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

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− | Checks whether a polynomial of a list of polynomials is | + | Checks whether a polynomial of a list of polynomials is homogeneous over a free associative <tt>K</tt>-algebra. |

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<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 LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, unit is represented as an empty string <quotes></quotes>. Then, polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. <tt>0</tt> polynomial is represented as an 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 LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, unit is represented as an empty string <quotes></quotes>. Then, polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. <tt>0</tt> polynomial is represented as an empty LIST [].</item> | ||

− | <item>@return: a BOOL value which is True if F is | + | <item>@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 system. It is false contrarily.</item> |

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## Revision as of 14:57, 3 May 2011

## NC.IsHomog

Checks whether a polynomial of a list of polynomials is homogeneous over a free associative `K`-algebra.

### 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 indeterminates) `X` and ordering through the functions NC.SetFp(Prime), NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. Default coefficient field is `Q`. 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 LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example,`xy^2x`is represented as "xyyx", unit is represented as an empty string "". Then, polynomial`F=xy-y+1`is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].`0`polynomial is represented as an 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 system. 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