ABSTRACT
From Section 3.3.3 recall that for a type-(1, k) reduction, m = 1 so that h : Gk → G and the form symmetry is a scalar function
H(u0, . . . , uk) = u0 ∗ h(u1, . . . , uk). (6.1)
This form symmetry is characterized by the change of variables
tn = h(xn−1, . . . , xn−k)
in Eq. (2.3), i.e.,
xn+1 = fn(xn, xn−1, . . . , xn−k) (6.2)
which yields the SC factorization
tn+1 = gn(tn) (6.3)
xn+1 = tn+1 ∗ h(xn, . . . , xn−k+1)−1. (6.4)
We note that the cofactor equation plays a role that is similar to that played by the factor equation in Chapter 5; i.e., the roles of factor and cofactor equations are switched. Because the form symmetry component function h is now multivariable and encodes more information, it may be more difficult to identify. On the other hand, since H is a scalar function more technical tools may be available for handling it.
