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>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 <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> | <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> | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>NCo.SetX</see> | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |
| − | <see>NCo.UnsetRelations</see> | + | <see>ApCoCoA-1:NCo.UnsetRelations|NCo.UnsetRelations</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
Revision as of 08:34, 7 October 2020
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
