Poincare: Add a README for the simplification

Change-Id: Ife72d5914a6968bdc7c52ad93a329b37fe2c01a6

poincare/src/simplify/README.md

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+# Poincare simplification architecture
+
+## A three-tiered architecture
+
+We formalize the simplification of an Expression the following way:
+1. Find an interesting pattern in an Expression
+2. Build a new Expression based on that pattern.
+
+So in other words, a simplification is the association of a pattern and a gene-
+ration rule. We formalize this approach with three classes : a `Simplification`
+is made out of an `ExpressionSelector` (whose job is to detect a pattern in an
+`Expression`) and of an `ExpressionBuilder` (which will build a new expression).
+
+To give more details, it goes this way :
+```
+Expression * inputExpression;
+ExpressionSelector * selector
+ExpressionBuilder * builder;
+
+ExpressionMatch * match = selector->match(inputExpression);
+Expression * simplifiedExpression = builder->build(match);
+```
+
+## Rules
+```
+Addition(Integer(a),Integer(b),c*) -> Addition($Sum(a,b),c*)
+```
+
+Addition(Integer(a),Integer(b)) -> Function(Sum,a,b)
+Addition(Addition(a*),b*) -> Addition(a*,b*)
+
+
+- Matches have to be exhaustive i.e : capture all children
+ -> We can tell it at compile time (e.g. "Hey, Addition(a,b) can miss children,
+you need a wildcard", but "ln(a)" is allright because ln has only one child)
+
+Addition(Integer(0),...) -> Addition(...)
+Product(Integer(0),...) -> Integer(0)
+
+Fraction(Fraction(a,b),c) -> Fraction(a,Product(b,c))
+
+Build(type=addition)
+ - integer(0)
+ - integer(1)
+ - and then all the clones of...
+ - and then all the clones of...
+
+
+a*b+a*c -> a*(b+c)
+
+
+a+(b+c)