# FreeBSD Manual Pages

```Math::Cephes::PolynomiUser)Contributed Perl DocumenMath::Cephes::Polynomial(3)

NAME
Math::Cephes::Polynomial	- Perl interface to the	cephes math polynomial
routines

SYNOPSIS
use Math::Cephes::Polynomial qw(poly);
# 'poly' is a shortcut	for Math::Cephes::Polynomial->new

require Math::Cephes::Fraction; # if coefficients are fractions
require Math::Cephes::Complex;	 # if coefficients are complex

my \$a = poly([1, 2, 3]);	    # a(x) = 1 + 2x + 3x^2
my \$b = poly([4, 5, 6,	7];	    # b(x) = 4 + 5x + 6x^2 + 7x^3
my \$c = \$a->add(\$b);		    # c(x) = 5 + 7x + 9x^2 + 7x^3
my \$cc	= \$c->coef;
for (my \$i=0; \$i<4; \$i++) {
print "term	\$i: \$cc->[\$i]\n";
}
my \$x = 2;
my \$r = \$c->eval(\$x);
print "At x=\$x, c(x) is \$r\n";

my \$u1	= Math::Cephes::Complex->new(2,1);
my \$u2	= Math::Cephes::Complex->new(1,-3);
my \$v1	= Math::Cephes::Complex->new(1,3);
my \$v2	= Math::Cephes::Complex->new(2,4);
my \$z1	= Math::Cephes::Polynomial->new([\$u1, \$u2]);
my \$z2	= Math::Cephes::Polynomial->new([\$v1, \$v2]);
my \$z3c = \$z3->coef;
for (my \$i=0; \$i<2; \$i++) {
print "term	\$i: real=\$z3c->{r}->[\$i], imag=\$z3c->{i}->[\$i]\n";
}
\$r = \$z3->eval(\$x);
print "At x=\$x, z3(x) has real=", \$r->r, " and	imag=",	\$r->i, "\n";

my \$a1	= Math::Cephes::Fraction->new(1,2);
my \$a2	= Math::Cephes::Fraction->new(2,1);
my \$b1	= Math::Cephes::Fraction->new(1,2);
my \$b2	= Math::Cephes::Fraction->new(2,2);
my \$f1	= Math::Cephes::Polynomial->new([\$a1, \$a2]);
my \$f2	= Math::Cephes::Polynomial->new([\$b1, \$b2]);
my \$f3c = \$f3->coef;
for (my \$i=0; \$i<2; \$i++) {
print "term	\$i: num=\$f3c->{n}->[\$i], den=\$f3c->{d}->[\$i]\n";
}
\$r = \$f3->eval(\$x);
print "At x=\$x, f3(x) has num=", \$r->n, " and den=", \$r->d, "\n";
\$r = \$f3->eval(\$a1);
print "At x=",	\$a1->n,	"/", \$a1->d,
",	f3(x) has num=", \$r->n,	" and den=", \$r->d, "\n";

DESCRIPTION
This module is a	layer on top of	the basic routines in the cephes math
library to handle polynomials. In the following,	a
Math::Cephes::Polynomial	object is created as

my \$p = Math::Cephes::Polynomial->new(\$arr_ref);

where \$arr_ref is a reference to	an array which can consist of one of

o   floating point numbers, for polynomials with	floating point
coefficients,

o   Math::Cephes::Fraction or Math::Fraction objects, for polynomials
with	fractional coefficients,

o   Math::Cephes::Complex or Math::Complex objects, for polynomials
with	complex	coefficients,

The maximum degree of the polynomials handled is	set by default to 256
- this can be changed by	setting	\$Math::Cephes::Polynomial::MAXPOL.

A copy of a Math::Cephes::Polynomial object may be done as

my \$p_copy = \$p->new();

and a string representation of the polynomial may be gotten through

print \$p->as_string;

Methods
The following methods are available.

coef: get coefficients of the polynomial
SYNOPSIS:

my \$c = \$p->coef;

DESCRIPTION:

This	returns	an array reference containing the coefficients of the
polynomial.

clr: set	a polynomial identically equal to zero
SYNOPSIS:

\$p->clr(\$n);

DESCRIPTION:

This	sets the coefficients of the polynomial	identically to 0, up
to \$p->[\$n].	If \$n is omitted, all elements are set to 0.

