B105 Value of a Polynomial

Function subprograms RPLNML, DPLNML calculate the value of the polynomial

$p$_n(x) = a₀+a₁x+a₂x²+...+a_nxⁿ

or

$q$_n(x) = a₀xⁿ+a₁x^n-1+a₂x^n-2+...+a_n

for real values x, whereas function subprograms CPLNML, WPLNML calculate the value of the polynomial

$r$_n(z) = c₀+c₁z+c₂z²+...+c_nzⁿ

or

$s$_n(x) = c₀zⁿ+c₁z^n-1+c₂z^n-2+...+c_n

for complex values z.

On CDC and Cray computers, the double-precision versions DPLNML and WPLNML are not available.

Structure:

FUNCTION subprograms
User Entry Names: RPLNML, DPLNML, CPLNML, WPLNML

Usage:

For $t=R$ (type REAL), $t=D$ (type DOUBLE PRECISION),

    tPLNML(X,N,A,MODE)

for $t=C$ (type COMPLEX), $t=W$ (type COMPLEX*16),

    tPLNML(Z,N,C,MODE)

X,Z

(type according to t) Arguments x or z, respectively.

N

( INTEGER) Degree n of $p$_n(x), q_n(x) or $r$_n(z), s_n(z) .

A,C

(type according to t) One-dimensional arrays of dimension (0:d) where $d\; \ge N$ , containing the coefficients $a$_k or $c$_k (k=0,...,n) in A(k) or C(k), respectively.

MODE

( INTEGER) Either +1 for $p$_n(x), r_n(z) or -1 for $q$_n(x), s_n(z) .

Method:

The Horner scheme is used.

Notes:

A reference with or MODE different from +1 or -1 returns the value zero.
$•$

B300

K.S. Kölbig