Gapplet

Let mu and pl be binary operations on Z. The left distributive law reads

mu(x,pl(y,z)) = pl(mu(x,y),mu(x,z)).

In the definition we have written mu = * and pl = +. Now if you express mu and pl by polynomials in x and y, we test if the distributive law holds.

Input a definition for mu 
e.g., x*y+x+y
 
Input a definition for pl
e.g., x - y
 
 
The left distributivity test