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

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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> | <itemize> | ||

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

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

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

Line 21: | Line 21: | ||

<types> | <types> | ||

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

+ | <type>ideal</type> | ||

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

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

+ | |||

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

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

## Revision as of 10:59, 23 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]] -------------------------------