There are 2 different issues in your question.
First, difference between %i and sqrt(-1):
When used in expression, one gives EXPR(COMPLEX INT),
the other gives EXPR INT:
(7) -> sin(%i)
(7) sin(%i)
Type: Expression(Complex(Integer))
(8) -> sin sqrt(-1)
+---+
(8) sin(\|- 1 )
Type: Expression(Integer)
And the integration code will treat differently for
Expression(Complex(Integer)) and Expression(Integer).
Second, the error in
integrate(x/( (x^2 - 1/5 - 2*sqrt(-1)/5)*sqrt(x^3 - x)),x)
That's because the interpreter can't automatically figure out
the type for this. Not sure if it's a bug. Give it a hint can help:
x/( (x^2 - 1/5 - 2*sqrt(-1::EXPR INT)/5)*sqrt(x^3 - x))
- Qian
On 6/19/22 16:02, 'Nasser M. Abbasi' via FriCAS - computer algebra
system wrote:
I was looking at another question at difference forum. I noticed
integrate hangs when
using %i for sqrt(-1) but returns right away when type sqrt(-1). But
returns with an error message.
But these two should be the same.
===========================
(14) -> %i*%i
(14) - 1
Type:
Complex(Integer)
(15) -> sqrt(-1)*sqrt(-1)
(15) - 1
=========================
So why this gives error
==========================
(16) -> setSimplifyDenomsFlag(true)
integrate(x/( (x^2 - 1/5 - 2*sqrt(-1)/5)*sqrt(x^3 - x)),x)
There are 9 exposed and 6 unexposed library operations named -
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op -
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named -
with argument type(s)
Polynomial(Fraction(Integer))
AlgebraicNumber
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
======================
But this does not give error (but seems to hang, or take long time for
me to wait)
integrate(x/( (x^2 - 1/5 - 2*%i/5)*sqrt(x^3 - x)),x)
I just changed sqrt(-1) by %i and nothing else.
--Nasser
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