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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!
97 lines
3.2 KiB
Plaintext
97 lines
3.2 KiB
Plaintext
NAME
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det - determinant
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SYNOPSIS
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det(m)
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TYPES
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m square matrix with elements of suitable type
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return zero or value of type determined by types of elements
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DESCRIPTION
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The matrix m has to be square, i.e. of dimension 2 with:
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matmax(m,1) - matmin(m,1) == matmax(m,2) - matmin(m,2).
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If the elements of m are numbers (real or complex), det(m)
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returns the value of the determinant of m.
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If some or all of the elements of m are not numbers, the algorithm
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used to evaluate det(m) assumes the definitions of *, unary -, binary -,
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being zero or nonzero, are consistent with commutative ring structure,
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and if the m is larger than 2 x 2, division by nonzero elements is
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consistent with integral-domain structure.
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If m is a 2 x 2 matrix with elements a, b, c, d, where a tests as
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nonzero, det(m) is evaluated by
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det(m) = (a * d) - (c * b).
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If a tests as zero, det(m) = - ((c * b) - (a * d)) is used.
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If m is 3 * 3 with elements a, b, c, d, e, f, g, h, i, where a and
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a * e - d * b test as nonzero, det(m) is evaluated by
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det(m) = ((a * e - d * b) * (a * i - g * c)
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- (a * h - g * b) * (a * f - d * c))/a.
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EXAMPLE
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; mat A[3,3] = {2, 3, 5, 7, 11, 13, 17, 19, 23}
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; c = config("mode", "frac")
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; print det(A), det(A^2), det(A^3), det(A^-1)
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-78 6084 -474552 -1/78
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; obj res {r}
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; global md
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; define res_test(a) = !ismult(a.r, md)
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; define res_sub(a,b) {local obj res v = {(a.r - b.r) % md}; return v;}
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; define res_mul(a,b) {local obj res v = {(a.r * b.r) % md}; return v;}
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; define res_neg(a) {local obj res v = {(-a.r) % md}; return v;}
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; define res(x) {local obj res v = {x % md}; return v;}
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; md = 0
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; mat A[2,2] = {res(2), res(3), res(5), res(7)}
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; md = 5
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; print det(A)
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obj res {4}
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; md = 6
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; print det(A)
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obj res {5}
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Note that if A had been a 3 x 3 or larger matrix, res_div(a,b) for
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non-zero b would have had to be defined (assuming at least one
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division is necessary); for consistent results when md is composite,
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res_div(a,b) should be defined only when b and md are relatively
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prime; there is no problem when md is prime.
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LIMITS
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none
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LINK LIBRARY
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VALUE matdet(MATRIX *m)
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SEE ALSO
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matdim, matmax, matmin, inverse
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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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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 1995/11/28 11:17:47
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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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