ApCoCoA-1:NC.IsHomog

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NC.IsHomog

Check whether a polynomial or a LIST of polynomials is homogeneous in a non-commutative polynomial ring.

Syntax

NC.IsHomog(F:LIST):BOOL

Description

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 F: a non-commutative polynomial or a LIST of non-commutative polynomials. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5 is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial 0 is represented as the empty LIST [].

  • @return: a BOOL, which is True if F is homogeneous and False otherwise.

Example

NC.SetX(<quotes>xy</quotes>); 
F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; 
F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; 
F := [F1,F2]; 
NC.IsHomog(F);
False
-------------------------------
NC.IsHomog(F1);
True
-------------------------------
NC.IsHomog(F2);
False
-------------------------------

See also

Use