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NAME
root - root of a number
SYNOPSIS
root(x, n, [, eps])
TYPES
x number
n positive integer
eps nonzero real, defaults to epsilon()
return real number
DESCRIPTION
For real x and positive integer n, n being odd if x is negative,
root(x,n,eps) returns a multiple of eps differing from the
real n-th root of x (nonnegative if x is positive) by less than
0.75 eps, usually by less than 0.5 eps. If the n-th root of
x is a multiple of eps, it will be returned exactly.
For complex x and positive integer n, or negative x with positive even
n, root(x, n, eps) returns a real or complex numbers whose real
and imaginary parts are multiples of eps differing from the real
and imaginary parts of the principal n-th root of x by less than
0.75 eps, usually by less than 0.5 eps.
For negative x and odd n, the principal n-th root of x may be
obtained by using power(x, 1/n, eps).
EXAMPLE
; print root(7, 4, 1e-5), root(7, 4, 1e-10), root(7, 4, 1e-15)
1.62658 1.6265765617 1.626576561697786
; print root(1+3i, 3, 1e-5), root(1 + 3i, 3, 1e-10)
1.34241+0.59361i 1.3424077452+0.5936127825i
; print root(-8, 3, 1e-5), root(-8, 34, 1e-5)
-2 ~1.05853505050032399594+~0.09807874962631613016i
; print root(1i, 100, 1e-20)
0.99987663248166059864+0.01570731731182067575i
LIMITS
n >= 0
eps != 0
LINK LIBRARY
void rootvalue(VALUE *x, VALUE *n, VALUE *eps, VALUE *result)
NUMBER *qroot(NUMBER *x, NUMBER *n, NUMBER *eps)
COMPLEX *c_root(COMPLEX *x, NUMBER *n, NUMBER *eps)
SEE ALSO
power
## Copyright (C) 1999,2021,2023 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 1995/10/25 04:03:46
## File existed as early as: 1995
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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