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fix: log as method gives symbolic output for non positive base #39986

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fix: log as method gives symbolic output for non positive base #39986

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14 changes: 11 additions & 3 deletions src/sage/rings/integer.pyx
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Expand Up @@ -2851,16 +2851,24 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
sage: ZZ(8).log(int(2))
3

Check that negative bases yield complex logarithms (:issue:`39959`)::

sage: 8.log(-2)
3*log(2)/(I*pi + log(2))

Check that zero base yield complex logarithms (:issue:`39959`)::

sage: 8.log(0)
0

TESTS::

sage: (-2).log(3) # needs sage.symbolic
(I*pi + log(2))/log(3)
"""
cdef int self_sgn
if m is not None and m <= 0:
raise ValueError("log base must be positive")
self_sgn = mpz_sgn(self.value)
if self_sgn < 0 and prec is None:
if self_sgn < 0 or (m is not None and m<=0) and prec is None:
from sage.symbolic.ring import SR
return SR(self).log(m)
if prec:
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