Seed the numerical search from the real axis, not the grid alone (#115)

[Rafael-SOWNet]

Closes #115.

arcsin(x) - x*pi/3 = 0 answered { 0 }. Its roots are -1/2, 0 and 1/2, and all three were already inside the region being searched, so this was not a matter of iterating harder.

What was wrong

The search starts from a grid over the complex plane, which is two-dimensional: a step count of N costs N² Newton runs but lays real starting points only (To - From) / N apart. At the default 10 over [-10, 10] that is 2, so the reporter’s three roots — spanning one unit in total — shared a single starting point.

Whether both of two close roots then get reached is left to where the iteration happens to go. A polynomial usually survives it, its basins being interleaved across the whole plane: x*(x - 1/2)*(x + 1/2) has roots the same 0.5 apart and gives all three. An expression that is real only on a small interval does not — outside [-1, 1] every starting point hands arcsin a complex value and the iteration wanders off. That is why this looked like a hard limit of the method and was not.

The fix

A sign change is a much cheaper witness of a root than a Newton run is: one evaluation against the sixty an iteration to precision 30 costs. So the real axis is now scanned at StepCount.Re * StepCount.Im points — as many as the grid has starting points — and Newton runs only from the brackets that scan finds.

The spacing that matters for a real root becomes (To - From) / N² rather than (To - From) / N: 0.2 at the default rather than 2, for about 2% of what the grid already spends.

It is additive and the grid is untouched. A sign change witnesses a root of odd multiplicity on an interval where the expression is real, so repeated roots (x^2 + 2x + 1) and roots off the real axis (x^2 + 1) stay the grid’s to find — a test pins both. Intervals where the value is not real are skipped, the intermediate value theorem having nothing to say there.

Measured

	before	after
arcsin(x) - x*pi/3 via SolveNt	1 root, {0}	3 roots
arcsin(x) - x*pi/3 via SolveEquation	{ 0 }	{ -1/2, 0, 1/2 }

Ten other equations covering polynomial, trigonometric and complex-rooted cases are unchanged in both roots and timing.

Full suite 4861 passed / 0 failed, F# 130/130, 117-problem corpus 112/117 with 0 wrong, 0 error, 0 timeout — all unchanged from master.

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