Difference between revisions of "ApCoCoA-1:NC.IsFinite"
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(New page: <command> <title>NC.IsFinite</title> <short_description> Check whether a <tt>K</tt>-algebra <tt>R/<M></tt> has finite <tt>K</tt>-dimension. </short_description> <syntax> NC.IsFinite(...) |
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<command> | <command> | ||
<title>NC.IsFinite</title> | <title>NC.IsFinite</title> | ||
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
| − | Please set non-commutative polynomial ring (via the command <ref>Use</ref>) before calling this function. For more information, please check the relevant commands and functions. | + | Please set non-commutative polynomial ring (via the command <ref>ApCoCoA-1:Use|Use</ref>) before calling this function. For more information, please check the relevant commands and functions. |
<itemize> | <itemize> | ||
<item>@param <em>M</em>: a LIST of words (or terms) in the defining ring. Note that each word is represented as a LIST, and that each element in the LIST involves only one indeterminate or none (a constant). For instance, the word <tt>x[2]y[1]x[2]^2</tt> is represented as the LIST [x[2], y[1], x[2]^2].</item> | <item>@param <em>M</em>: a LIST of words (or terms) in the defining ring. Note that each word is represented as a LIST, and that each element in the LIST involves only one indeterminate or none (a constant). For instance, the word <tt>x[2]y[1]x[2]^2</tt> is represented as the LIST [x[2], y[1], x[2]^2].</item> | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>NC.AdMatrix</see> | + | <see>ApCoCoA-1:NC.AdMatrix|NC.AdMatrix</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
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<key>NC.IsFinite</key> | <key>NC.IsFinite</key> | ||
<key>IsFinite</key> | <key>IsFinite</key> | ||
| − | <wiki-category>Package_ncpoly</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> |
</command> | </command> | ||
Latest revision as of 10:14, 7 October 2020
| This article is about a function from ApCoCoA-1. |
NC.IsFinite
Check whether a K-algebra R/<M> has finite K-dimension.
Syntax
NC.IsFinite(M:LIST):BOOL
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Please set non-commutative polynomial ring (via the command Use) before calling this function. For more information, please check the relevant commands and functions.
@param M: a LIST of words (or terms) in the defining ring. Note that each word is represented as a LIST, and that each element in the LIST involves only one indeterminate or none (a constant). For instance, the word x[2]y[1]x[2]^2 is represented as the LIST [x[2], y[1], x[2]^2].
@return: a BOOL value which is True if K-vector space R/<M> is finite and False otherwise.
Example
Use ZZ/(2)[x[1..3]]; M:=[[x[3]^3], [x[1], x[2]], [x[2]^2], [x[1]^2], [x[2], x[3], x[1]], [x[1], x[3], x[1]], [x[1], x[3]^2], [x[2], x[3], x[2], x[3]], [x[1], x[3], x[2], x[3]]]; NC.IsFinite(M); False ------------------------------- The output at the ApCoCoAServer is as follows. Found 2 cycles: [3,2,1] [2,1,3] [1,3,2] [3,3,2] [3,2,3] [2,3,3] The group has polynomial growth of at most degree 2.
See also
