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

Line 2: | Line 2: | ||

<title>NC.IsHomog</title> | <title>NC.IsHomog</title> | ||

<short_description> | <short_description> | ||

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

</short_description> | </short_description> | ||

<syntax> | <syntax> | ||

Line 8: | Line 8: | ||

</syntax> | </syntax> | ||

<description> | <description> | ||

− | + | 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 ring | ||

<itemize> | <itemize> | ||

− | <item>@param <em>F</em>: a polynomial or a LIST of polynomials | + | <item>@param <em>F</em>: 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 <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: a BOOL | + | <item>@return: a BOOL, which is True if F is homogeneous and False otherwise.</item> |

</itemize> | </itemize> | ||

<example> | <example> | ||

Line 32: | Line 30: | ||

</description> | </description> | ||

<seealso> | <seealso> | ||

− | <see> | + | <see>Use</see> |

</seealso> | </seealso> | ||

<types> | <types> | ||

<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||

− | <type> | + | <type>polynomial</type> |

− | |||

<type>non_commutative</type> | <type>non_commutative</type> | ||

</types> | </types> |

## Revision as of 12:23, 29 April 2013

## 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