Maxima Function
poissubst (a, b, c)
Substitutes a for b in c. c is a Poisson series.
(1) Where B is a variable u, v, w, x, y, or z,
then a must be an
expression linear in those variables (e.g., 6*u + 4*v
).
(2) Where b is other than those variables, then a must also be free of those variables, and furthermore, free of sines or cosines.
poissubst (a, b, c, d, n)
is a special type of substitution which
operates on a and b as in type (1) above, but where d is a Poisson
series, expands cos(d)
and sin(d)
to order n so as to provide the
result of substituting a + d
for b in c. The idea is that d is an
expansion in terms of a small parameter. For example,
poissubst (u, v, cos(v), %e, 3)
yields cos(u)*(1 - %e^2/2) - sin(u)*(%e - %e^3/6)
.