Function
src/algebra/algorithms/groebnerBase.ts:1039solveRationalSystem
solveRationalSystem(polys: MultiPoly[], vars: string[], opts?: Omit<GroebnerBasisOptions, "order" | "reduced">): RationalSolution[]Solves a zero-dimensional polynomial system for rational coordinates.
remarks
This is the low-level exact solver used with the Groebner representation, not the ordinary expression solver. It computes a reduced lexicographic basis, walks variables from least to most significant, applies the Rational Root Theorem to univariate constraints, and substitutes each partial assignment into its own basis copy. Irrational and complex roots are outside this routine's result set.
throws
GroebnerBudgetExceeded Thrown when basis computation exceeds a budget.
Parameters
| Name | Type | Description |
|---|---|---|
polys | MultiPoly[] | Exact integer-coefficient system generators. |
vars | string[] | Variables in lexicographic elimination order, most significant first. |
opts | Omit<GroebnerBasisOptions, "order" | "reduced"> | Pair strategy and budgets forwarded to basis computation. |
Returns
RationalSolution[] — New solution maps. An empty array can mean inconsistency, no rational roots, or a non-finite/unsupported triangular result; these cases are not distinguished.