&dr

Preben Alsholm — Mon, 04 Feb 2013 21:16:50 Z

Certainly you can define infix operators as in your image:

If f and g are procedures:
`&dl`:=proc(f,g) D(f)*g end proc;
`&dr`:=proc(f,g) f*D(g) end proc;
f &dl g;
sin &dl cos;
f &dr g;
#If the variable is known to be x and f and g are expressions in x:
`&dl`:=proc(f,g) diff(f,x)*g end proc;
`&dr`:=proc(f,g) f*diff(f,x) end proc;
f(x) &dl g(x);
sin(x) &dl cos(x);
f(x) &dr g(x);

######
But I don't see how to use that for accomplishing the intention in your last statement:

f exp(left_derivative_x right_derivative_x) g

In fact I don't understand it.

The idea of such left and right derivatives

pascal thibaudeau — Tue, 05 Feb 2013 14:35:19 Z

The idea of such left and right derivatives is to calculate the star product as defined there

http://en.wikipedia.org/wiki/Phase_space_formulation#Star_product

when the exponential function can be interpreted as a power series

MaplePrimes - answers and comments on Question, How to define left and right derivatives as binary operators?

&dr

The idea of such left and right derivatives