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AntiderivativeBreaks

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Description

Summary

The points strictly inside a numeric range where an antiderivative can stop being
continuous, so that a definite integral is taken through it piece by piece.

Remarks

F(b) - F(a) is the integral only where F is continuous on [a, b]. A pole
of the integrand between the bounds is a point where F is not even defined: the
integral of 1/x^2 over [-1, 1] came back as -1/x at 1 less -1/x at -1, which is -2, a negative answer for a positive integrand whose integral
diverges. An antiderivative can also jump where the integrand is continuous, and the
answer through it is then wrong by the jump: arccot(x) jumps at 0 in this library's
convention, and a half-angle substitution writes tan(x/2).
 The places read are where a node of the antiderivative stops being continuous: the zeros
of a denominator, of a base raised to a negative power, of a logarithm's argument, of the
argument of sgn, arccot, arcsec and arccsc, and the zeros of the
cosine or the sine under a tangent, secant, cotangent or cosecant of a linear argument.
Where one of them cannot be listed -- a root with a symbol in it, a periodic argument
that is not linear, more breaks than MostBreaks -- the caller is told so,
and integrates as it did before.
 A break is carried as its exact point, where the one-sided limits are taken, and its
decimal value, which only orders the breaks and places them in the range.
https://github.com/asc-community/AngouriMath/issues/1508

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