Bug with definite integral

[rwst]

Two similar integrals, differing by an exponent 1/3 vs 1/5, behave differently.

Here, three ways to compute an integral agree:

sage: q = 1/3
sage: g = (1 + x)^q / (1 - x)
sage: a = g.integrate(x, 2., 3., hold=True)  # hold
sage: b = g.integrate(x, 2., 3.)  # no hold
sage: c = g.nintegral(x, 2., 3.)  # numerical
sage: print(f'  a ≈ {a.n()}\n  b ≈ {b.n()}\n  c ≈ {c[0]}')
  a ≈ -1.045820326411141
  b ≈ -1.04582032641114
  c ≈ -1.045820326411141

Here they do not:

sage: Q = 1/5
sage: G = (1 + x)^Q / (1 - x)
sage: A = G.integrate(x, 2., 3., hold=True)  # hold
sage: B = G.integrate(x, 2., 3.)  # no hold  # long time!
sage: C = G.nintegral(x, 2., 3.)  # numerical
sage: print(f'  A ≈ {A.n()}\n  B ≈ {B.n()}\n  C ≈ {C[0]}')
  A ≈ -0.8870832386197556
  B ≈ -0.963974668699275 - 0.0295059317724807*I
  C ≈ -0.8870832386197555

CC: @slel

Component: calculus

Keywords: integral

Issue created by migration from https://trac.sagemath.org/ticket/22671

[fchapoton]

Changed keywords from none to integral

[fchapoton]

comment:6

This may be an issue with the maxima result

sage: B = G.integrate(x, 2., 3., algorithm="mathematica_free")
sage: B.n()
-0.887083000000000
sage: B = G.integrate(x, 2., 3., algorithm="giac")
sage: B.n()
-0.887083238620000

[slel]

comment:7

Perhaps the integration engine

• uses a dedicated "real cube root" function in one case
• lacks a "real fifth root" function for the other case