In this file we implemenet the handling of expressions.
We have two types of expressions: Expr and GenExpr.
The Expr can only handle polynomial expressions.
In addition, one can recover easily information from them.
A polynomial is a dictionary between `terms` and coefficients.
A `term` is a tuple of variables
For examples, 2*x*x*y*z - 1.3 x*y*y + 1 is stored as a
{Term(x,x,y,z) : 2, Term(x,y,y) : -1.3, Term() : 1}
Addition of common terms and expansion of exponents occur automatically.
Given the way `Expr`s are stored, it is easy to access the terms: e.g.
expr = 2*x*x*y*z - 1.3 x*y*y + 1
expr[Term(x,x,y,z)] returns 1.3
expr[Term(x)] returns 0.0
On the other hand, when dealing with expressions more general than polynomials, that is, absolute values, exp, log, sqrt or any general exponent, we use GenExpr. GenExpr stores expression trees in a rudimentary way. Basically, it stores the operator and the list of children. We have different types of general expressions that in addition to the operation and list of children stores SumExpr: coefficients and constant ProdExpr: constant Constant: constant VarExpr: variable PowExpr: exponent UnaryExpr: nothing We do not provide any way of accessing the internal information of the expression tree, nor we simplify common terms or do any other type of simplification. The `GenExpr` is pass as is to SCIP and SCIP will do what it see fits during presolving.
TODO: All this is very complicated, so we might wanna unify Expr and GenExpr. Maybe when consexpr is released it makes sense to revisit this. TODO: We have to think about the operations that we define: __isub__, __add__, etc and when to copy expressions and when to not copy them. For example: when creating a ExprCons from an Expr expr, we store the expression expr and then we normalize. When doing the normalization, we do ``` c = self.expr[CONST] self.expr -= c ``` which should, in princple, modify the expr. However, since we do not implement __isub__, __sub__ gets called (I guess) and so a copy is returned. Modifying the expression directly would be a bug, given that the expression might be re-used by the user.
Definition in file expr.pxi.
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