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We do not know how to compute the signature of within arguments of trigonometrics.
plays a very specific role in trigonometric functions.
So far all attempts to find so that the trigonometric
functions compute correctly yield values which make too many
mistakes.
The reason for the apparent failures to find a signature are
illustrated in the following.
Since
for integer *k* and
is reduced to
and
all signatures are integers, the signature of sin of any expression
times becomes 0.
In other words, the condition *k* is an integer is not unique
when we are dealing with signatures, all expressions are mapped
to integers.
New ideas are needed to resolve this problem.

*Gaston Gonnet*

*1999-07-04*