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Coursera: (x+y) is equivalent to (y+x): launching mathematical expressions checking
Several of our classes involve students using mathematical expressions, but there was no way for us to automatically check this work. The stated solution to a problem may be x+y, but if a student answers y+x, our system needs to understand that this is also correct. This equivalence should not be limited to simply associativity and commutativity; expressions like 1-cos^2(x) should also be accepted in place of sin^2(x). For the solution, we considered a number of factors: how the language or framework we chose would integrate into our system, how much we could customize this solution (in order to fix bugs or add additional capabilities), and the solution’s fit for our problem. While building an equivalence checker from scratch would have given us the greatest flexibility and control over our tool, this would have been an inefficient use of engineering effort — the problem of algebraic manipulation and equivalence checking has already been deeply explored by systems such as…