[Pkg-octave-commit] [SCM] octave-symbolic branch, master, updated. a718b53403d9f164f8c2a3df521385a01d28a11b

[watsma]

The following commit has been merged in the master branch:
commit ed456f993f54509fd6a317f801a4851c119e66e0
Author: watsma <watsma at 416fae20-06d0-4450-9b69-c6c34d4b5f03>
Date:   Wed May 14 20:15:28 2003 +0000

    Initial commit. Break down symbolic polynomial in coefficients.
    
    
    git-svn-id: https://octave.svn.sourceforge.net/svnroot/octave/trunk/octave-forge/main/symbolic@935 416fae20-06d0-4450-9b69-c6c34d4b5f03

diff --git a/sym2poly.m b/sym2poly.m
new file mode 100644
index 0000000..75bc0bd
--- /dev/null
+++ b/sym2poly.m
@@ -0,0 +1,150 @@
+## Copyright (C) 2003 Willem J. Atsma
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or
+## modify it under the terms of the GNU General Public
+## License as published by the Free Software Foundation;
+## either version 2, or (at your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied
+## warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+## PURPOSE.  See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public
+## License along with Octave; see the file COPYING.  If not,
+## write to the Free Software Foundation, 59 Temple Place -
+## Suite 330, Boston, MA 02111-1307, USA.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} @var{c} = sym2poly (@var{p}, @var{x})
+## Returns the coefficients of the symbolic polynomial expression @var{p}
+## as a vector. If there is only one free variable in @var{p} the
+## coefficient vector @var{c} is a plain numeric vector. If there is more
+## than one free variable in @var{p}, a second argument @var{x} specifies the
+## free variable and the function returns a list of symbolic expressions.
+## The coefficients correspond to decreasing exponent of the free variable.
+##
+## Example:
+## @example
+## symbols
+## x=sym("x"); y=sym("y");
+## c = sym2poly (x^2+3*x-4);    # c = [2,3,-4]
+## c = sym2poly (x^2+y*x,x);    # c = list(2,y,0)
+## @end example
+##
+## If @var{p} is not a polynomial the result has no warranty.
+##
+## @end deftypefn
+## @seealso{poly2sym,polyval,roots}
+
+## Author: Willem J. Atsma <watsma(at)users.sf.net>
+## Created: 18 April 2003
+## Changed: 25 April 2003
+##    Removed the use of differentiate to get to coefficients - round-off
+##     errors cause problems. Now using newly created sumterms().
+## Changed: 6 May 2003
+##    Removed the attempt to use ldegree(), degree() and coeff() - results
+##     with these are inconsistent.
+
+function c = sym2poly(p,x)
+
+BADPOLY_COEFF_LIMIT = 500;
+
+if is_vpa(p)
+	# polynomial is one vpa number
+	c = to_double(p);
+	if length(c)!=1
+		error("Argument is not a polynomial.");
+	endif
+	return
+endif
+
+if !is_ex(p)
+	error("Argument has to be a symbolic expression.")
+endif
+
+pvars = findsymbols(p);
+if isempty(pvars)
+	# It is possible that we get an expression without any symbols.
+	c = to_double(p);
+	return;
+endif
+nvars = length(pvars); 
+
+if nvars>1 & exist("x")!=1
+	error("Symbolic expression has more than 1 free variable; no variable specified.")
+elseif exist("x")!=1
+	x = pvars{1};
+endif
+
+p = expand(p);
+
+## GiNaC has commands to access coefficients directly, but in octave this often
+## does not work, because for example x^2 typed in octave results in a 
+## non-integer power in GiNaC: x^2.0 .
+
+[num,den] = numden(p);
+tmp = findsymbols(den);
+for i=1:length(tmp)
+	if tmp{i}==x
+		error("Symbolic expression is a ratio of polynomials.")
+	endif
+endfor
+
+p = expand(p);
+p_terms = sumterms(p);
+# if this is well behaved, I can find the coefficients by dividing with x
+c_ex = list;
+for i=1:length(p_terms)
+	tmp = p_terms{i};
+	for j=1:BADPOLY_COEFF_LIMIT
+		if disp(differentiate(tmp,x))=="0"
+			break;
+		endif
+		tmp = tmp/x;
+	endfor
+	if j==BADPOLY_COEFF_LIMIT
+		printf("Please examine your code or adjust this function.\n");
+		printf("This error may occur because the passed expression is not a polynomial.\n");
+		error("Reached the set limit (%d) for the number of coefficients.",BADPOLY_COEFF_LIMIT)
+	endif
+	if (length(c_ex)<j) || isempty(c_ex{j})
+		c_ex(j)=tmp;
+	else
+		c_ex(j) = c_ex{j}+tmp;
+	endif		
+endfor
+order = length(c_ex)-1;
+
+all_numeric = true;
+for i=1:(order+1)
+	if isempty(c_ex{i})
+		c_ex(i) = vpa(0);
+	endif
+	cvar=findsymbols(c_ex{i});
+	ncvar = length(cvar);
+	if ncvar
+		all_numeric=false;
+		for j=1:ncvar
+			if disp(cvar{j})==disp(x)
+				printf("Possibly this error occurs because two symbols with the same name\n");
+				printf("are different to GiNaC. Make sure the free variable exists as a\n");
+				printf("symbol in your workspace.\n");
+				error("The symbolic expression is not a polynomial.")
+			endif
+		endfor
+	endif
+endfor
+
+c_ex = reverse(c_ex);
+
+if all_numeric
+	for i=1:(order+1)
+		c(1,i)=to_double(c_ex{i});
+	endfor
+else
+	c = c_ex;
+endif

-- 
octave-symbolic