# Difference between revisions of "ApCoCoA-1:NC.Deg"

From ApCoCoAWiki

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− | Please set ring | + | 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. |

<itemize> | <itemize> | ||

− | <item>@param <em>F</em>: a polynomial | + | <item>@param <em>F</em>: a non-commutative polynomial. 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 <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |

− | <item>@return: an INT which represents the | + | <item>@return: an INT which represents the standard degree of F. Note that the standard degree of <tt>0</tt> is 0. </item> |

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− | <see> | + | <see>Use</see> |

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## Revision as of 18:12, 25 April 2013

## NC.Deg

The (standard) degree of a polynomial in a non-commutative polynomial ring.

### Syntax

NC.Deg(F:LIST):INT

### 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. 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: an INT which represents the standard degree of F. Note that the standard degree of

`0`is 0.

#### Example

NC.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NC.Deg(F); 3 ------------------------------- NC.Deg([]); -- 0 polynomial 0 -------------------------------

### See also