On Wednesday, 28 January 2026 at 14:10:53 UTC+1 Fabian wrote:
Kurt: complexNumeric eval(J,x=1/2) also gives approximately 0, when I
include your code in a Sage code and run it in the SageMathCell. With
I:=complexIntegrate(acos(x^2),x) the following line gives almost 0:
complexNumeric eval(D(I,x)+acos(x^2),x=1/2)
This suggests that D(I,x)=-acos(x^2) . This differs from the correct
expression acos(x^2) by a sign. I suspect that the mistake comes from
choosing wrong branches of the logarithm and square root function.
This might explain it, however the culprit must be 'eval' since the lines
below ~prove that D(F,x)=f=acos(x^2) holds.
FriCAS Computer Algebra System
Version: FriCAS 2025.12.23git built with sbcl 2.2.9.debian
Timestamp: Fri 9 Jan 20:25:59 CET 2026
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system commands.
Issue )quit to leave FriCAS and return to shell.
-----------------------------------------------------------------------------
Function declaration sixel : TexFormat -> Void has been added to
workspace.
Function declaration lisp : String -> SExpression has been added to
workspace.
f:=acos(x^2);
Type:
Expression(Integer)
F:=complexIntegrate(f,x);
Type:
Expression(Integer)
R:=complexNormalize(D(F,x)-f);
Type:
Expression(Integer)
real R --> 0
(14) 0
Type:
Expression(Integer)
c:=numer imag R ;
Type:
SparseMultivariatePolynomial(Integer,Kernel(Expression(Integer)))
subst(c, sqrt(x^4-1)=sqrt(x^2+1)*sqrt(x^2-1) ) --> 0
(16) 0
Type:
Expression(Integer)
(17) ->
Fabian
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