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Converts a into a Poisson encoding.
Categories: Poisson series
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.
Categories: Poisson series
Differentiates a with respect to b. b must occur only in the trig arguments or only in the coefficients.
Categories: Poisson series
Functionally identical to intopois (a^b).
b must be a positive integer.
Categories: Poisson series
Integrates in a similarly restricted sense (to poisdiff). Non-periodic
terms in b are dropped if b is in the trig arguments.
Categories: Poisson series
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)].
Categories: Poisson series
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.
Categories: Poisson series
Is functionally identical to intopois (a + b).
Categories: Poisson series
Converts a into a Poisson series for a in general representation.
Categories: Poisson series
The symbol /P/ follows the line label of Poisson series
expressions.
Categories: Poisson series
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).
Categories: Poisson series
Is functionally identical to intopois (a*b).
Categories: Poisson series
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.
Categories: Poisson series
Prints a Poisson series in a readable format. In common
with outofpois, it will convert a into a Poisson encoding first, if
necessary.
Categories: Poisson series Display functions
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