README.md in symath-0.1.0 vs README.md in symath-0.1.1

- old
+ new

@@ -302,13 +302,20 @@ => 3*y**2 </pre> ### Integration -Integration is available as the int-operator. With one argument, the -operator evaluates to the antiderivative of the expression: +Integration is available as the int-operator. The algorithm is only a +very simple one, imitating the most basic techniques of finding the +anti-derivative, combined with a few well known equation patterns. The +operation also has a limitation when it comes to non-commutable +terms (matrices, quaternions, etc.). In that case, the result is not +reliable. +With one argument, the operator evaluates to the antiderivative of the +expression: + <pre> > int(2**:x).evaluate => 2**x/ln(2) + C </pre> @@ -523,9 +530,24 @@ {a=>y**2, b=>x**2 + 3}, {a=>3, b=>x**2 + y**2}, {a=>x**2 + y**2, b=>3}, {a=>x**2 + 3, b=>y**2}, {a=>y**2 + 3, b=>x**2}] +</pre> + +#### Match/replace operation + +The match_replace method tries to find an occurence of a pattern in +the expression, and replaces it if it is found. The method can be used +together with the iterate method. The latter repeats a method until +there are no more changes: + +<pre> + > a = sin(sin(sin(:a + :b) - sin(:f))) + > a.match_replace(sin(:x), :e*:x, [:x]) + => e*sin(sin(a + b) - sin(f)) + > a.iterate('match_replace', sin(:x), :e*:x, [:x]) + => e*e*(e*(a + b) - e*f) </pre> #### Factorization and product expansion The factorization method has been ripped from the python