import { type ExactRing, type ExactValue } from './exact.js';
/**
 * A finite Coxeter diagram: `matrix[i][j]` is the Coxeter number m(i,j)
 * (order of sᵢsⱼ) — 1 on the diagonal, 2 for commuting mirrors, ≥ 3 for
 * a diagram link. Marks up to 5 are supported exactly: the doubled-Gram
 * entry −2cos(π/m) is then 0, −1, −√2, or −φ, all elements of a single
 * quadratic ring per diagram (mixing marks 4 and 5 would need both √2
 * and φ and is rejected).
 */
export interface CoxeterDiagram {
    readonly id: string;
    readonly rank: number;
    /** Expected group order; enumeration verifies against it. */
    readonly order: number;
    readonly matrix: ReadonlyArray<ReadonlyArray<number>>;
    readonly ring: ExactRing;
    /** C = 2G in exact form: C[i][j] = −2cos(π/m(i,j)), C[i][i] = 2. */
    readonly twoGram: ReadonlyArray<ReadonlyArray<ExactValue>>;
}
export declare function createCoxeterDiagram(id: string, matrix: ReadonlyArray<ReadonlyArray<number>>, order: number): CoxeterDiagram;
/** Dihedral I₂(m): two mirrors at π/m. */
export declare const coxeterI2: (m: number) => CoxeterDiagram;
export declare const coxeterA3: () => CoxeterDiagram;
export declare const coxeterB3: () => CoxeterDiagram;
export declare const coxeterH3: () => CoxeterDiagram;
export declare const coxeterA4: () => CoxeterDiagram;
export declare const coxeterB4: () => CoxeterDiagram;
export declare const coxeterF4: () => CoxeterDiagram;
export declare const coxeterH4: () => CoxeterDiagram;
/**
 * E8: a seven-node chain with a one-node branch at the trivalent node.
 *
 * The full Weyl group is intentionally not meant to be enumerated into a
 * chamber table. Its root orbit has only 240 elements and is reached with
 * `orbitDistanceTuples`, whose work is proportional to the orbit rather
 * than the 696,729,600 group elements.
 */
export declare const coxeterE8: () => CoxeterDiagram;
/** D₄: node 0 is the branch center, joined to 1, 2, 3 by marks of 3. */
export declare const coxeterD4: () => CoxeterDiagram;
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