Gapplet
You input a polynomial
f 
Z[x,y].
We then view it as the recipee for a binary operation
on Z,
mapping (a,b)
Z×Z
to
f(a,b) Z,
and we analyse whether the operation is associative.
Input a polynomial f in x, y with integral coefficients, e.g., x*y+x+y. |
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Test whether the corresponding binary map is associative | |
We compute f(x,f(y,z))
and f(f(x,y),z),
and compare the two.
By arguments as in Lagrange interpolation,
equality of these two polynomials in x, y, z is equivalent to associativity.
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