[Octave-bug-tracker] [bug #56066] Symbolic integration of heaviside.

[Colin Macdonald]

Follow-up Comment #1, bug #56066 (project octave):

I can confirm:

>> syms t
>> f = heaviside(t - 1)
f = (sym) Heaviside(t - 1)
>> F = int(f, t)
F = (sym)

  ⎧           0              for │t│ < 1
  ⎪                                     
  ⎨╭─╮0, 2 ⎛2, 1       │  ⎞             
  ⎪│╶┐     ⎜           │ t⎟   otherwise 
  ⎩╰─╯2, 2 ⎝      1, 0 │  ⎠             


that expression does seem to be technically correct for t >= -1:


>> double(subs(F, t, -1))
ans =          0
>> double(subs(F, t, sym(1)/2))
ans =          0
>> double(subs(F, t, 2))
ans =          1
>> double(subs(F, t, 3))
ans =          2
>> double(subs(F, t, 10))
ans =          9


But it seems to be wrong for t <= -1, where it should be zero.

There are various upstream SymPy bugs about heaviside and integrals:
Does this look like https://github.com/sympy/sympy/issues/12632?

A workaround is probably

>> g = rewrite(f, 'Piecewise')
g = (sym)

  ⎧     0        for t - 1 < 0
  ⎪                           
  ⎨Heaviside(0)  for t - 1 = 0
  ⎪                           
  ⎩     1        for t - 1 > 0

>> int(g, t)
ans = (sym)

  ⎧  0    for t < 1
  ⎨                
  ⎩t - 1  otherwise


    _______________________________________________________

Reply to this item at:

  <https://savannah.gnu.org/bugs/?56066>

_______________________________________________
  Message sent via Savannah
  https://savannah.gnu.org/