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hurwitz_zeta bug?

asked 2012-07-17 08:57:50 -0500

petropolis gravatar image

updated 2017-03-10 03:16:00 -0500

tmonteil gravatar image

The doc (reference/sage/combinat/combinat.html) says:

"hurwitz_zeta(s,x,N) returns the value of the zeta(s,x) to N decimals, where s and x are real."

With Sage 5.0 I get:

hurwitz_zeta(3,1,32) = 1.202056903159594285...
hurwitz_zeta(-3,1,32) -> SyntaxError: unexpected EOF while parsing
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answered 2012-07-17 10:28:48 -0500

DSM gravatar image

updated 2012-07-17 10:29:09 -0500

This is a bug, and it's due to an unanticipated behaviour when Maxima returns unevaluated:

maxima.eval('load ("bffac")')
s = maxima.eval("bfhzeta (%s,%s,%s)"%(s,x,N))

#Handle the case where there is a 'b' in the string
#'1.2000b0' means 1.2000 and
#'1.2000b1' means 12.000
i = s.rfind('b')
if i == -1:
    return sage_eval(s)
else:
    if s[i+1:] == '0':
        return sage_eval(s[:i])
    else:
        return sage_eval(s[:i])*10**sage_eval(s[i+1:])

return s  ## returns an odd string

Unfortunately, Maxima doesn't evaluate these terms:

sage: maxima.eval('bfhzeta (%s,%s,%s)' % (-3,1,32))
'bfhzeta(-3,1,32)'

The rfind then picks up the initial "b" at 0, so sage_eval(s[:i]) is sage_eval(''), which throws the SyntaxError.

This could be hacked around to return unevaluated, but the right solution would be to implement hurwitz_zeta along the lines of some of the new special function implementations. This would give a symbolic front and improved backend evaluation. As a workaround in the short term, mpmath can handle this:

sage: import mpmath
sage: mpmath.mp.dps = 50
sage: mpmath.hurwitz(-3, 1)
mpf('0.0083333333333333333333333333333333333333333333333333319')
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Comments

Thank you DSM! It does not solve my problem, though. from mpmath import * mp.dps = 50 def Mat(m) : M = matrix(QQ, m) for n in range(m) : for k in range(m) : M[n,k] = zeta(k - n, k + 1) ### hurwitz_zeta(k - n,k + 1, 32) if M.det() == 0 : return return M.inverse() Mat(3) # TypeError: could not interpret given arguments

petropolis gravatar imagepetropolis ( 2012-07-17 11:36:04 -0500 )edit

http://trac.sagemath.org/ticket/15095 implements a symbolic version of `hurwitz_zeta`.

Eviatar Bach gravatar imageEviatar Bach ( 2013-08-29 08:39:32 -0500 )edit
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answered 2013-06-03 05:34:40 -0500

tmonteil gravatar image

updated 2017-03-10 03:16:39 -0500

This has been reported as trac ticket 14679, and actually fixed as trac ticket 15095.

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Asked: 2012-07-17 08:57:50 -0500

Seen: 189 times

Last updated: Mar 10