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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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {[@var{q}]} polygcd (@var{b}, @var{a}, @var{tol}) |
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19 ## |
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20 ## Find greatest common divisor of two polynomials. This is equivalent |
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21 ## to the polynomial found by multiplying together all the common roots. |
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22 ## Together with deconv, you can reduce a ratio of two polynomials. |
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23 ## Tolerance defaults to |
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24 ## @example |
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25 ## sqrt(eps). |
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26 ## @end example |
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27 ## Note that this is an unstable |
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28 ## algorithm, so don't try it on large polynomials. |
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29 ## |
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30 ## Example |
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31 ## @example |
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32 ## polygcd(poly(1:8),poly(3:12)) - poly(3:8) |
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33 ## deconv(poly(1:8),polygcd(poly(1:8),poly(3:12))) - poly(1:2) |
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34 ## @end example |
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35 ## @end deftypefn |
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36 ## |
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37 ## @seealso{poly, polyinteg, polyderiv, polyreduce, roots, conv, deconv, |
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38 ## residue, filter, polyval, and polyvalm} |
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39 |
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40 function x = polygcd(b,a,tol) |
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41 if (nargin<2 || nargin>3) |
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42 usage("x=polygcd(b,a [,tol])"); |
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43 endif |
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44 if (nargin<3), tol=sqrt(eps); endif |
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45 if (length(a)==1 || length(b)==1) |
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46 if a==0, x=b; |
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47 elseif b==0, x=a; |
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48 else x=1; |
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49 endif |
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50 return; |
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51 endif |
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52 a = a./a(1); |
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53 while (1) |
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54 [d, r] = deconv(b, a); |
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55 nz = find(abs(r)>tol); |
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56 if isempty(nz) |
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57 x = a; |
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58 return; |
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59 else |
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60 r = r(nz(1):length(r)); |
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61 endif |
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62 b = a; |
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63 a = r./r(1); |
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64 endwhile |
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65 endfunction |
