Hello FriCAS group,
Thank you Kurt, Qian, and Waldek for your prompt replies. I have tried out
the suggestion by Kurt to use complexIntegrate. The following check
indicates that this does not work for acos(x^2):
from sage.interfaces.fricas import fricas
fricas.eval(
"f:=acos(x^2);"
"F:=complexIntegrate(f,x);"
)
print(fricas("complexNumeric(eval(D(F,x)-f,x=1/2))"))
This produces the output - 2.63..., which is not close to desired value 0.
Fabian
On Wednesday, January 28, 2026 at 3:33:46 AM UTC+1 Waldek Hebisch wrote:
> On Wed, Jan 28, 2026 at 10:09:14AM +0800, Qian Yun wrote:
> > Thanks for the report.
> >
> > Git bisect points to
> >
> https://github.com/fricas/fricas/commit/1f42999f91ce516a8d027a61be4ecbf32ad2ada4
> >
> > "Handle some elliptic integrals", June 14, 2022.
> > (Between 1.3.7 and 1.3.8)
> >
> > Before this commit, the result is a integral sign
> > which means fricas proves it does not have elemental
> > integral, which is correct.
>
> The reason is that transformations used in postprocessing result
> of integration may incorrectly transform elliptic integrals to
> 0.
>
> >
> > - Best,
> > - Qian
> >
> > On 1/28/26 1:42 AM, Fabian wrote:
> > > Hello FriCAS group,
> > >
> > > It looks like I found a bug in FriCAS:
> > > F:=integrate(acos(x^2),x)
> > > gives:
> > > +--------+
> > > | 4 2 2
> > > - 2 \|- x + 1 + x acos(x )
> > > ----------------------------
> > > x
> > >
> > > D(F,x)-acos(x^2)
> > > gives the following instead of 0:
> > > 2
> > > -------------
> > > +--------+
> > > 2 | 4
> > > x \|- x + 1
> > >
> > > I use FriCAS via https://sagecell.sagemath.org/ . Here is some
> Sage-code
> > > that produces the above output:
> > >
> > > from sage.interfaces.fricas import fricas
> > > fricas.eval(
> > > "F:=integrate(acos(x^2),x)"
> > > )
> > > print("F=\n",fricas("F"))
> > > fricas.eval("f:=D(F,x)-acos(x^2)")
> > > print("F'-acos(x^2)=\n",fricas("f"))
> > >
> > > The FriCAS version is 1.3.12. (print(fricas.eval(")lisp |
> > > $build_version|") tells me this.)
> > >
> > > The SageMath version is 10.8, Release Date: 2025-12-18. (version()
> tells
> > > me this.)
> > >
> > > Fabian
> > >
> > > --
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> https://groups.google.com/d/msgid/fricas-
> > > devel/e5fde980-d9d7-4e5d-9fb9-d1cc5c45c021n%40googlegroups.com
> <https://
> > > groups.google.com/d/msgid/fricas-devel/e5fde980-d9d7-4e5d-9fb9-
> > > d1cc5c45c021n%40googlegroups.com?utm_medium=email&utm_source=footer>.
> >
> > --
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> .
>
> --
> Waldek Hebisch
>
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