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

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(New page: <command> <title>NC.IsGB</title> <short_description> Checks whether a polynomial of a list of polynomials is homogenous over a free associative <tt>K</tt>-algebra. </short_description> <sy...)
 
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<title>NC.IsGB</title>
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<title>NC.IsHomog</title>
 
<short_description>
 
<short_description>
Checks whether a polynomial of a list of polynomials is homogenous over a free associative <tt>K</tt>-algebra.
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Checks whether a polynomial of a list of polynomials is homogeneous over a free associative <tt>K</tt>-algebra.
 
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<syntax>
 
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<item>@param <em>F</em>: a polynomial or a LIST of polynomials in <tt>K&lt;X&gt;</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&lt;X&gt;</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 homogenous and False otherwise. Note that if F is a set of homogenous polynomials, then F generates a homogenous system. It is false contrarily.</item>
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<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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<example>
 
<example>

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

NC.Add

NC.Deg

NC.FindPolynomials

NC.GB

NC.HF

NC.Intersection

NC.IsGB

NC.IsHomog

NC.KernelOfHomomorphism

NC.LC

NC.LT

NC.LTIdeal

NC.MinimalPolynomial

NC.Multiply

NC.NR

NC.ReducedGB

NC.SetFp

NC.SetOrdering

NC.SetRelations

NC.SetRules

NC.SetX

NC.Subtract

NC.UnsetFp

NC.UnsetOrdering

NC.UnsetRelations

NC.UnsetRules

NC.UnsetX

Introduction to CoCoAServer