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

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(New page: <command> <title>NCo.IsHomog</title> <short_description> Check whether a polynomial or a list of polynomials is homogeneous in a free monoid ring. </short_description> <syntax> NCo.IsHomog...)
 
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{{Version|1}}
 
<command>
 
<command>
 
<title>NCo.IsHomog</title>
 
<title>NCo.IsHomog</title>
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<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>NCo.SetFp</ref>, <ref>NCo.SetX</ref> and <ref>NCo.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.
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Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> via the function <ref>ApCoCoA-1:NCo.SetX|NCo.SetX</ref> before calling the function. 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&lt;X&gt;</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>&lt;X&gt;</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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<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 monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item>
 
<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 ideal. It is false contrarily.</item>
 
<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 ideal. It is false contrarily.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
NCo.SetX(<quotes>xy</quotes>);  
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NCo.SetX("xy");  
F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]];  
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F1 := [[1,"x"], [1,"y"]];  
F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]];  
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F2 := [[1,"xx"],[1,"xy"],[1,"x"]];  
 
F := [F1,F2];  
 
F := [F1,F2];  
 
NCo.IsHomog(F);
 
NCo.IsHomog(F);
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</description>
 
</description>
 
<seealso>
 
<seealso>
<see>NCo.SetFp</see>
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<see>ApCoCoA-1:NCo.SetX|NCo.SetX</see>
<see>NCo.SetX</see>
 
<see>Introduction to CoCoAServer</see>
 
 
</seealso>
 
</seealso>
 
<types>
 
<types>
 
<type>apcocoaserver</type>
 
<type>apcocoaserver</type>
<type>groebner</type>
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<type>polynomial</type>
<type>ideal</type>
 
 
<type>non_commutative</type>
 
<type>non_commutative</type>
 
</types>
 
</types>
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<key>NCo.IsHomog</key>
 
<key>NCo.IsHomog</key>
 
<key>IsHomog</key>
 
<key>IsHomog</key>
<wiki-category>Package_gbmr</wiki-category>
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<wiki-category>ApCoCoA-1:Package_gbmr</wiki-category>
 
</command>
 
</command>

Latest revision as of 13:40, 29 October 2020

This article is about a function from ApCoCoA-1.

NCo.IsHomog

Check whether a polynomial or a list of polynomials is homogeneous in a free monoid ring.

Syntax

NCo.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 alphabet (or set of indeterminates) X via the function NCo.SetX before calling the function. 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

NCo.SetX("xy"); 
F1 := [[1,"x"], [1,"y"]]; 
F2 := [[1,"xx"],[1,"xy"],[1,"x"]]; 
F := [F1,F2]; 
NCo.IsHomog(F);
False
-------------------------------
NCo.IsHomog(F1);
True
-------------------------------
NCo.IsHomog(F2);
False
-------------------------------

See also

NCo.SetX