# normalize -- rescale a differential operator to a canonical form

• Usage:
normalize D
• Inputs:
• Outputs:

## Description

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

 i1 : R = QQ[x,y,t]; i2 : D = diffOp{x^2*t => 3*x^3 + 2*y, t^2 => x+y} 3 2 2 o2 = (3x + 2y)dx dt + (x + y)dt o2 : DiffOp i3 : normalize D 3 2 2 1 1 2 o3 = (x + -y)dx dt + (-x + -y)dt 3 3 3 o3 : DiffOp

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 R i5 : nops = noetherianOperators(I, Strategy => "MacaulayMatrix"); i6 : nops // sort / normalize == {diffOp{1_R => 1}, diffOp{y => 1}, diffOp{y^2 => t, x => 2}, diffOp{y^3 => t, x*y => 6}} o6 = true

## Ways to use normalize :

• "normalize(DiffOp)"

## For the programmer

The object normalize is .