Symbolic sum giving incorrect answers

[Peter Taylor]

"sum" is not specific enough a keyword to filter down the discussions. None of the titles of the "Mathematically incorrect answers" list on Trac are obviously about this issue, but is it new?

Code:

s, n, x, y, t = var('s, n, x, y, t')
print(sum(binomial(n,s) * (x+y)^s * x^(n-s), s, 0, n))
print(sum(binomial(n,s) * (x+1)^s * x^(n-s), s, 0, n))

Observed in version 9.4 using sagecell.sagemath.org:

(2*x + y)^n

(2*x)^n

Expected:

(2*x + y)^n

(2*x + 1)^n

Link to reproduce: https://sagecell.sagemath.org/?z=eJyFjEEKg0AQBO-Cf-ibM2Yi-gC_IqxBwkJ2Ijsq6-9dghcPklM3TVWbe09N8PZqRqc6xTOIy6IsTKCCJNgFC3psLlJ1GasfN0evC9kaaPT6Dd59SMUYNSg9dh4stzSQPo0F2W_zBfMfr7vzDlIMMqI=&lang=sage&interacts=eJyLjgUAARUAuQ==

Regards,

Peter Taylor

[Dima Pasechnik]

On Fri, Feb 11, 2022 at 5:00 PM 'Peter Taylor' via sage-devel
<sage-...@googlegroups.com> wrote:
>
> "sum" is not specific enough a keyword to filter down the discussions. None of the titles of the "Mathematically incorrect answers" list on Trac are obviously about this issue, but is it new?
>
> Code:
>
> s, n, x, y, t = var('s, n, x, y, t')
> print(sum(binomial(n,s) * (x+y)^s * x^(n-s), s, 0, n))
> print(sum(binomial(n,s) * (x+1)^s * x^(n-s), s, 0, n))

This looks like a Maxima bug:

sage: SR(binomial(n,s) * (x+1)^s * x^(n-s)).sum( s, 0, n,
algorithm='giac') # correct
x^n*e^(n*log(2*x + 1) - n*log(x))
sage: SR(binomial(n,s) * (x+1)^s * x^(n-s)).sum( s, 0, n) # wrong
(actually, maxima is the default)
(2*x)^n
sage: SR(binomial(n,s) * (x+1)^s * x^(n-s)).sum( s, 0, n,
algorithm='maxima') # wrong
(2*x)^n

(this is with Sage 9.6.beta0)

>
> Observed in version 9.4 using sagecell.sagemath.org:
>
> (2*x + y)^n
> (2*x)^n
>
> Expected:
>
> (2*x + y)^n
> (2*x + 1)^n
>
> Link to reproduce: https://sagecell.sagemath.org/?z=eJyFjEEKg0AQBO-Cf-ibM2Yi-gC_IqxBwkJ2Ijsq6-9dghcPklM3TVWbe09N8PZqRqc6xTOIy6IsTKCCJNgFC3psLlJ1GasfN0evC9kaaPT6Dd59SMUYNSg9dh4stzSQPo0F2W_zBfMfr7vzDlIMMqI=&lang=sage&interacts=eJyLjgUAARUAuQ==
>
> Regards,
> Peter Taylor
>

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[Samuel Lelievre]

Possibly related

- Sage Trac ticket 31418
  Incorrect (Maxima) symbolic sum
  https://trac.sagemath.org/ticket/31418

[dmo...@deductivepress.ca]

Thanks for the bug report.  I think this is new (although it is similar to #31844), so I opened ticket #33326.  It is a bug in maxima.