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 |