AngouriMath
BySlope(AngouriMath.Numerics.PreciseComplexInterval,System.Func{AngouriMath.Entity.Number.Complex,AngouriMath.Entity.Number.Complex},System.Func{AngouriMath.Numerics.PreciseComplexInterval,AngouriMath.Numerics.PreciseComplexInterval},PeterO.Numbers.EDecimal)
Method (no overloads)
Summary
A special function over the rectangle: its value at the middle, which the library
works out with ten digits to spare, widened by the most the function can move within
the rectangle, and by a unit in the last place of the working precision for its own
error. The most it can move is a bound on the slope times the farthest the rectangle
reaches from the middle, since along the segment from the middle to any point the
function changes by the integral of its derivative there. The bound is the
derivative 's magnitude in intervals over the whole rectangle, and
where that has no value -- a singularity inside -- neither has the function. Off the
real line, a rectangle over the cut along the real line up to
cutEnd is undefined as well: the function jumps there, and the
segment crosses the jump. On the real line itself there is no jump to cross, and the
value is the one the function takes on the cut.
works out with ten digits to spare, widened by the most the function can move within
the rectangle, and by a unit in the last place of the working precision for its own
error. The most it can move is a bound on the slope times the farthest the rectangle
reaches from the middle, since along the segment from the middle to any point the
function changes by the integral of its derivative there. The bound is the
where that has no value -- a singularity inside -- neither has the function. Off the
real line, a rectangle over the cut along the real line up to
segment crosses the jump. On the real line itself there is no jump to cross, and the
value is the one the function takes on the cut.
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