import { type Expr, type NodeId } from "../expr.js";
import { type Rule } from "../rule.js";
export interface FactorOutParams {
    /** A factor INSTANCE inside one term of the Sum at `location`. */
    readonly factorA: NodeId;
    /**
     * An instance inside a different term: structurally equal to factorA, OR
     * an integer literal that factorA's signed literal value divides.
     */
    readonly factorB: NodeId;
}
/**
 * The factor positions a term offers for factoring out: the term itself
 * (cofactor 1), a Product's direct factors, a negated term's body (cofactor
 * −1), and a negated product's factors. Shared with move enumeration.
 */
export declare function factorInstancesOf(term: Expr): readonly Expr[];
/**
 * Pull a shared factor out of two terms of a Sum — the inverse of
 * distribute, and the move that makes LIKE TERMS work:
 *   3x + 2x ~> (3 + 2)·x        x + 2x ~> (1 + 2)·x        x − 2x ~> (1 + (−2))·x
 * The kept instance (factorA) survives by identity; the dragged-away one
 * merges into it. The cofactor Sum is a real Sum, so combine-integers folds
 * it with the gesture the user already knows.
 */
export declare const factorOut: Rule<FactorOutParams>;
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