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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<command> | <command> | ||
<title>NCo.SetRelations</title> | <title>NCo.SetRelations</title> | ||
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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>ApCoCoA-1:NCo.SetX|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 "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( | + | NCo.SetX("abc"); |
| − | + | R:=[["ba","ab"], ["ca","ac"], ["cb","bc"]]; --ba=ab, ca=ac, cb=bc | |
| − | NCo.SetRelations( | + | NCo.SetRelations(R); |
NCo.RingEnv(); | NCo.RingEnv(); | ||
Coefficient ring : Q | Coefficient ring : Q | ||
Alphabet : abc | Alphabet : abc | ||
Ordering : LLEX | Ordering : LLEX | ||
| − | Relations : [[ | + | 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> | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |
| − | <see>NCo.UnsetRelations | + | <see>ApCoCoA-1:NCo.UnsetRelations|NCo.UnsetRelations</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> | + | <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
