Hi Burcin and Karl-Dieter,

// 1 // And what do you think about log ? Look at these test :

exp(x).operator() == exp # is True, and all(?) trigonometric functions are fine log(x).operator() == ln # is True, yes the alias ln is better than the log name log(x).operator() == log # is False (this feature looks like the binomial one)
log(x).operator() == sage.function.log.function_log # is True

// 2 //

Do you want I place somewhere the rewrite function I test and improve ? Where ?

I code a syntax with strings "from2target", by example "tancot2sincos" or "trigo2exp".

Do you prefer the syntax with a parameter as rewrite (expr, source = "trigo", target=exp)

But in this case It's impossible to compose these rewrite rules.
The syntax "_from_2_to_" allows the composed rewrite rules.

tan(x)^2 -> 1/cos(x)^2 - 1 -> 2 / (exp(I*x) . . .) - 1 -> 1/cos(x)^2 - 1 -> tan^2(x)

sage: rewrite (tan(x)^2, "tancot22sincos", "sincos2exp", "lessIinExp", "cos22tan")
tan(x)^2


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