import { type Expr, type NodeId } from "../expr.js";
import { type Rule } from "../rule.js";
export interface SplitTermParams {
    /** A direct child of the Sum at `location` with an integer coefficient. */
    readonly termId: NodeId;
    /** Coefficient of the first part; the second part gets (coeff − first). */
    readonly first: bigint;
}
/**
 * A term read as coeff·body: the integer literal factor (sign folded in from
 * a wrapping Neg) and the remaining factors. A bare literal has empty body;
 * a term with no literal factor has coefficient 1. Shared with move
 * enumeration, which uses it to spot the a·B² + b·B + c trinomial pattern.
 */
export declare function coeffAndBody(term: Expr): {
    coeff: bigint;
    body: readonly Expr[];
};
/**
 * Signed integer coefficient and single variable of a simple linear term
 * (`v`, `−v`, `c·v`, `−c·v`, `(−c)(−v)`), or undefined if the term isn't that
 * shape. Linear ⟺ the body is a single variable; a second `coeffAndBody` peels
 * any residual sign a double-negative product (e.g. (−2)(−y)) leaves in it.
 */
export declare function linearTerm(t: Expr): {
    coeff: bigint;
    variable: string;
} | undefined;
/** coeff·body as a canonical term (Neg outside, no 1· prefix). */
export declare function termFromCoeff(coeff: bigint, body: readonly Expr[]): Expr;
/**
 * Split one integer-coefficient term of a Sum into two adjacent parts —
 * the inverse of factor-out + combine-integers, and the step that unlocks
 * factoring by grouping:
 *   −6x ~> −3x + −3x        x ~> 3x + −2x        5x ~> 2x + 3x
 * An exact identity: emits nothing. The first part keeps the original body
 * nodes (and so their ids); the second part's body is a fresh clone.
 */
export declare const splitTerm: Rule<SplitTermParams>;
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