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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
160 lines
4.4 KiB
Plaintext
160 lines
4.4 KiB
Plaintext
NAME
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poly - evaluate a polynomial
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SYNOPSIS
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poly(a, b, ..., x)
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poly(clist, x, y, ...)
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TYPES
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For first case:
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a, b, ... Arithmetic
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x Arithmetic
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return Depends on argument types
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For second case:
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clist List of coefficients
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x, y, ... Coefficients
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return Depends on argument types
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Here an arithmetic type is one for which the required + and *
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operations are defined, e.g. real or complex numbers or square
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matrices of the same size. A coefficient is either of arithmetic
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type or a list of coefficients.
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DESCRIPTION
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If the first argument is not a list, and the necessary operations are
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defined:
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poly(a_0, a_1, ..., a_n, x)
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returns the value of:
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a_n + (a_n-1 + ... + (a_1 + a_0 * x) * x ...) * x
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If the coefficients a_0, a_1, ..., a_n and x are elements of a
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commutative ring, e.g. if the coefficients and x are real or complex
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numbers, this is the value of the polynomial:
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a_0 * x^n + a_1 * x^(n-1) + ... + a_(n-1) * x + a_n.
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For other structures (e.g. if addition is not commutative),
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the order of operations may be relevant.
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In particular:
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poly(a, x) returns the value of a.
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poly(a, b, x) returns the value of b + a * x
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poly(a, b, c, x) returns the value of c + (b + a * x) * x
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If the first argument is a list as if defined by:
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clist = list(a_0, a_1, ..., a_n)
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and the coefficients a_i and x are are of arithmetic type,
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poly(clist, x) returns:
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a_0 + (a_1 + (a_2 + ... + a_n * x) * x)
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which for a commutative ring, expands to:
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a_0 + a_1 * x + ... + a_n * x^n.
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If clist is the empty list, the value returned is the number 0.
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Note that the order of the coefficients for the list case is the
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reverse of that for the non-list case.
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If one or more elements of clist is a list and there are more than
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one arithmetic arguments x, y, ..., the coefficient corresponding
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to such an element is the value of poly for that list and the next
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argument in x, y, ... For example:
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poly(list(list(a,b,c), list(d,e), f), x, y)
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returns:
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(a + b * y + c * y^2) + (d + e * y) * x + f * x^2.
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Arguments in excess of those required for clist are ignored, e.g.:
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poly(list(1,2,3), x, y)
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returns the same as poly(list(1,2,3), x). If the number of
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arguments is less than greatest depth of lists in clist, the
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"missing" arguments are deemed to be zero. E.g.:
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poly(list(list(1,2), list(3,4), 5), x)
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returns the same as:
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poly(list(1, 3, 5), x).
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If in the clist case, one or more of x, y, ... is a list, the
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arguments to be applied to the polynomial are the successive
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non-list values in the list or sublists. For example, if the x_i
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are not lists:
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poly(clist, list(x_0, x_1), x_2, list(list(x_3, x_4), x_5))
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returns the same as:
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poly(clist, x_0, x_1, x_2, x_3, x_4, x_5).
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EXAMPLE
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; print poly(2, 3, 5, 7), poly(list(5, 3, 2), 7), 5 + 3 * 7 + 2 * 7^2
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124 124 124
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; mat A[2,2] = {1,2,3,4}
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; mat I[2,2] = {1,0,0,1}
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print poly(2 * I, 3 * I, 5 * I, A)
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mat [2,2] (4 elements, 4 nonzero)
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[0,0] = 22
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[0,1] = 26
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[1,0] = 39
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[1,1] = 61
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; P = list(list(0,0,1), list(0,2), 3); x = 4; y = 5
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; print poly(P,x,y), poly(P, list(x,y)), y^2 + 2 * y * x + 3 * x^2
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113 113 113
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LIMITS
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The number of arguments is not to exceed 1024
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LINK LIBRARY
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BOOL evalpoly(LIST *clist, LISTELEM *x, VALUE *result);
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SEE ALSO
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list
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## Copyright (C) 1999-2006 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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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 1995/12/02 02:40:43
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## File existed as early as: 1995
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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