ApCoCoA-1:NC.IsFinite
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| 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
