LIST)

### Description

Before calling the function, please set ring environment alphabet (or set of indeterminates) `X` through the functions NCo.SetX. For more information, please check the relevant functions.

@param

*R:*a finite set of relations. It is of LIST type. Each element in Relations is of the form [W1, W2], where W1 and W2 are words in`<X>`. Each word is represented as a STRING. For example, the word`xy^2x`is represented as "xyyx", and the identity is represented as the empty string "". Thus, the relation`(yx, xy)`is represented as ["yx", "xy"], and the set of relations`{(yx, xy),(zx,xz),(zy,yz)}`is represented as [["yx", "xy"],["zx", "xz"],["zy", "yz"]].

#### Example

NCo.RingEnv(); Coefficient ring : Q Ordering : LLEX ------------------------------- NCo.SetX(<quotes>abc</quotes>); R:=[[<quotes>ba</quotes>,<quotes>ab</quotes>], [<quotes>ca</quotes>,<quotes>ac</quotes>], [<quotes>cb</quotes>,<quotes>bc</quotes>]]; --ba=ab, ca=ac, cb=bc NCo.SetRelations(R); NCo.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : LLEX Relations : [[<quotes>ba</quotes>, <quotes>ab</quotes>], [<quotes>ca</quotes>, <quotes>ac</quotes>], [<quotes>cb</quotes>, <quotes>bc</quotes>]] -- relations generated by {ba=ab, ca=ac, cb=bc} -------------------------------

### See also