QSA exact rational polynomial Sturm algebra - #84
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Staged successor above accepted PR83 for exact univariate rational polynomial algebra useful to Brain's typed mathematical reasoning and QSA's general exact-mathematics platform.
The current core provides arbitrary-precision
QRationalpolynomial coefficients with opaque caller-admitted variable identity, canonical normalized coefficient state, exact Horner evaluation, derivative, addition/subtraction/multiplication, Euclidean division, monic normalization, polynomial GCD, square-free reduction, exact Sturm sequences, and exact distinct-real-root counts over rational intervals. Exact-root interval endpoints fail closed instead of being silently perturbed. Degree and algorithm-step caps bound the work.A focused native test covers exact evaluation/derivative, Euclidean division, repeated-factor GCD, square-free reduction, three-root and single-subinterval Sturm counts, repeated-root distinct counting, a no-real-root control, endpoint-root rejection, zero-polynomial infinite-root rejection, variable-identity isolation, degree/multiplication caps, arbitrary-precision coefficients, and receipt identity.
The existing Structural Hardening carrier directly builds and runs that exact test; no new workflow was created. This PR is not research-accepted yet. It still needs exact-head gates and then a typed QMath-language integration decision before any broader claim.
Brain boundary is unchanged: Brain supplies admitted symbolic/variable meaning. QSA operates only on the resulting typed exact polynomial state and never parses raw language or chooses semantic truth.
Draft, unmerged, non-production; no merge or production promotion is authorized.