Basic algebraic identities

*To*: mathgroup at smc.vnet.net*Subject*: [mg87809] Basic algebraic identities*From*: Boris Blankleider <boris.blankleider at flinders.edu.au>*Date*: Thu, 17 Apr 2008 06:59:28 -0400 (EDT)

1. Which basic algebraic identities does Mathematica know? For example, it does not appear to know the orthogonality relation for Legendre polynomials: Integrate[ LegendreP[m, x] LegendreP[n, x], {x,-1,1}] - 2/(2 n+1) KroneckerDelta[n,m] = 0 When I try this out, I find that the left hand side does not evaluate to zero - even if I add assumptions about n & m being positive integers. Yet a similar check shows that it does know about Cos[x]^2 + Sin[x]^2] - 1 = 0 (although one does need to use Simplify[%] before it reveals its knowledge). 2. If it really does not know the orthogonality relation for Legendre polys, how would I teach it?