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

(New page: <command> <title>NC.Subtract</title> <short_description> Subtraction of two polynomials in a non-commutative polynomial ring. </short_description> <syntax> NC.Sub(F1:LIST, F2:LIST):LIST </...) |
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<command> | <command> | ||

− | <title>NC. | + | <title>NC.Sub</title> |

<short_description> | <short_description> | ||

Subtraction of two polynomials in a non-commutative polynomial ring. | Subtraction of two polynomials in a non-commutative polynomial ring. | ||

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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. | ||

<par/> | <par/> | ||

− | Please set ring | + | 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 polynomials | + | <item>@param <em>F1, F2:</em> two non-commutative polynomials, which are left and right operands of subtraction 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>@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> | ||

<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 | |

− | F1 := [[1, | + | F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2 |

− | F2 := [[ | + | NC.Sub(F1,F2); |

− | NC. | + | |

− | [[ | + | [[2x[1], x[2]], [-2y[1], y[2]], [-6y[2]], [3]] |

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

− | NC. | + | NC.Sub([],F2); -- 0-F2 |

− | + | ||

− | + | [[-2y[1], y[2]], [12y[2]], [-2]] | |

− | |||

− | |||

− | |||

− | |||

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− | [ ] | ||

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

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

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

<seealso> | <seealso> | ||

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

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

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

+ | </seealso> | ||

<types> | <types> | ||

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

Line 49: | Line 40: | ||

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

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

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

− | <key>NC. | + | <key>NC.Sub</key> |

− | <key> | + | <key>Sub</key> |

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

</command> | </command> |

## Latest revision as of 13:36, 29 October 2020

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

## NC.Sub

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

### Syntax

NC.Sub(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 subtraction 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.Sub(F1,F2); [[2x[1], x[2]], [-2y[1], y[2]], [-6y[2]], [3]] ------------------------------- NC.Sub([],F2); -- 0-F2 [[-2y[1], y[2]], [12y[2]], [-2]] -------------------------------

### See also