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Converts a into a Poisson encoding.
Converts a from Poisson encoding to general representation. If a is
not in Poisson form, outofpois carries out the conversion,
i.e., the return value is outofpois (intopois (a)).
This function is thus a canonical simplifier
for sums of powers of sine and cosine terms of a particular type.
Differentiates a with respect to b. b must occur only in the trig arguments or only in the coefficients.
Functionally identical to intopois (a^b).
b must be a positive integer.
Integrates in a similarly restricted sense (to poisdiff). Non-periodic
terms in b are dropped if b is in the trig arguments.
Default value: 5
poislim determines the domain of the coefficients in
the arguments of the trig functions. The initial value of 5
corresponds to the interval [-2^(5-1)+1,2^(5-1)], or [-15,16], but it
can be set to [-2^(n-1)+1, 2^(n-1)].
will map the functions sinfn on the sine terms and cosfn on the cosine terms of the Poisson series given. sinfn and cosfn are functions of two arguments which are a coefficient and a trigonometric part of a term in series respectively.
Is functionally identical to intopois (a + b).
Converts a into a Poisson series for a in general representation.
The symbol /P/ follows the line label of Poisson series
expressions.
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).
Is functionally identical to intopois (a*b).
is a reserved function name which (if the user has defined
it) gets applied during Poisson multiplication. It is a predicate
function of 6 arguments which are the coefficients of the u, v, ..., z
in a term. Terms for which poistrim is true (for the coefficients of
that term) are eliminated during multiplication.
Prints a Poisson series in a readable format. In common
with outofpois, it will convert a into a Poisson encoding first, if
necessary.
Previous: Functions and Variables for Fourier series, Up: Sums, Products, and Series [Contents][Index]