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

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(New page: <command> <title>NCo.SetRelations</title> <short_description> Set relations for a finitely presented monoid ring. </short_description> <syntax> NCo.SetRelations(Relations:LIST) </syntax> <...)
 
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{{Version|1}}
 
<command>
 
<command>
 
<title>NCo.SetRelations</title>
 
<title>NCo.SetRelations</title>
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</short_description>
 
</short_description>
 
<syntax>
 
<syntax>
NCo.SetRelations(Relations:LIST)
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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.
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Before calling the function, please set ring environment alphabet (or set of indeterminates) <tt>X</tt> through the functions <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref>. For more information, please check the relevant functions.
 
<itemize>
 
<itemize>
<item>@param <em>Relations:</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>&lt;X&gt;</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>
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<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>&lt;X&gt;</tt>. Each word is represented as a STRING. For example, the word <tt>xy^2x</tt> is represented as "xyyx", and the identity is represented as the empty string "". Thus, the relation <tt>(yx, xy)</tt> is represented as ["yx", "xy"], and the set of relations <tt>{(yx, xy),(zx,xz),(zy,yz)}</tt> is represented as [["yx", "xy"],["zx", "xz"],["zy", "yz"]].</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
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Ordering : LLEX
 
Ordering : LLEX
 
-------------------------------
 
-------------------------------
NCo.SetX(<quotes>abc</quotes>);
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NCo.SetX("abc");
Relations:=[[<quotes>ba</quotes>,<quotes>ab</quotes>], [<quotes>ca</quotes>,<quotes>ac</quotes>], [<quotes>cb</quotes>,<quotes>bc</quotes>]]; --ba=ab, ca=ac, cb=bc
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R:=[["ba","ab"], ["ca","ac"], ["cb","bc"]]; --ba=ab, ca=ac, cb=bc
NCo.SetRelations(Relations);
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NCo.SetRelations(R);
 
NCo.RingEnv();
 
NCo.RingEnv();
 
Coefficient ring : Q
 
Coefficient ring : Q
 
Alphabet : abc
 
Alphabet : abc
 
Ordering : LLEX
 
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}
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Relations : [["ba", "ab"], ["ca", "ac"], ["cb", "bc"]] -- relations generated by {ba=ab, ca=ac, cb=bc}
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
 
</description>
 
</description>
 
<seealso>
 
<seealso>
<see>NCo.SetX</see>
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<see>ApCoCoA-1:NCo.SetX|NCo.SetX</see>
<see>NCo.UnsetRelations</see>
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<see>ApCoCoA-1:NCo.UnsetRelations|NCo.UnsetRelations</see>
<see>Introduction to CoCoAServer</see>
 
 
</seealso>
 
</seealso>
 
<types>
 
<types>
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<key>NCo.SetRelations</key>
 
<key>NCo.SetRelations</key>
 
<key>SetRelations</key>
 
<key>SetRelations</key>
<wiki-category>Package_gbmr</wiki-category>
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<wiki-category>ApCoCoA-1:Package_gbmr</wiki-category>
 
</command>
 
</command>

Latest revision as of 13:44, 29 October 2020

This article is about a function from ApCoCoA-1.

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

See also

NCo.SetX

NCo.UnsetRelations