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NoetherianOperators :: DiffOp ? DiffOp

DiffOp ? DiffOp -- comparison of differential operators

Synopsis

Description

The ordering of DiffOps a product ordering of the undelying ring, where the $dx$ monomoial are compared first, and ties are broken with coefficients.

i1 : R = QQ[x,y, MonomialOrder => Lex]

o1 = R

o1 : PolynomialRing
i2 : D1 = diffOp{x^2 => y, y => x^2}

         2    2
o2 = y*dx  + x dy

o2 : DiffOp
i3 : D2 = diffOp{y => y^2}

      2
o3 = y dy

o3 : DiffOp
i4 : D3 = diffOp{x^2 => y, y => x^2 + y^2}

         2     2    2
o4 = y*dx  + (x  + y )dy

o4 : DiffOp
i5 : D1 ? D1

o5 = ==

o5 : Keyword
i6 : D1 ? D2

o6 = >

o6 : Keyword
i7 : D1 ? D3

o7 = <

o7 : Keyword
i8 : D1 + D2 == D3

o8 = true
i9 : D1 + D2 - D3 == 0

o9 = true