# normalize -- rescale a differential operator

• Usage:
normalize D
• Inputs:
• Outputs:

## Description

Rescales a differential operator so that the leading term of the leading coefficient is 1.

 i1 : S = diffOpRing (QQ[x,y,t]); i2 : D = diffOp(3*x^3*dx^2*dt + (x+y)*dt^2) o2 = | 3x3dx^2dt+(x+y)dt^2 | 1 o2 : DiffOp in S i3 : normalize D o3 = | x3dx^2dt+(1/3x+1/3y)dt^2 | 1 o3 : DiffOp in S

This can be useful when computing "canonical" sets of Noetherian operators, as a valid set of Noetherian operators stays valid even after rescaling.

 i4 : I = ideal(x^2,y^2 - x*t); o4 : Ideal of QQ[x..y, t] i5 : nops = noetherianOperators(I, Strategy => "MacaulayMatrix"); i6 : nops / normalize == {diffOp 1_S, diffOp dy, diffOp(t*dy^2 + 2*dx), diffOp(t*dy^3 + 6*dx*dy)} o6 = true

## Ways to use normalize :

• "normalize(DiffOp)"

## For the programmer

The object normalize is .