ELWO 3CW "01 March 2010" "mathcw-1.00"

Table of contents


NAME

elwof, elwo, elwol, elwow, elwoq, elwoll, elwodf, elwod, elwodl, elwodll - Weierstrass elliptic function support routines

SYNOPSIS

cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ]

#include <mathcw.h>

extern void elwof (float *pomega1, float *pomega2, float e1, float e2);

extern void elwo (double *pomega1, double *pomega2, double e1, double e2);

extern void elwol (long double *pomega1, long double *pomega2, long double e1, long double e2);

extern void elwow (__float80 *pomega1, __float80 *pomega2, __float80 e1, __float80 e2);

extern void elwoq (__float128 *pomega1, __float128 *pomega2, __float128 e1, __float128 e2);

extern void elwoll (long_long_double *pomega1, long_long_double *pomega2,
                    long_long_double e1, long_long_double e2);

extern void elwodf (decimal_float *pomega1, decimal_float *pomega2,
                    decimal_float e1, decimal_float e2);

extern void elwod (decimal_double *pomega1, decimal_double *pomega2,
                   decimal_double e1, decimal_double e2);

extern void elwodl (decimal_long_double *pomega1, decimal_long_double *pomega2,
                    decimal_long_double e1, decimal_long_double e2);

extern void elwodll (decimal_long_long_double *pomega1, decimal_long_long_double *pomega2,
                    decimal_long_long_double e1, decimal_long_long_double e2);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Given e1 and e2, which are any two of the three roots of the Weierstrass cubic polynomial, where the sum of the roots is zero, compute the periods omega1 and omega2 of the real and imaginary parts of the Weierstrass elliptic functions. The returned value of omega2 must be multiplied by the imaginary unit, i, to obtain the true mathematical value.

Mathematical texts commonly parameterize the Weierstrass functions with the cubic polynomial coefficents g2 and g3, instead of the roots e1 and e2. Convert between the two argument conventions with elwe(3CW) and elwg(3CW).

See M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Chapter 18, for definitions of the Weierstrass elliptic, sigma, and zeta functions.


RETURN VALUES

Return the periods omega1 and omega2 through the pointer arguments, but suppress storage if the corresponding pointer is NULL.

ERRORS

If any argument is a NaN, set errno to EDOM and set the two results to that argument.

SEE ALSO

elk(3CW), elkm1(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW), elwdp(3CW), elwe(3CW), elwg(3CW), elwip(3CW), elwk(3CW), elwp(3CW), elws(3CW), elwz(3CW),