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

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(New page: <command> <title>NC.Add</title> <short_description> Addition of two polynomials in a free monoid ring. </short_description> <syntax> NC.Add(F1:LIST, F2:LIST):LIST </syntax> <description> <...)
 
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<command>
 
<command>
−
<title>NC.Add</title>
+
<title>NCo.Add</title>
 
<short_description>
 
<short_description>
 
Addition of two polynomials in a free monoid ring.
 
Addition of two polynomials in a free monoid ring.
 
</short_description>
 
</short_description>
 
<syntax>
 
<syntax>
−
NC.Add(F1:LIST, F2:LIST):LIST
+
NCo.Add(F1:LIST, F2:LIST):LIST
 
</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>F1, F2:</em> two polynomials in <tt>K&lt;X&gt;</tt>, which are left and right operands of addition respectively. 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>F1, F2:</em> two polynomials in <tt>K&lt;X&gt;</tt>, which are left and right operands of addition respectively. 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>abc</quotes>);
+
NCo.SetX(<quotes>abc</quotes>);
−
NC.SetOrdering(<quotes>ELIM</quotes>);  
+
NCo.SetOrdering(<quotes>ELIM</quotes>);  
−
NC.RingEnv();
+
NCo.RingEnv();
 
Coefficient ring : Q
 
Coefficient ring : Q
 
Alphabet : abc
 
Alphabet : abc
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F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]];
 
F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]];
 
F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
 
F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
−
NC.Add(F1,F2); -- over Q
+
NCo.Add(F1,F2); -- over Q
 
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]
 
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]
 
-------------------------------
 
-------------------------------
−
NC.SetFp(); -- set default Fp = F2
+
NCo.SetFp(); -- set default Fp = F2
−
NC.RingEnv();
+
NCo.RingEnv();
 
Coefficient ring : Fp = Z/(2)
 
Coefficient ring : Fp = Z/(2)
 
Alphabet : abc
 
Alphabet : abc
 
Ordering : ELIM
 
Ordering : ELIM
 
-------------------------------
 
-------------------------------
−
NC.Add(F1,F2); -- over F2
+
NCo.Add(F1,F2); -- over F2
 
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]
 
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]
 
-------------------------------
 
-------------------------------
−
NC.Add(F1,F1); -- over F2
+
NCo.Add(F1,F1); -- over F2
 
[ ]
 
[ ]
 
-------------------------------
 
-------------------------------
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</description>
 
</description>
 
<seealso>
 
<seealso>
−
<see>NC.Add</see>
+
<see>NCo.SetFp</see>
−
<see>NC.Deg</see>
+
<see>NCo.SetOrdering</see>
−
<see>NC.FindPolynomials</see>
+
<see>NCo.SetX</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>
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</types>
 
</types>
 
<key>gbmr.Add</key>
 
<key>gbmr.Add</key>
−
<key>NC.Add</key>
+
<key>NCo.Add</key>
 
<key>Add</key>
 
<key>Add</key>
 
<wiki-category>Package_gbmr</wiki-category>
 
<wiki-category>Package_gbmr</wiki-category>
 
</command>
 
</command>

Revision as of 14:32, 25 April 2013

NCo.Add

Addition of two polynomials in a free monoid ring.

Syntax

NCo.Add(F1:LIST, F2:LIST):LIST

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 F1, F2: two polynomials in K<X>, which are left and right operands of addition respectively. 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 LIST which represents the polynomial equal to F1+F2.

Example

NCo.SetX(<quotes>abc</quotes>); 				
NCo.SetOrdering(<quotes>ELIM</quotes>); 
NCo.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : ELIE
-------------------------------	
F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]];
F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
NCo.Add(F1,F2); -- over Q
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]
-------------------------------
NCo.SetFp(); -- set default Fp = F2
NCo.RingEnv();
Coefficient ring : Fp = Z/(2)
Alphabet : abc
Ordering : ELIM
-------------------------------
NCo.Add(F1,F2); -- over F2
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]
-------------------------------
NCo.Add(F1,F1); -- over F2
[ ]
-------------------------------

See also

NCo.SetFp

NCo.SetOrdering

NCo.SetX

Introduction to CoCoAServer




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