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

From ApCoCoAWiki
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<command>
 
<command>
<title>NC.IsHomog</title>
+
<title>NCo.IsHomog</title>
 
<short_description>
 
<short_description>
Check whether a polynomial of a list of polynomials is homogeneous in a free monoid 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
+
NCo.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>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.
+
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.
 
<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>
 
<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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</itemize>
 
</itemize>
 
<example>
 
<example>
NC.SetX(<quotes>xy</quotes>);  
+
NCo.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);
+
NCo.IsHomog(F);
 
False
 
False
 
-------------------------------
 
-------------------------------
NC.IsHomog(F1);
+
NCo.IsHomog(F1);
 
True
 
True
 
-------------------------------
 
-------------------------------
NC.IsHomog(F2);
+
NCo.IsHomog(F2);
 
False
 
False
 
-------------------------------
 
-------------------------------
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</description>
 
</description>
 
<seealso>
 
<seealso>
<see>NC.Add</see>
 
<see>NC.Deg</see>
 
<see>NC.FindPolynomials</see>
 
<see>NC.GB</see>
 
<see>NC.HF</see>
 
<see>NC.Interreduction</see>
 
<see>NC.Intersection</see>
 
<see>NC.IsFinite</see>
 
<see>NC.IsGB</see>
 
<see>NC.IsHomog</see>
 
<see>NC.KernelOfHomomorphism</see>
 
<see>NC.LC</see>
 
<see>NC.LT</see>
 
<see>NC.LTIdeal</see>
 
<see>NC.MB</see>
 
<see>NC.MinimalPolynomial</see>
 
<see>NC.Multiply</see>
 
<see>NC.NR</see>
 
<see>NC.ReducedGB</see>
 
<see>NC.SetFp</see>
 
<see>NC.SetOrdering</see>
 
<see>NC.SetRelations</see>
 
<see>NC.SetRules</see>
 
<see>NC.SetX</see>
 
<see>NC.Subtract</see>
 
<see>NC.TruncatedGB</see>
 
<see>NC.UnsetFp</see>
 
<see>NC.UnsetOrdering</see>
 
<see>NC.UnsetRelations</see>
 
<see>NC.UnsetRules</see>
 
<see>NC.UnsetX</see>
 
 
<see>Introduction to CoCoAServer</see>
 
<see>Introduction to CoCoAServer</see>
 
</seealso>
 
</seealso>
Line 71: Line 40:
 
<type>non_commutative</type>
 
<type>non_commutative</type>
 
</types>
 
</types>
<key>gbmr.IsHomog</key>
+
<key>ncpoly.IsHomog</key>
<key>NC.IsHomog</key>
+
<key>NCo.IsHomog</key>
 
<key>IsHomog</key>
 
<key>IsHomog</key>
<wiki-category>Package_gbmr</wiki-category>
+
<wiki-category>Package_ncpoly</wiki-category>
 
</command>
 
</command>

Revision as of 17:20, 25 April 2013

NCo.IsHomog

Check whether a polynomial or a list of polynomials is homogeneous in a non-commutative polynomial 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 coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NCo.SetFp, NCo.SetX and NCo.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

NCo.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]; 
NCo.IsHomog(F);
False
-------------------------------
NCo.IsHomog(F1);
True
-------------------------------
NCo.IsHomog(F2);
False
-------------------------------

See also

Introduction to CoCoAServer