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1 ## Copyright (C) 2000 Paul Kienzle |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2 of the License, or |
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6 ## (at your option) any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, |
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9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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11 ## GNU General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this program; if not, write to the Free Software |
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15 ## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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16 ## 02110-1301 USA |
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17 |
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18 ## -*- texinfo -*- |
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19 ## @deftypefn {Function File} {@var{q} =} polygcd (@var{b}, @var{a}, @var{tol}) |
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20 ## |
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21 ## Find greatest common divisor of two polynomials. This is equivalent |
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22 ## to the polynomial found by multiplying together all the common roots. |
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23 ## Together with deconv, you can reduce a ratio of two polynomials. |
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24 ## Tolerance defaults to |
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25 ## @example |
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26 ## sqrt(eps). |
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27 ## @end example |
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28 ## Note that this is an unstable |
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29 ## algorithm, so don't try it on large polynomials. |
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30 ## |
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31 ## Example |
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32 ## @example |
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33 ## polygcd (poly(1:8), poly(3:12)) - poly(3:8) |
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34 ## deconv (poly(1:8), polygcd (poly(1:8), poly(3:12))) - poly(1:2) |
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35 ## @end example |
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36 ## @seealso{poly, polyinteg, polyderiv, polyreduce, roots, conv, deconv, |
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37 ## residue, filter, polyval, and polyvalm} |
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38 ## @end deftypefn |
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39 |
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40 function x = polygcd (b, a, tol) |
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41 |
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42 if (nargin == 2 || nargin == 3) |
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43 if (nargin == 2) |
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44 tol = sqrt (eps); |
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45 endif |
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46 if (length (a) == 1 || length (b) == 1) |
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47 if (a == 0) |
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48 x = b; |
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49 elseif (b == 0) |
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50 x = a; |
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51 else |
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52 x = 1; |
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53 endif |
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54 else |
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55 a /= a(1); |
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56 while (1) |
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57 [d, r] = deconv (b, a); |
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58 nz = find (abs (r) > tol); |
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59 if (isempty (nz)) |
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60 x = a; |
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61 break; |
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62 else |
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63 r = r(nz(1):length(r)); |
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64 endif |
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65 b = a; |
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66 a = r / r(1); |
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67 endwhile |
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68 endif |
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69 else |
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70 usage ("x = polygcd (b, a [,tol])"); |
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71 endif |
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72 |
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73 endfunction |
