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

Line 1: | Line 1: | ||

<command> | <command> | ||

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

<short_description> | <short_description> | ||

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

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

<syntax> | <syntax> | ||

− | + | NC.IsHomog(F:LIST):BOOL | |

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

<description> | <description> | ||

<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 ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref> | + | Please set ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NC.SetFp</ref>, <ref>NC.SetX</ref> and <ref>NC.SetOrdering</ref>, respectively, before calling the function. The default coefficient field is <tt>Q</tt>. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. |

<itemize> | <itemize> | ||

<item>@param <em>F</em>: a polynomial or a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | <item>@param <em>F</em>: a polynomial or a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | ||

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

<example> | <example> | ||

− | + | NC.SetX(<quotes>xy</quotes>); | |

F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; | F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; | ||

F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; | F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; | ||

F := [F1,F2]; | F := [F1,F2]; | ||

− | + | NC.IsHomog(F); | |

False | False | ||

------------------------------- | ------------------------------- | ||

− | + | NC.IsHomog(F1); | |

True | True | ||

------------------------------- | ------------------------------- | ||

− | + | NC.IsHomog(F2); | |

False | False | ||

------------------------------- | ------------------------------- | ||

Line 41: | Line 41: | ||

</types> | </types> | ||

<key>ncpoly.IsHomog</key> | <key>ncpoly.IsHomog</key> | ||

− | <key> | + | <key>NC.IsHomog</key> |

<key>IsHomog</key> | <key>IsHomog</key> | ||

<wiki-category>Package_ncpoly</wiki-category> | <wiki-category>Package_ncpoly</wiki-category> | ||

</command> | </command> |

## Revision as of 17:26, 25 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 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 ring environment *coefficient field* `K`, *alphabet* (or set of indeterminates) `X` and *ordering* via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is `Q`. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*F*: a polynomial or a LIST of polynomials in`K<X>`. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in`<X>`and C is the coefficient of W. For example, the polynomial`F=xy-y+1`is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial`0`is represented as the empty LIST [].@return: a BOOL value which is True if F is homogeneous and False otherwise. Note that if F is a set of homogeneous polynomials, then F generates a homogeneous ideal. It is false contrarily.

#### 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