I'd suggest that the original sin here is calling some particular
numerical integration routine 'integrate', which gives the user an
illusory sense of power.... Functions have to be well-behaved in
various ways for quadrature to work well, and you've got to expect
things like
> integrate(function(x)tan(x),0,pi)
Error in integrate(function(x) tan(x), 0, pi) :
roundoff error is detected in the extrapolation table <<< a 'good'
error -- tells the user something's wrong
> integrate(function(x)tan(x)^2,0,pi)
1751.054 with absolute error < 0 <<< oops
> integrate(function(x)1/(x-pi/2)^2,0,pi) <<< the same
> pole (analytically)
Error in integrate(function(x) 1/(x - pi/2)^2, 0, pi) : <<<
gets a useful error in this form
non-finite function value
But by that argument, I suppose you shouldn't call floating-point
addition "+" :-)
-s
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