SYNOPSIS:

DESCRIPTION:

This	sets \$c	equal to \$a + \$b.

sub: subtract two polynomials
SYNOPSIS:

\$c = \$a->sub(\$b);

DESCRIPTION:

This	sets \$c	equal to \$a - \$b.

mul: multiply two polynomials
SYNOPSIS:

\$c = \$a->mul(\$b);

DESCRIPTION:

This	sets \$c	equal to \$a * \$b.

div: divide two polynomials
SYNOPSIS:

\$c = \$a->div(\$b);

DESCRIPTION:

This	sets \$c	equal to \$a / \$b, expanded by a	Taylor series.
Accuracy is approximately equal to the degree of the	polynomial,
with	an internal limit of about 16.

sbt: change of variables
SYNOPSIS:

\$c = \$a->sbt(\$b);

DESCRIPTION:

If a(x) and b(x) are	polynomials, then

c(x) = a(b(x))

is a	polynomial found by substituting b(x) for x in a(x). This
method is not available for polynomials with	complex	coefficients.

eval: evaluate a	polynomial
SYNOPSIS:

\$s = \$a->eval(\$x);

DESCRIPTION:

This	evaluates the polynomial at the	value \$x. The returned value
is of the same type as that used to represent the coefficients of
the polynomial.

sqt: square root	of a polynomial
SYNOPSIS:

\$b = \$a->sqt();

DESCRIPTION:

This	finds the square root of a polynomial, evaluated by a Taylor
expansion. Accuracy is approximately	equal to the degree of the
polynomial, with an internal	limit of about 16.  This method	is not
available for polynomials with complex coefficients.

sin: sine of a polynomial
SYNOPSIS:

\$b = \$a->sin();

DESCRIPTION:

This	finds the sine of a polynomial,	evaluated by a Taylor
expansion. Accuracy is approximately	equal to the degree of the
polynomial, with an internal	limit of about 16.  This method	is not
available for polynomials with complex coefficients.

cos: cosine of a	polynomial
SYNOPSIS:

\$b = \$a->cos();

DESCRIPTION:

This	finds the cosine of a polynomial, evaluated by a Taylor
expansion. Accuracy is approximately	equal to the degree of the
polynomial, with an internal	limit of about 16.  This method	is not
available for polynomials with complex coefficients.

atn: arctangent of the ratio of two polynomials
SYNOPSIS:

\$c = \$a->atn(\$b);

DESCRIPTION:

This	finds the arctangent of	the ratio \$a / \$b of two polynomial,
evaluated by	a Taylor expansion. Accuracy is	approximately equal to
the degree of the polynomial, with an internal limit	of about 16.
This	method is not available	for polynomials	with complex
coefficients.

rts: roots of a polynomial
SYNOPSIS:

my	\$w = Math::Cephes::Polynomial->new([-2,	0, -1, 0, 1]);
my	(\$flag,	\$r) = \$w->rts();
for (my \$i=0; \$i<4; \$i++) {
print "Root \$i has real=", \$r->[\$i]->r, " and imag=", \$r->[\$i]->i, "\n";
}

DESCRIPTION:

This	finds the roots	of a polynomial. \$flag,	if non-zero, indicates
a failure of	some kind. \$roots in an	array reference	of
Math::Cephes::Complex objects holding the real and complex values
of the roots	found.	This method is not available for polynomials
with	complex	coefficients.

ACCURACY:

Termination depends on evaluation of	the polynomial at the trial
values of the roots.	 The values of multiple	roots or of roots that
are nearly equal may	have poor relative accuracy after the first
root	in the neighborhood has	been found.

BUGS
Please report any to Randy Kobes	<randy@theoryx5.uwinnipeg.ca>

The C code for the Cephes Math Library is Copyright 1984, 1987, 1989,
2002 by Stephen L. Moshier, and is available at
http://www.netlib.org/cephes/.  Direct inquiries	to 30 Frost Street,
Cambridge, MA 02140.

The perl	interface is copyright 2000, 2002 by Randy Kobes.  This
library is free software; you can redistribute it and/or	modify it
under the same terms as Perl itself.

perl v5.32.1			  2016-05-06	   Math::Cephes::Polynomial(3)
```

NAME | SYNOPSIS | DESCRIPTION | BUGS | COPYRIGHT

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