# ApCoCoA-1:DA.DiffGB

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## 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]] -------------------------------