An exact zero test for algebraic numbers, for when downcasting is removed #2164

A constant built from radicals currently reaches 0 by evaluation. It is computed to 100 digits, and downcasting takes any residual under 1e-50 as 0 (measured on #2143). So a check that answers 0 cannot tell an identity from a near miss. For example, take 8y^3 + 4y^2 - 4y - 1 at the Cardano root for cos(2pi/7):

• as written, it simplifies to 0;
• with one 7 changed to 7 + 10^(-50), it also simplifies to 0, although its value is 2.48e-52 - 3.26e-52 i.

#1019 removes downcasting in v3. A constant like this one then no longer reaches 0 at all, and two things depend on it reaching 0 today:

• GroebnerSystemSolver.Satisfies accepts a candidate root when InnerSimplified comes out 0 (A root check says what it tolerates: zero to about fifty digits #2163).
• The trigonometric table's radical entries, such as the one sin(pi/7) is rewritten into, are checked only numerically, by TrigTest, to about 97 digits.

Proposal: decide e = 0 exactly for an algebraic e, in two steps:

1. Compute a polynomial that e is a root of, from the polynomials that define its radicals, as SymPy's minimal_polynomial does.
2. If 0 is one of that polynomial's roots, decide whether e is that root, using an isolating interval from the interval evaluator (The integrator's sampled-point checks evaluate in intervals, which read no setting #1497).

For sin(pi/7), the steps are the four in the answer on #2143.

References: Algebraic number, Minimal polynomial (field theory).