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Question: How to "simplify" a RootOf result?

Question:How to "simplify" a RootOf result?

mmcdara 6635 Maple
solve identity erf edited-question etiquette
July 21 2023
2

I rephrased my previous question in a more synthetic form
(there was probably a lot in it that I thought was important for understanding the problem, but I realized afterwards that it only added confusion).

The true question is yellow-highlighted in the code below

> 

restart
> 

# The result below seems natural: we were taught in school that exp 
# being a bijective function we can get rid of it in the equality to
# solve and write simply x=Pi.

x = solve(exp(x)=exp(Pi), x)

x = Pi

 (1)
> 

# But the solution method solve uses is not that natural (and I
# don't really understand it).
# infolevel[solve] := 10:
# x = solve(exp(x)=exp(Pi), x);
> 

# Replacing now exp by some undefined function f produces a
# kind of "no-solution" answer: this seems quite normal because
# not knowing the properties of f one cannot simply get rid of it.

infolevel[solve] := 0:
x = solve(f(x)=f(Pi), x)

x = RootOf(f(_Z)-f(Pi))

 (2)
> 

# Finally replace f by a bijective function with no analytic expression.

s = solve(erf(x)=erf(Pi), x) assuming x::real

s = RootOf(erf(_Z)-erf(Pi))

 (3)
> 

# It would have seem reasonable for Maple to answer x=Pi, or
# at least it is what I would have done given the properties
# of the erf function.
#
# How can I "force" Maple to "simplify" it's RootOf result to get
# x=Pi?


Download solve_erf.mw

For those interested in the motivations of this quastion, see here Where_does_the_question_come_from.mw

The original question is here Original_question.pdf
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