An inversion with no written preimage returns null, not an exception

[Rafael-SOWNet]

From the review of #1504 (comment). An inversion that couldn't write its preimage threw CannotInvertException, and the analytical solvers caught it. It now returns null.

• Invert and InvertNode return IEnumerable<Entity>?. null means the preimage has no written form. An empty sequence still means there are provably no roots.
• A node that inverts a child passes the child's null on. Where several inversions must all be written, such as the two branches of sin and cos, the roots of 1 for a whole power, or the cases of a boolean node, the first null ends it, and the parts after it are never computed.
• AnalyticalEquationSolver.Solve and AnalyticalSetSolver.Solve answer the set-builder on null, at the level where it was met, as they did on the exception. So (x - 1) x! = 0 is still { 1 } together with the x for which x! = 0.
• The exponential and trigonometric solvers invert their substitutions through InvertEach, which declines on null. Their substitutions are powers of the variable, and those always have a written preimage, so this changes no answer.

Nullable annotations are on and warnings are errors, so the compiler rejects any caller that doesn't handle null.

Measured

• The unit suite passes on net10.0: 12824 passed, 14 skipped, none failed, of 12838, the same as master. No answer changes, and no test did.
• The allocation gate passes on all 19 gated benchmarks. SolveHard allocates 0.7% less: it meets inversions with no written preimage, and those allocated an exception each.
• Time. The first version of this was 3% slower on SolveHard. It computed every part of a composite inversion before looking for a null, where the exception had abandoned the rest at once. Stopping at the first null puts it back: 66.0 ms against 66.9 ms on master, over six alternating runs of each. Solves that meet such an inversion directly, such as x mod 3 = 1, gcd(x, 4) = 2 and erf(x) = 1/2, take 2 to 10% less time.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura