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80 lines
2.7 KiB
Plaintext
80 lines
2.7 KiB
Plaintext
NAME
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root - root of a number
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SYNOPSIS
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root(x, n, [, eps])
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TYPES
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x number
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n positive integer
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eps nonzero real, defaults to epsilon()
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return real number
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DESCRIPTION
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For real x and positive integer n, n being odd if x is negative,
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root(x,n,eps) returns a multiple of eps differing from the
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real n-th root of x (nonnegative if x is positive) by less than
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0.75 eps, usually by less than 0.5 eps. If the n-th root of
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x is a multiple of eps, it will be returned exactly.
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For complex x and positive integer n, or negative x with positive even
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n, root(x, n, eps) returns a real or complex numbers whose real
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and imaginary parts are multiples of eps differing from the real
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and imaginary parts of the principal n-th root of x by less than
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0.75 eps, usually by less than 0.5 eps.
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For negative x and odd n, the principal n-th root of x may be
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obtained by using power(x, 1/n, eps).
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EXAMPLE
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> print root(7, 4, 1e-5), root(7, 4, 1e-10), root(7, 4, 1e-15)
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1.62658 1.6265765617 1.626576561697786
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> print root(1+3i, 3, 1e-5), root(1 + 3i, 3, 1e-10)
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1.34241+.59361i 1.3424077452+.5936127825i
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> print root(-8, 3, 1e-5), root(-8, 34, 1e-5)
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-2 ~1.05853505050032399594+~.09807874962631613016i
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> print root(1i, 100, 1e-20)
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.99987663248166059864+.01570731731182067575i
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LIMITS
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n >= 0
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eps > 0
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LINK LIBRARY
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void rootvalue(VALUE *x, VALUE *n, VALUE *eps, VALUE *result)
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NUMBER *qroot(NUMBER *x, NUMBER *n, NUMBER *eps)
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COMPLEX *qroot(COMPLEX *x, NUMBER *n, NUMBER *eps)
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SEE ALSO
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power
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## Copyright (C) 1999 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
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##
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## @(#) $Revision: 29.1 $
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## @(#) $Id: root,v 29.1 1999/12/14 09:16:05 chongo Exp $
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## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/root,v $
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##
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## Under source code control: 1995/10/25 04:03:46
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## File existed as early as: 1995
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##
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## chongo <was here> /\oo/\ http://reality.sgi.com/chongo/
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## Share and enjoy! :-) http://reality.sgi.com/chongo/tech/comp/calc/
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