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NoetherianOperators :: DiffOp RingElement

DiffOp RingElement -- apply a differential operator

Synopsis

Description

The differential operators of the ring $R = \mathbb{F}[x_1,\dots,x_n]$ act naturally on elements of $R$. The operator $dx_i$ acts as a partial derivarive with respect to $x_i$, and a polynomial acts by multiplication.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing
i2 : dx = diffOp{x^2 => 1}

       2
o2 = dx

o2 : DiffOp
i3 : D = diffOp{1_R => x^2 + y^2}

      2    2
o3 = x  + y

o3 : DiffOp
i4 : dx(x^4 + x^3 + y)

        2
o4 = 12x  + 6x

o4 : R
i5 : D(x^2 - y^2)

      4    4
o5 = x  - y

o5 : R