# Difference between revisions of "ApCoCoA-1:NCo.BAdd"

(New page: <command> <title>NCo.BAdd</title> <short_description> Addition of two polynomials in a free monoid ring over the binary field F_{2}={0,1}. </short_description> <syntax> NCo.BAdd(F1:LIST, F...) |
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Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is the length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | Please set ring environment <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>word ordering</em> via the functions <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before calling this function. The default ordering is the 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 the free monoid ring <tt>F_{2}<X></tt>, which are left and right operands of addition respectively. Each polynomial is represented as a LIST of words (or terms) in <tt><X></tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the polynomial <tt>f=xy-y+1 | + | <item>@param <em>F1,F2:</em> two polynomials in the free monoid ring <tt>F_{2}<X></tt>, which are left and right operands of addition respectively. Each polynomial is represented as a LIST of words (or terms) in <tt><X></tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>. Thus, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[<quotes>xy</quotes>, <quotes>y</quotes>, <quotes></quotes>]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |

<item>@return: a LIST which represents the polynomial equal to <tt>F1+F2</tt>.</item> | <item>@return: a LIST which represents the polynomial equal to <tt>F1+F2</tt>.</item> | ||

</itemize> | </itemize> |

## Revision as of 16:50, 30 April 2013

## NCo.BAdd

Addition of two polynomials in a free monoid ring over the binary field F_{2}={0,1}.

### Syntax

NCo.BAdd(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 *alphabet* (or set of indeterminates) `X` and *word ordering* via the functions NCo.SetX and NCo.SetOrdering, respectively, before calling this function. The default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*F1,F2:*two polynomials in the free monoid ring`F_{2}<X>`, which are left and right operands of addition respectively. Each polynomial is represented as a LIST of words (or terms) in`<X>`. Each word is represented as a STRING. For example,`xy^2x`is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial`f=xy-y+1`is represented as F:=["xy", "y", ""]. 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>xX</quotes>); NCo.SetOrdering(<quotes>LLEX</quotes>); F1:=[<quotes>xX</quotes>,<quotes></quotes>]; F2:=[<quotes>Xx</quotes>,<quotes></quotes>]; NCo.BAdd(F1,F2); [<quotes>xX</quotes>, <quotes>Xx</quotes>] ------------------------------- NCo.BAdd(F1,F1); [ ] ------------------------------- NCo.BAdd([],F1); [<quotes>xX</quotes>, <quotes></quotes>] -------------------------------

### See also