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Highlights from
groebner

groebner

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19 Jun 2009 (Updated )

manipulate and solve systems of multivariate polynomial equations by computing the groebner basis

Pset=str2poly(strcell,varnames)
function Pset=str2poly(strcell,varnames)
% POLY2STR - convert multivariate polynomials from strings to arrays
% usage: Pset=poly2str(strcell,varnames)
%
% INPUTS: strcell, varnames
%  strcell is a cell array of strings, one per polynomial
%    all numbers must be whole or decimal form (no scientific notation)
%    brackets and double negatives are not allowed.
%    All spaces in the strings are ignored.
%  varnames (optional) is a cell array of strings which must include all
%    variable names that occur in strcell [default: {'x1','x2',...}]
%
% OUTPUTS: Pset
%  Pset is a cell array of polynomial coefficients where row j of Pset{i}
%    is [c,k1,k2,...] representing the monomial c*x1^k1*x2^k2*...
%
% EXAMPLE:
%  str2poly({'x1*x2^2'})    % returns {[1,1,2]}
%  str2poly({'-x1*x2^2'})   % returns {[-1,1,2]}
%  str2poly({'-1*x1*x2^2'}) % returns {[-1,1,2]}
%  str2poly({'- 1 * x 1 * x 2 ^ 2'}) % returns {[-1,1,2]}
%
% SEE ALSO:
%  groebner, poly2str

% Author: Ben Petschel 19/6/2009
%
% Change history:
%  19/6/2009 - first release
%  22/6/2009 - fixed bug in handling "-x1" etc.
%  17/7/2009 - allow whitespace in strings
%  20/3/2010 - changed array representation to rectangular instead of n-d

if nargin<2,
  varnames = {}; % will fill in varnames later, as needed
end;
Pset = cell(size(strcell));

for i=1:numel(strcell),
  str = strcell{i};
  
  % ignore all spaces
  remain = str;
  remain = strrep(remain,' ','');
  
  % first insert "+" before every "-", for easier term separation later
  str = '';
  while ~isempty(remain),
    if remain(1)=='-',
      if isempty(str),
        str = '-';
      else
        str = [str,'+-'];
      end;
    end;
    [tok,remain]=strtok(remain,'-');
    str = [str,tok];
  end;
  
  % now separate into terms
  remain = str;
  terms = [];
  while ~isempty(remain),
    coeff = 1;
    exps = [];
    [term,remain]=strtok(remain,'+');
    % process term, separating into products
    rem2 = term;
    while ~isempty(rem2),
      [part,rem2]=strtok(rem2,'*');
      if ~isnan(str2double(part)),
        % part is a number, multiply it by the coefficient
        coeff = coeff * str2double(part);
      else
        % part is var^n or var or -var^n or -var
        if part(1)=='-',
          coeff = -coeff;
          part=part(2:end);
          if isempty(part),
            error('isolated minus sign');
          end;
        end;
        ind = find(part=='^');
        if isempty(ind),
          var = part;
          expo = 1;
        else
          ind = ind(1);
          var = part(1:ind-1);
          expo = str2double(part(ind+1:end));
          if isnan(expo),
            % exponent is not valid
            error('invalid exponent in part %s',part);
          end;
        end;
        if isempty(varnames),
          % see if var is of form 'x1' etc
          if (length(var)>1) && (var(1)=='x') && ~isnan(str2double(var(2:end))),
            % variable name is ok
            k = str2double(var(2:end));
          else
            error('variable name not of form "x1","x2",...');
          end;
        else
          ind = strmatch(var,varnames);
          if isempty(ind),
            error('variable name not in list');
          end;
          k = ind(1);
        end;
        if length(exps)<k,
          exps = [exps,zeros(1,k-length(exps))];
        end;
        exps(k) = exps(k)+expo;
      end;
    end; % while ~isempty(rem2),
    % term is processed, now add it to the list of terms
    if size(terms,2)<(length(exps)+1),
      terms = [terms,zeros(size(terms,1),length(exps)+1-size(terms,2))];
    elseif length(exps)<size(terms,2)-1,
      exps = [exps,zeros(1,size(terms,2)-1-length(exps))];
    end;
    terms = [terms;coeff,exps];
  end; % while ~isempty(remain),
  
  Pset{i}=terms;
end; % for i=1:numel(strcell),    
  

end % main function str2poly(...)

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