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

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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. | ||

<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<X></tt>. Each polynomial in <tt>K<X></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<x,y></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<X></tt>. Each polynomial in <tt>K<X></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<x,y></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<X></tt>.</item> | <item>@param <em>F2</em>: right operand of addition operator. It is a polynomial in <tt>K<X></tt>.</item> | ||

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<see>NC.UnsetRules</see> | <see>NC.UnsetRules</see> | ||

<see>NC.UnsetX</see> | <see>NC.UnsetX</see> | ||

− | <see> | + | <see>NC.MRAdd</see> |

− | <see> | + | <see>NC.MRBP</see> |

− | <see> | + | <see>NC.MRIntersection</see> |

− | <see> | + | <see>NC.MRKernelOfHomomorphism</see> |

− | <see> | + | <see>NC.MRMinimalPolynomials</see> |

− | <see> | + | <see>NC.MRMultiply</see> |

− | <see> | + | <see>NC.MRSubtract</see> |

<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||

</seealso> | </seealso> | ||

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<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