# Difference between revisions of "ApCoCoA-1:DA.DiffGB"

From ApCoCoAWiki

S schuster (talk | contribs) |
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<command> | <command> | ||

− | <title> | + | <title>DA.DiffGB</title> |

− | <short_description> | + | <short_description>Calculates a differential Groebner basis.</short_description> |

<syntax> | <syntax> | ||

− | + | DA.DiffGB(I:IDEAL):LIST | |

</syntax> | </syntax> | ||

<description> | <description> | ||

Returns a differential Groebner basis of the ideal I which is differentially generated by G wrt. the current differential term ordering. This function only terminates if the ideal I is zero dimensional and has a finite differential Groebner basis. | Returns a differential Groebner basis of the ideal I which is differentially generated by G wrt. the current differential term ordering. This function only terminates if the ideal I is zero dimensional and has a finite differential Groebner basis. | ||

+ | <itemize> | ||

+ | <item>@param I A differential ideal.</item> | ||

+ | <item>@return If terminating, a list of differential polynomials that form a differential Groebner basis of I.</item> | ||

+ | </itemize> | ||

<example>Use Q[x[1..1,0..20]]; | <example>Use Q[x[1..1,0..20]]; | ||

− | Use Q[x[1..1,0..20]], Ord( | + | Use Q[x[1..1,0..20]], Ord(DA.DiffTO("Lex")); |

− | + | DA.DiffGB([x[1,1]^4+x[1,0]]); | |

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

[x[1,3] - 8x[1,1]x[1,2]^3, x[1,1]^2x[1,2]^2 + 1/4x[1,2], x[1,0]x[1,2] - 1/4x[1,1]^2, x[1,1]^4 + x[1,0]] | [x[1,3] - 8x[1,1]x[1,2]^3, x[1,1]^2x[1,2]^2 + 1/4x[1,2], x[1,0]x[1,2] - 1/4x[1,1]^2, x[1,1]^4 + x[1,0]] | ||

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

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

+ | <types> | ||

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

+ | <type>groebner</type> | ||

+ | </types> | ||

+ | <key>DiffGB</key> | ||

+ | <key>DA.DiffGB</key> | ||

+ | <key>diffalg.DiffGB</key> | ||

+ | <key>differential.DiffGB</key> | ||

<wiki-category>Package_diffalg</wiki-category> | <wiki-category>Package_diffalg</wiki-category> | ||

</command> | </command> |

## Revision as of 12:34, 22 April 2009

## DA.DiffGB

Calculates a differential Groebner basis.

### Syntax

DA.DiffGB(I:IDEAL):LIST

### Description

Returns a differential Groebner basis of the ideal I which is differentially generated by G wrt. the current differential term ordering. This function only terminates if the ideal I is zero dimensional and has a finite differential Groebner basis.

@param I A differential ideal.

@return If terminating, a list of differential polynomials that form a differential Groebner basis of I.

#### Example

Use Q[x[1..1,0..20]]; Use Q[x[1..1,0..20]], Ord(DA.DiffTO("Lex")); DA.DiffGB([x[1,1]^4+x[1,0]]); ------------------------------- [x[1,3] - 8x[1,1]x[1,2]^3, x[1,1]^2x[1,2]^2 + 1/4x[1,2], x[1,0]x[1,2] - 1/4x[1,1]^2, x[1,1]^4 + x[1,0]] -------------------------------