Difference between revisions of "ApCoCoA-1:NCo.SetRelations"
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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. | 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>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 | + | <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:=[[ | + | R:=[["ba","ab"], ["ca","ac"], ["cb","bc"]]; --ba=ab, ca=ac, cb=bc |
NCo.SetRelations(R); | NCo.SetRelations(R); | ||
NCo.RingEnv(); | NCo.RingEnv(); | ||
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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> | ||
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
