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week 3

Hi, At the start of this week I wrote a method to check if a given solution lies in the domain of the equation or not. The problem it targeted was equations like (x - 1)/(1 + 1/(x - 1)) though at x = 1 the eqution has value zero the point is not present in the domain of the given equation. Though there is some disagreement on the implementation, the idea was to traverse the expression tree and check if any of the subexpression goes unbounded for the given value. Later I observed that caching was messing with the tests. Sometimes the tests passed and sometimes the same test suit run without any modification in the code failed. To do the check on the subexpressions I need to have a copy of the original equation before the solver performs any simplification on it. Being not sure of the mutability of the equations I used deepcopy to copy the original equation to a variable. Later in a meeting we figured out that deepcopy was messing with caching. Aaron told me that every expression in sympy is immutable so don't need to perform deepcopy on anything.

This week we will restart working on the sets to represent infinite solutions, Almost every equation in complex domain other than polynomials and rationals has infinitly many solutions. For example even the simple equation exp(x) == 1 has infinitely many solutions that is i*2*n*pi where n is an integer. To return these solutions we first need to have infrastructure to handle them. The old(current) solvers does it wrong, it implicity mixes up the complex and real domains, the answer it returns to exp(x) == 1 is only [0]. Earlier I was also doing it wrong so I decided that I should have two seperate solvers for reals and complex instead of one. This also simplifed the code for the reals solvers to a large extent.

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