Fix integral(1/max_symbolic(x, 1)^2, x, 0, oo, algorithm='giac')

[fchapoton]

Compare

sage: integral(1/max_symbolic(x,1)**2,x,0,oo,algorithm='maxima')                
integrate(max(1, x)^(-2), x, 0, +Infinity)
sage: integral(1/max_symbolic(x,1)**2,x,0,oo,algorithm='sympy')                 
2
sage: integral(1/max_symbolic(x,1)**2,x,0,oo,algorithm='giac')                  
+Infinity

The correct answer is sympy's answer.

Related problem:

sage: ex=1/max_symbolic(x,1)**2                                                 
sage: integral(ex,x,0,2,algorithm='giac')                                       
undef

Upstream: Fixed upstream, but not in a stable release.

CC: @slel @sagetrac-parisse @tscrim @kliem

Component: calculus

Keywords: integral

Author: Frédéric Chapoton

Branch/Commit: 39edec7

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/32354

[fchapoton]

comment:2

inside Giac:

  --> Switching to Giac <--

giac: integrate(1/max(x,1)^2,x,0,2)                                             
Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):
Check [abs(x-1)]
when2sign does not work properly with infinities. Replace inf by Inf and run limit after.
Unable to cancel step at 1 of -4*1/2/(x+x)-infinity
undef
giac: integrate(1/max(x,1)^2,x,0,1)                                             
1
giac: integrate(1/max(x,1)^2,x,1,2)                                             
1/2

[fchapoton]

comment:5

un petit souci avec cette intégrale assez simple de la fonction max, dans giac

[sagetrac-parisse]

comment:6

Fixed in my source tree. I will certainly make a 1.7.0-27 release next week.

[fchapoton]

comment:7

Merci !

[slel]

Upstream: Fixed upstream, but not in a stable release.

[fchapoton]

comment:11

now works, should be doctested

[fchapoton]

Author: Frédéric Chapoton

[fchapoton]

Commit: 819c06d

[fchapoton]

comment:13

voilà un test

---

New commits:

f1da83e	partial cleanup in partition.py
819c06d	add doctest for integral of max_symbolic with giac

[fchapoton]

Branch: u/chapoton/32354

[sagetrac-git]

Changed commit from 819c06d to 39edec7

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

39edec7

doctest for integral of max_symbolic with giac

[fchapoton]

comment:15

lights are morally green, so please review

[tscrim]

comment:16

LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

Changed branch from u/chapoton/32354 to 39edec7