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

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<command> | <command> | ||

<title>NC.Add</title> | <title>NC.Add</title> | ||

<short_description> | <short_description> | ||

− | Addition of two polynomials | + | Addition of two polynomials in a non-commutative polynomial ring. |

</short_description> | </short_description> | ||

<syntax> | <syntax> | ||

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<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. | ||

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+ | Please set non-commutative polynomial ring (via the command <ref>ApCoCoA-1:Use|Use</ref>) and word ordering (via the function <ref>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</ref>) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions. | ||

<itemize> | <itemize> | ||

− | + | <item>@param <em>F1, F2:</em> two non-commutative polynomials, which are left and right operands of addition respectively. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | |

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

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

</itemize> | </itemize> | ||

<example> | <example> | ||

− | + | USE ZZ/(31)[x[1..2],y[1..2]]; | |

− | + | F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5 | |

− | NC. | + | F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2 |

− | + | NC.Add(F1,F2); | |

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− | + | [[2x[1], x[2]], [2y[1], y[2]], [y[2]], [7]] | |

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------------------------------- | ------------------------------- | ||

</example> | </example> | ||

</description> | </description> | ||

<seealso> | <seealso> | ||

− | <see> | + | <see>ApCoCoA-1:Use|Use</see> |

− | <see>NC. | + | <see>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</see> |

− | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | |

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

<types> | <types> | ||

<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||

− | <type> | + | <type>polynomial</type> |

+ | <type>non_commutative</type> | ||

</types> | </types> | ||

− | <key> | + | <key>ncpoly.Add</key> |

<key>NC.Add</key> | <key>NC.Add</key> | ||

<key>Add</key> | <key>Add</key> | ||

− | <wiki-category> | + | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> |

</command> | </command> |

## Latest revision as of 13:33, 29 October 2020

This article is about a function from ApCoCoA-1. |

## NC.Add

Addition of two polynomials in a non-commutative polynomial ring.

### 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.

Please set non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.

@param

*F1, F2:*two non-commutative polynomials, which are left and right operands of addition respectively. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial`f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5`is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial`0`is represented as the empty LIST [].@return: a LIST which represents the polynomial equal to

`F1+F2`.

#### Example

USE ZZ/(31)[x[1..2],y[1..2]]; F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5 F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2 NC.Add(F1,F2); [[2x[1], x[2]], [2y[1], y[2]], [y[2]], [7]] -------------------------------

### See also