@uor-foundation/geometry/dist/differential.d.ts

Layer 5: Geometric manifolds - the shape of mathematical space

import type { FieldSubstrate } from '@uor-foundation/field-substrate';
import type { ResonanceDynamics } from '@uor-foundation/resonance';
import type { TangentSpace, TangentVector } from './index';
export interface VectorField {
    name: string;
    evaluate(point: bigint): TangentVector;
    isSmooth: boolean;
}
export interface DifferentialForm {
    degree: number;
    evaluate(point: bigint, vectors: TangentVector[]): number;
}
export interface Flow {
    vectorField: VectorField;
    flowMap(start: bigint, time: number): bigint;
    isComplete: boolean;
}
export interface PoissonBracket {
    f: (n: bigint) => number;
    g: (n: bigint) => number;
    bracket: (n: bigint) => number;
}
export declare class DifferentialStructure {
    private fieldSubstrate;
    private resonance;
    private metric;
    constructor(fieldSubstrate: FieldSubstrate, resonance: ResonanceDynamics);
    createTangentSpace(basePoint: bigint): TangentSpace;
    createGradientField(potential: (n: bigint) => number): VectorField;
    createHamiltonianField(hamiltonian: (n: bigint) => number): VectorField;
    createArithmeticFlow(): VectorField;
    computeFlow(field: VectorField, _start: bigint, time: number, steps?: number): Flow;
    create0Form(f: (n: bigint) => number): DifferentialForm;
    create1Form(components: ((n: bigint) => number)[]): DifferentialForm;
    create2Form(components: ((n: bigint) => number)[][]): DifferentialForm;
    exteriorDerivative(form: DifferentialForm): DifferentialForm;
    lieDerivative(field: VectorField, form: DifferentialForm): DifferentialForm;
    computePoissonBracket(f: (n: bigint) => number, g: (n: bigint) => number): PoissonBracket;
    covariantDerivative(vector: TangentVector, direction: TangentVector, point: bigint): TangentVector;
    riemannCurvatureTensor(point: bigint): number[][][][];
    private computeMetricTensor;
    private computeDeterminant;
    private getMinor;
    private createBasisVector;
}
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