I want to use custom transformation functions in Simplify, but Mathematica does not seem to use them properly. Consider the following
t1[a] := 1
t2[b] := 0
FullSimplify[a + b, TransformationFunctions -> {t1, t2}]
As intended this evaluates to 1. However, if I add the standard transformation functions nothing happens:
FullSimplify[a + b, TransformationFunctions -> {Automatic, t1, t2}]
This gives a + b. Why did Mathematica forget about my custom functions? Ideas?
Interesting question. I don't know if this behavior is intended but I think I can at least give some insight into the problem.
We can use a custom ComplexityFunction with an embedded Print to take a look at what transformed expressions are tested.
cf = (Print[#]; LeafCount[#] + Count[#, _Symbol, {0, -1}]) &;
We will also need to make use of ClearSystemCache[] to see all simplification attempts.
First without Automatic:
ClearSystemCache[]
Simplify[a + b, TransformationFunctions -> {t1, t2}, ComplexityFunction -> cf]
Observe that for whatever reason t1 and t2 are not applied to atomic elements when Automatic is included:
ClearSystemCache[]
Simplify[a + b, TransformationFunctions -> {Automatic, t1, t2}, ComplexityFunction -> cf]
While the cause is not clear the solution is: write your transformation functions so that they work on compound expressions.
For example:
t3 = # /. {a -> 1, b -> 0} &;
Simplify[a + b, TransformationFunctions -> {Automatic, t3}]
1
