Your code doesn't do what you probaby mean to do. Sequentially, your function :
computes integrate(f, x) (using Sage's default integrator), then
creates a Fricas object representing this integral, and returns it
Your code then tries to pretty_print this fricas object, which fails (the error message is pretty specific...).
A couple suggestions :
Integrating via Fricas is more easily done by integrate(f, x, algorithm="fricas"), which returns the Sage object representing the Fricas value returned by Fricas' integrator. (EDIT : typo fixed).
You can also do this manually with fricas.integrate(*map(fricas, (f, x))).sage(), which returns -((x - 1)*log(x - 1) - (x - 1)*log(x) + 1)/(x - 1).
Quite intentionally, I leave the necessary explanations of this syntax to your explorations of Python and Sage documentations...
pretty_print may be platform-dependent but also object-dependant...EDIT : On Sagemath 9.8.beta4 running locally, I get :
sage: %cpaste
Pasting code; enter '--' alone on the line to stop or use Ctrl-D.
:f = 1/(x*(x-1)^2)
:print("default : ",f.integrate(x))
:print("maxima : ",f.integrate(x, algorithm="maxima"))
:print("giac : ",f.integrate(x, algorithm="giac"))
:print("sympy : ",f.integrate(x, algorithm="sympy"))
:print("mathematica_free : ",f.integrate(x, algorithm="mathematica_free"))
:print("fricas : ",f.integrate(x, algorithm="fricas"))
:--
default : -1/(x - 1) - log(x - 1) + log(x)
maxima : -1/(x - 1) - log(x - 1) + log(x)
giac : -1/(x - 1) + log(abs(-1/(x - 1) - 1))
sympy : -1/(x - 1) - log(x - 1) + log(x)
mathematica_free : -1/(x - 1) - log(x - 1) + log(x)
fricas : -((x - 1)*log(x - 1) - (x - 1)*log(x) + 1)/(x - 1)
On SageCell on 2022-12-06, reults are similar for default, maxima, giac and sympy integrators ; fricas fails and mathematica_free "never" returns.
HTH,
The code you suggested:
f = 1/(x*(x-1)^2)
integrate(x, f,algorithm="fricas")
does not work either on sagecell or my notebook. The code
f = 1/(x*(x-1)^2)
fricas.integrate(*map(fricas, (f, x))).sage()
does not work also in sagecell.
Finally, I 'm not sure about your first remark. If you provide
sage:f = 1/sqrt((x^2+1)*(x+1))
sage:integrate_fricas(f)
8 80 3 x + 1
2 weierstrassPInverse(- -,- --,-------)
3 27 3
instead from
sage:integrate(f,x)
you get
integrate(1/sqrt((x^2 + 1)*(x + 1)), x)
Your remark seems reasonable, but it seems that sagemath does something else.
integrate(x, f,algorithm="fricas") is a typo for integrate(f, x,algorithm="fricas"). My abject apologies :-)...
fricas.integrate(*map(fricas, (f, x))).sage() WorksForMe ... on my local 9.8.beta4. Indeed, id does not (yet ?) works on Sagecell. I don't know why.
I do not get your third remark. Could you clarify ?
BTW :
sage: (1/sqrt((x^2+1)*(x+1))).integrate(x, algorithm="fricas")
2*weierstrassPInverse(-8/3, -80/27, x + 1/3)
Same result as you, but converted to Sage...
sage: mathematica.Integrate((1/sqrt((x^2+1)*(x+1))), x).sage()
(x + 1)*sqrt(-(I + 1)*x - I + 1)*sqrt((2*I - 2)*x + 2*I + 2)*elliptic_f(arcsin(1/2*sqrt(2)*sqrt((I + 1)*x + I + 1)), -I)/(sqrt(x^3 + x^2 + x + 1)*sqrt((I + 1)*x + I + 1))
Quite a different antiderivative. May or may not be OK.
I meant that the command
fricas(integrate(f,x))
and
f.integrate(x, algorithm="fricas")
provide the same results, and the command alone (ie. the built in sagemath without calling fricas)
integrate(f,x)
does not do anything (for f=1/sqrt((x^2+1)*(x+1)) ). So your first comment about "Your code doesn't do what you probably mean to do" is not true. Thank you for your answer.
does not do anything (for f=1/sqrt((x^2+1)*(x+1)) )
When Sage returns the unevaluated integrate command, this means that the choosen integrator fails to find an antiderivative (or a defined integral).
More generally : Sage 9.8.beta4 (locally installed) gives more answers than Sagecell as of 20222-12-06 : see my second edit to my answer.
Asked: 2022-12-04 18:37:27 +0200
Seen: 148 times
Last updated: Dec 06 '22
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