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1 ## Copyright (C) 2000, 2006, 2007 Paul Kienzle |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {@var{p} =} factor (@var{q}) |
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21 ## @deftypefnx {Function File} {[@var{p}, @var{n}] =} factor (@var{q}) |
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22 ## |
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23 ## Return prime factorization of @var{q}. That is @code{prod (@var{p}) |
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24 ## == @var{q}}. If @code{@var{q} == 1}, returns 1. |
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25 ## |
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26 ## With two output arguments, returns the unique primes @var{p} and |
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27 ## their multiplicities. That is @code{prod (@var{p} .^ @var{n}) == |
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28 ## @var{q}}. |
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29 ## |
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30 ## @end deftypefn |
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31 |
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32 ## Author: Paul Kienzle |
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33 |
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34 ## 2002-01-28 Paul Kienzle |
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35 ## * remove recursion; only check existing primes for multiplicity > 1 |
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36 ## * return multiplicity as suggested by Dirk Laurie |
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37 ## * add error handling |
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38 |
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39 function [x, m] = factor (n) |
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40 |
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41 if (nargin < 1) |
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42 print_usage (); |
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43 endif |
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44 |
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45 if (! isscalar (n) || n != fix (n)) |
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46 error ("factor: n must be a scalar integer"); |
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47 endif |
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48 |
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49 ## Special case of no primes less than sqrt(n). |
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50 if (n < 4) |
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51 x = n; |
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52 m = 1; |
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53 return; |
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54 endif |
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55 |
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56 x = []; |
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57 ## There is at most one prime greater than sqrt(n), and if it exists, |
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58 ## it has multiplicity 1, so no need to consider any factors greater |
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59 ## than sqrt(n) directly. [If there were two factors p1, p2 > sqrt(n), |
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60 ## then n >= p1*p2 > sqrt(n)*sqrt(n) == n. Contradiction.] |
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61 p = primes (sqrt (n)); |
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62 while (n > 1) |
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63 ## Find prime factors in remaining n. |
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64 q = n ./ p; |
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65 p = p (q == fix (q)); |
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66 if (isempty (p)) |
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67 ## Can't be reduced further, so n must itself be a prime. |
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68 p = n; |
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69 endif |
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70 x = [x, p]; |
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71 ## Reduce n. |
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72 n = n / prod (p); |
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73 endwhile |
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74 x = sort (x); |
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75 |
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76 ## Determine muliplicity. |
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77 if (nargout > 1) |
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78 idx = find ([0, x] != [x, 0]); |
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79 x = x(idx(1:length(idx)-1)); |
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80 m = diff (idx); |
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81 endif |
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82 |
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83 endfunction |
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84 |
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85 ## test: |
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86 ## assert(factor(1),1); |
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87 ## for i=2:20 |
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88 ## p = factor(i); |
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89 ## assert(prod(p),i); |
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90 ## assert(all(isprime(p))); |
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91 ## [p,n] = factor(i); |
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92 ## assert(prod(p.^n),i); |
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93 ## assert(all([0,p]!=[p,0])); |
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94 ## end |
