Add doctest for integrating exp(t)/(t + 1)^2 with giac

[nasser1]

This ticket is to add a doctest:

sage: t = SR.var('t')
sage: integrate(exp(t)/(t + 1)^2, t, algorithm="giac")
(t*Ei(t + 1) + Ei(t + 1) - e^(t + 1))/(t*e + e)

---

[Original report]

Using sage 8.3.beta6:

sage: var('t')
sage: integrate(exp(t)/(t + 1)^2, t, algorithm="giac")
undef

whereas used directly, giac integrates with no problem:

>giac
// Using locale /usr/share/locale/
// en_US.utf8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 8
Help file /usr/share/giac/doc/en/aide_cas not found
Added 26 synonyms
Welcome to giac readline interface
(c) 2001,2017 B. Parisse & others
Homepage http://www-fourier.ujf-grenoble.fr/~parisse/giac.html
Released under the GPL license 3.0 or above
See http://www.gnu.org for license details
May contain BSD licensed software parts (lapack, atlas, tinymt)
-------------------------------------------------
0>> integrate(exp(t)/(t + 1)^2, t)
 (t*Ei(t+1)+Ei(t+1)-exp(1)*exp(t))/(t*exp(1)+exp(1))
// Time 0.01
1>>

So why did Sage return undef for this computation?

First time reporting bug to Sage.

CC: @frederichan-IMJPRG @sagetrac-parisse @rwst @slel

Component: interfaces

Keywords: giac, integral

Author: Rajat Sirohi

Branch: cdae633

Reviewer: Kwankyu Lee

Issue created by migration from https://trac.sagemath.org/ticket/25626

[slel]

comment:1

Regarding the bug: maybe the Ei in the result could not be converted to Sage?

Regarding the Trac ticket: not sure if this belongs to "interfaces" or "symbolics".

Was this fixed in another ticket? This is what I get with Sage 8.3.rc3:

sage: version()
'SageMath version 8.3.rc3, Release Date: 2018-07-28'
sage: t = SR.var('t')
sage: integrate(exp(t)/(t + 1)^2, t, algorithm="giac")
integrate(e^t/(t + 1)^2, t)

[slel]

comment:2

Oh, I see, instead of undef I got the unevaluated integral back.

Slightly better than undef, but if Giac can compute it we would like to get the evaluated result.

[fchapoton]

comment:4

Giac does the following

giac: integrate(exp(t)*(t+1)^-2,t)                                              
integrate(exp(1/(t+1)^-1-1)*(t+1)^-2,t)
giac: integrate(exp(t)/(t+1)^2,t)                                               
(t*Ei(t+1)+Ei(t+1)-exp(1)*exp(t))/(t*exp(1)+exp(1))

[frederichan-IMJPRG]

comment:5

NB: it seems that it is not giac himself that is changing the quotient to a product but the conversion filter called before using giac:

sage: t=var('t')                                                                                              
sage: F=exp(t)/(1+t)^2                                                                                        
sage: giac(F)                                                                                                 
(t+1)^-2*exp(t)
sage: giac(str(F))                                                                                            
exp(t)/(t+1)^2
sage: giac(str(F)).integrate(t)                                                                               
(t*Ei(t+1)+Ei(t+1)-exp(1)*exp(t))/(t*exp(1)+exp(1))

[fchapoton]

comment:7

Well, the expression itself is not considered as a quotient in sage:

sage: t = SR.var('t')                                                           
sage: F = exp(t)/(t + 1)^2                                                      
sage: F.operands()                                                              
[(t + 1)^(-2), e^t]
sage: F.operator()                                                              
<function mul_vararg at 0x7f4b14362310>

[slel]

comment:8

I don't think Sage's symbolic expressions are ever
recorded as differences or quotients, only as sums
(summing the opposite for a difference) and products
(multiplying by the inverse for a quotient).

[slel]

comment:9

In Sage 9.3.rc0:

sage: t = SR.var('t')
sage: integrate(exp(t)/(t + 1)^2, t, algorithm="giac")
(t*Ei(t + 1) + Ei(t + 1) - e^(t + 1))/(t*e + e)

Probably one of the giac or giacpy_sage upgrades solved that.

Should we add a doctest?

[mkoeppe]

comment:11

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review.

[fchapoton]

Changed keywords from giac to giac, integral

[Rajat-Sirohi]

Branch: u/gh-Rajat-Sirohi/add_doctest_for_integrating_exp_t___t___1__2_with_giac

[Rajat-Sirohi]

New commits:

cdae633

Trac #25626: Add doctest for integrating exp(t)/(t + 1)^2 with giac

[Rajat-Sirohi]

Author: Rajat Sirohi

[Rajat-Sirohi]

Commit: cdae633

[kwankyu]

comment:18

Perfect.

[kwankyu]

Reviewer: Kwankyu Lee

[kiwifb]

comment:19

Well, with giac 1.9 which has just been allowed from the system I get

sage -t --long --random-seed=138683552333987748337622634611718883378 /usr/lib/python3.10/site-packages/sage/calculus/calculus.py
**********************************************************************
File "/usr/lib/python3.10/site-packages/sage/calculus/calculus.py", line 387, in sage.calculus.calculus
Failed example:
    integrate(exp(t)/(t + 1)^2, t, algorithm="giac")
Expected:
    (t*Ei(t + 1) + Ei(t + 1) - e^(t + 1))/(t*e + e)
Got:
    ((t + 1)*(1/(t + 1) - 1)*Ei(-(t + 1)*(1/(t + 1) - 1) + 1) - Ei(-(t + 1)*(1/(t + 1) - 1) + 1) + e^(-(t + 1)*(1/(t + 1) - 1) + 1))/((t + 1)*(1/(t + 1) - 1)*e - e)

I haven't really checked whether it can be simplified to the previous form or not.

[Rajat-Sirohi]

comment:20

Replying to @kiwifb:

Well, with giac 1.9 which has just been allowed from the system I get

sage -t --long --random-seed=138683552333987748337622634611718883378 /usr/lib/python3.10/site-packages/sage/calculus/calculus.py
**********************************************************************
File "/usr/lib/python3.10/site-packages/sage/calculus/calculus.py", line 387, in sage.calculus.calculus
Failed example:
    integrate(exp(t)/(t + 1)^2, t, algorithm="giac")
Expected:
    (t*Ei(t + 1) + Ei(t + 1) - e^(t + 1))/(t*e + e)
Got:
    ((t + 1)*(1/(t + 1) - 1)*Ei(-(t + 1)*(1/(t + 1) - 1) + 1) - Ei(-(t + 1)*(1/(t + 1) - 1) + 1) + e^(-(t + 1)*(1/(t + 1) - 1) + 1))/((t + 1)*(1/(t + 1) - 1)*e - e)

I haven't really checked whether it can be simplified to the previous form or not.

In fact, when you simplify the second expression, it is indeed equivalent to the first.

[vbraun]

Changed branch from u/gh-Rajat-Sirohi/add_doctest_for_integrating_exp_t___t___1__2_with_giac to cdae633

[kiwifb]

comment:22

Follow up at #34037

[kiwifb]

Changed commit from cdae633 to none