Difference between revisions of "ApCoCoA-1:NCo.IsHomog"
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<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 | + | 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<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, | + | <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,"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( | + | NCo.SetX("xy"); |
| − | F1 := [[1, | + | F1 := [[1,"x"], [1,"y"]]; |
| − | F2 := [[1, | + | 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. | + | <see>ApCoCoA-1:NCo.SetX|NCo.SetX</see> |
| − | |||
| − | |||
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
| − | <type> | + | <type>polynomial</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> | + | <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
