respectively the positions of particles and , and is the distance between them. If a given system is holonomic, rigidly attaching additional parts to components of the system in question cannot make it non-holonomic, assuming that the degrees of freedom are not reduced (in other words, assuming the configuration space is unchanged). Pfaffian form Consider the following differential form of a constraint: where are the coefficients of the differentials for the ith constraint equation. This form is called the Pfaffian form or the differential form. If the differential form is integrable, i.e., if there is a function satisfying the equality then this constraint is a holonomic constraint; otherwise, it is nonholonomic. Therefore, all holonomic and some nonholonomic constraints can be expressed using the differential form. Examples of nonholonomic constraints that cannot be expressed this way are those that are dependent on generalized velocities. With a constraint equation in Pfaffian form, whether the constraint is holonomic or nonholonomic depends on whether the Pfaffian form is integrable. See Universal test for holonomic constraints below for a description of a test to verify the integrability (or lack of) of a Pfaffian form constraint. Universal test for holonomic constraints When the constraint equation of a system is written in Pfaffian constraint form, there exists a mathematical test to determine whether the system is holonomic. For a constraint equation, or sets of constraint equations (note that variable(s) representing time can be included, as from above and in the following form): we can use the test equation: where in combinations of test equations per constraint equation, for all sets of constraint equations. In other words, a system of three variables would have to be tested once with one test equation with the terms being terms in the constraint equation (in any order), but to test a system of four variables the test would have to be performed up to four times with four different test equations, with the terms being terms , , , and in the constraint equation (each in any order) in four different tests. For a system of five variables, ten tests would have to be performed on a holonomic system to verify that fact, and for a system of five variables with three sets of constraint equations, thirty tests (assuming a simplification like a change-of-variable could not be performed to reduce that number). For this reason, it is advisable when using this