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Dmodules :: Dtransposition

Dtransposition -- standard transposition for Weyl algebra

Synopsis

Description

The standard transposition is the involution of the Weyl algebra which sends xadb to (-d)bxa. It provides the equivalence in the Weyl algebra between left and right D-modules.

i1 : makeWA(QQ[x,y])

o1 = QQ[x..y, dx, dy]

o1 : PolynomialRing, 2 differential variables
i2 : L = x^2*dy + y*dy^2 + 3*dx^5*dy

        5      2         2
o2 = 3dx dy + x dy + y*dy

o2 : QQ[x..y, dx, dy]
i3 : Dtransposition L

        5      2         2
o3 = 3dx dy - x dy + y*dy  + 2dy

o3 : QQ[x..y, dx, dy]

Caveat

The standard transposition of a left ideal should be a right ideal, however M2 currently doesn't support right modules. Thus the output is left ideal generated by the transposition of the previous generators.

See also

Ways to use Dtransposition :

For the programmer

The object Dtransposition is a method function.