Hi Waldek
I've done some elementary tests to try to understand how FriCAS looks at
n-rooths and log, but now I am even more confused.
* (1) puzzles me: from your previous answer I have understood that (...)^(1/n) with n>1
was "mostly" seen by FriCAS as a multivalued and possibly complex algebraic
number. Is (1) an exception?
* (3) seems to suggest that for positive integer n and positive x x^(1/n) =
e^(log(x)/n), but this is violated by (7)
* (6) and (8) are consistent, but how is defined x^a with a irrational and
positive x?
(1) -> (1 = (1)^(1/2))::Boolean
(1) true
Type: Boolean
(2) -> (1 = e^(1/2*log(1)))::Boolean
(2) true
Type: Boolean
(3) -> (sqrt(1) = e^(1/2*log(1)))::Boolean
(3) true
Type: Boolean
(4) -> (1 = (1)^(sqrt(3)))::Boolean
(4) false
Type: Boolean
(5) -> (1 = e^(sqrt(3)*log(1)))::Boolean
(5) true
Type: Boolean
(6) -> ((1)^(sqrt(3)) = e^(sqrt(3)*log(1)))::Boolean
(6) false
Type: Boolean
(7) -> (sqrt(2) = e^(1/2*log(2)))::Boolean
(7) false
Type: Boolean
(8) -> (2^sqrt(2) = e^(sqrt(2)*log(2)))::Boolean
(8) false
Type: Boolean
I guess that the present status of the code is, as usual, "quite intricated",
but, if not already done, would it be possible for you to take the time (on the medium
term) to write a short note or some rule of thumbs to explain to new users how FriCAS
behaves in view of irrational powers, log, inverse functions, which relations are
expected to hold, and how integrate and complex integrate behave in view of explicitly
trascendental numbers, integration variable and external parameters, like a or a^b or
log(a)?
Furthermore, your view on what should be the ideal target behavior to nicely
resolve these ambiguities and have a homogeneous interface would surely be a
relief ...
Best regards
Riccardo
PS Speaking of oddities, to me (11) and (12) should behave in the same way: as
elements of R->R or or as complex multivalued.
(9) -> sin(0)
(9) 0
Type: Expression(Integer)
(10) -> sinh(0)
(10) 0
Type: Expression(Integer)
(11) -> asin(0)
(11) 0
Type: Expression(Integer)
(12) -> asinh(0)
(12) asinh(0)
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