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

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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. | ||

+ | <par/> | ||

+ | Before calling the function, please set ring environment alphabet <tt>X</tt> through the functions <ref>NC.SetX</ref>(X). | ||

<itemize> | <itemize> | ||

− | |||

<item>@param <em>F</em>: 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>F</em>: 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>@return: a INT which is (standard) degree <tt>F</tt>. If <tt>F=0</tt>, then return <tt>0</tt>. </item> | <item>@return: a INT which is (standard) degree <tt>F</tt>. If <tt>F=0</tt>, then return <tt>0</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.deg</key> | ||

<key>NC.Deg</key> | <key>NC.Deg</key> | ||

<key>Deg</key> | <key>Deg</key> | ||

<wiki-category>Package_gbmr</wiki-category> | <wiki-category>Package_gbmr</wiki-category> | ||

</command> | </command> |

## Revision as of 09:37, 22 July 2010

## NC.Deg

(Standard) degree of a polynomial over a free associative K-algebra.

### Syntax

NC.Deg(F:LIST):INT

### 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 alphabet `X` through the functions NC.SetX(X).

@param

*F*: 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,""]].@return: a INT which is (standard) degree

`F`. If`F=0`, then return`0`.

#### Example

NC.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NC.Deg(F); 3 ------------------------------- NC.Deg([]); -- 0 polynomial 0 -------------------------------

### See also