I will an example below.
The reason I am asking, is that I am calling giac from sagemath. And sagemath gives an exception when it gets back result with these warning in them as it does not how to parse them. And so now these integrals are counted as failed.
Here is an example
Code : Tout sélectionner
>giac
0>> integrate(1/(2*x^(1/2)+(1+x)^(1/2))^2,x)
Warning, choosing root of [1,0,%%%{-4,[1]%%%}+%%%{-2,[0]%%%},0,1] at parameters values [92.1017843988]
Warning, choosing root of [1,0,%%%{-4,[1]%%%}+%%%{-2,[0]%%%},0,1] at parameters values [1.14118046779]
2*((-5*x-1)/6/(3*x-1)+5/18*ln(abs(3*x-1))+2*(2/9*ln(sqrt(x+1)-sqrt(x))+5/36*ln(abs((sqrt(x+1)-sqrt(x))^2-3))-5/36*ln(abs(3*(sqrt(x+1)-sqrt(x))^2-1))-(10*(sqrt(x+1)-sqrt(x))^2-6)/9/(3*(sqrt(x+1)-sqrt(x))^4-10*(sqrt(x+1)-sqrt(x))^2+3)))
// Time 0.02
1>>
Code : Tout sélectionner
2*((-5*x-1)/6/(3*x-1)+5/18*ln(abs(3*x-1))+2*(2/9*ln(sqrt(x+1)-sqrt(x))+5/36*ln(abs((sqrt(x+1)-sqrt(x))^2-3))-5/36*ln(abs(3*(sqrt(x+1)-sqrt(x))^2-1))-(10*(sqrt(x+1)-sqrt(x))^2-6)/9/(3*(sqrt(x+1)-sqrt(x))^4-10*(sqrt(x+1)-sqrt(x))^2+3)))
Code : Tout sélectionner
>sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.0, Release Date: 2023-05-20 │
│ Using Python 3.10.9. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage: var('x')
x
sage: integrate(1/(2*x^(1/2)+(1+x)^(1/2))^2,x, algorithm="giac")
NotImplementedError: unable to parse Giac output: Warning, choosing root of [1,0,%%%{-4,[1]%%%}+%%%{-2,[0]%%%},0,1] at parameters values [5.38357630698]
Warning, choosing root of [1,0,%%%{-4,[1]%%%}+%%%{-2,[0]%%%},0,1] at parameters values [81.1195442914]
2*((-5*(sageVARx+1)+4)/6/(3*(sageVARx+1)-4)+5/18*ln(abs(3*(sageVARx+1)-4))+2*(1/9*ln((sqrt(sageVARx)-sqrt(sageVARx+1))^2)+5/36*ln(abs((sqrt(sageVARx)-sqrt(sageVARx+1))^2-3))-5/36*ln(abs(3*(sqrt(sageVARx)-sqrt(sageVARx+1))^2-1))-(10*(sqrt(sageVARx)-sqrt(sageVARx+1))^2-6)/9/(3*(sqrt(sageVARx)-sqrt(sageVARx+1))^4-10*(sqrt(sageVARx)-sqrt(sageVARx+1))^2+3)))
sage:
Using sagemath 10 and giac 1.9.0-55
--Nasser