WeylAlgebra

WeylAlgebra -- an option used when creating a polynomial ring to specify that a Weyl algebra is to be produced.

A Weyl algebra is an algebra in which some of the variables behave as derivatives with respect to the other variables.

i1 : R = ZZ/101[x,dx,y,dy,WeylAlgebra => {x=>dx, y=>dy}];

The list {x=>dx, y=>dy} indicates that the variable dx is to play the role of the derivative with respect to x, and that y is to play the role of the derivative with respect to y.

i2 : dx*x

o2 = x*dx + 1

o2 : R
i3 : dx*x^10

      10        9
o3 = x  dx + 10x 

o3 : R
i4 : dx*y^10

         10
o4 = dx*y  

o4 : R

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