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slightly stronger wording in the documentation [ci skip]

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Fredrik Johansson 2017-02-16 14:21:29 +01:00
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13
doc/source/acb_elliptic.rst
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@ -231,14 +231,17 @@ in [Car1995]_ and chapter 19 in [NIST2012]_.
`x,y,z,p` are close enough to use a multivariate Taylor polynomial
of total degree 7.
The duplication algorithm might not be correct for all possible
combinations of complex variables, i.e. taking square roots
during the computation might introduce spurious branch cuts.
The duplication algorithm is not correct for all possible
combinations of complex variables, since the square roots taken
during the computation can introduce spurious branch cuts.
According to [Car1995]_, a sufficient (but not necessary) condition
for correctness is that *x*, *y*, *z* have nonnegative
real part and that *p* has positive real part.
In other cases, the algorithm *may* still be correct, but the user
should verify the results.
In other cases, the algorithm *might* still be correct, but no attempt
is made to check this; it is up to the user to verify that
the duplication algorithm is appropriate for the given parameters
before calling this function.
The special case `R_D(x, y, z) = R_J(x, y, z, z)`
may be computed by setting *z* and *p* to the same variable.