# On smooth families of exact forms

## TL;DR

This paper presents an algorithm and explicit formulas for smoothly computing primitive families of exact forms on manifolds, using a cech-de Rham complex approach.

## Contribution

It introduces a novel algorithm and explicit formulas for constructing smooth primitive families of exact forms in parameterized settings.

## Key findings

- Algorithm for smooth primitive family computation
- Explicit formulas for primitives
- Application of cech-de Rham complex in the method

## Abstract

For a smooth family of exact forms on a smooth manifold, an algorithm for computing a primitive family smoothly dependent on parameters is given. The algorithm is presented in the context of a diagram chasing argument in the \v{C}ech-de Rham complex. In addition, explicit formulas for such primitive family are presented.