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

From ApCoCoAWiki
Line 10: Line 10:
 
<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.
 
<itemize>
 
<itemize>
<item>Before calling the function, please set ring environment coefficient field <tt>K</tt>, alphabet <tt>X</tt> and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is <tt>Q</tt>. Default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.</item>
+
<item>Before calling the function, please set ring environment coefficient field <tt>K</tt>, alphabet <tt>X</tt> and ordering through the functions <ref>NC.SetFp</ref>(Prime) (or <ref>NC.UnsetFp</ref>()), <ref>NC.SetX</ref>(X) and <ref>NC.SetOrdering</ref>(Ordering) respectively. Default coefficient field is <tt>Q</tt>. Default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.</item>
 
<item>@param <em>F1</em>: left operand of addition operator. It is a polynomial in <tt>K&lt;X&gt;</tt>. Each polynomial in <tt>K&lt;X&gt;</tt> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in <tt>K</tt> and w is a word in <tt>X*</tt>.  Unit in <tt>X*</tt> is empty word represented as an empty STRING <quotes></quotes>. <tt>0</tt> polynomial is represented as an empty LIST []. For example, polynomial <tt>F:=xy-y+1</tt> in <tt>K&lt;x,y&gt;</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]].</item>
 
<item>@param <em>F1</em>: left operand of addition operator. It is a polynomial in <tt>K&lt;X&gt;</tt>. Each polynomial in <tt>K&lt;X&gt;</tt> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in <tt>K</tt> and w is a word in <tt>X*</tt>.  Unit in <tt>X*</tt> is empty word represented as an empty STRING <quotes></quotes>. <tt>0</tt> polynomial is represented as an empty LIST []. For example, polynomial <tt>F:=xy-y+1</tt> in <tt>K&lt;x,y&gt;</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]].</item>
 
<item>@param <em>F2</em>: right operand of addition operator. It is a polynomial in <tt>K&lt;X&gt;</tt>.</item>
 
<item>@param <em>F2</em>: right operand of addition operator. It is a polynomial in <tt>K&lt;X&gt;</tt>.</item>
Line 67: Line 67:
 
<see>NC.UnsetRules</see>
 
<see>NC.UnsetRules</see>
 
<see>NC.UnsetX</see>
 
<see>NC.UnsetX</see>
<see>Gbmr.MRAdd</see>
+
<see>NC.MRAdd</see>
<see>Gbmr.MRBP</see>
+
<see>NC.MRBP</see>
<see>Gbmr.MRIntersection</see>
+
<see>NC.MRIntersection</see>
<see>Gbmr.MRKernelOfHomomorphism</see>
+
<see>NC.MRKernelOfHomomorphism</see>
<see>Gbmr.MRMinimalPolynomials</see>
+
<see>NC.MRMinimalPolynomials</see>
<see>Gbmr.MRMultiply</see>
+
<see>NC.MRMultiply</see>
<see>Gbmr.MRSubtract</see>
+
<see>NC.MRSubtract</see>
 
<see>Introduction to CoCoAServer</see>
 
<see>Introduction to CoCoAServer</see>
 
</seealso>
 
</seealso>
Line 80: Line 80:
 
<type>groebner</type>
 
<type>groebner</type>
 
</types>
 
</types>
 +
<key>gbmr.add</key>
 
<key>NC.Add</key>
 
<key>NC.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 09:34, 22 July 2010

NC.Add

Addition of two polynomials over a free associative K-algebra.

Syntax

NC.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.

  • Before calling the function, please set ring environment coefficient field K, alphabet X and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

  • @param F1: left operand of addition operator. It is a polynomial in K<X>. Each polynomial in K<X> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in K and w is a word in X*. Unit in X* is empty word represented as an empty STRING "". 0 polynomial is represented as an empty LIST []. For example, polynomial F:=xy-y+1 in K<x,y> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].

  • @param F2: right operand of addition operator. It is a polynomial in K<X>.

  • @return: a LIST which represents polynomial F1+F2.

Example

NC.SetX(<quotes>abc</quotes>); 				
NC.SetOrdering(<quotes>ELIM</quotes>); 
NC.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : ELIM

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

-------------------------------
NC.Add(F1,F2); -- over F2
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]
-------------------------------
NC.Add(F1,F1); -- over F2
[ ]
-------------------------------

See also

NC.Deg

NC.GB

NC.Intersection

NC.IsGB

NC.KernelOfHomomorphism

NC.LC

NC.LT

NC.LTIdeal

NC.MinimalPolynomial

NC.Multiply

NC.NR

NC.SetFp

NC.SetOrdering

NC.SetRelations

NC.SetRules

NC.SetX

NC.Subtract

NC.UnsetFp

NC.UnsetOrdering

NC.UnsetRelations

NC.UnsetRules

NC.UnsetX

NC.MRAdd

NC.MRBP

NC.MRIntersection

NC.MRKernelOfHomomorphism

NC.MRMinimalPolynomials

NC.MRMultiply

NC.MRSubtract

Introduction to CoCoAServer