function strcell=poly2str(Pset,varnames)
% POLY2STR - convert multivariate polynomials from arrays to strings
% usage: strcell=poly2str(Pset,varnames)
%
% INPUTS: Pset, varnames
% 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*...
% Pset can be the output of groebner(...)
% varnames (optional) is a cell array of strings of length at least the
% maximum dimension of the arrays in Pset [default: {'x1','x2',...}]
%
% OUTPUTS: strcell
% strcell is a cell array of strings, one per polynomial
%
% EXAMPLE:
% poly2str({[1,1,2]}) % returns {'x1*x2^2'}
%
% SEE ALSO:
% groebner, str2poly
% Author: Ben Petschel 19/6/2009
%
% Change history:
% 19/6/2009 - first release
% 20/3/2010 - changed array representation to rectangular instead of n-d
% 2/11/2010 - bugfix for maxnvars calc that was broken in the array rep update
maxnvars = max(cellfun(@(x)size(x,2)-1,Pset)); % determine nvars from array size
if nargin<2,
varnames = cell(1,maxnvars);
for i=1:maxnvars,
varnames{i} = sprintf('x%d',i);
end;
elseif maxnvars>numel(varnames),
error('not enough variable names provided');
end;
strcell = cell(size(Pset));
for i=1:numel(Pset),
str = '';
P = Pset{i};
s = size(P);
c = cell(1,length(s));
for j=size(P,1):-1:1,
if P(j,1)~=0,
if (P(j,1)>0) && ~isempty(str),
str = [str,'+'];
end;
if P(j,1)==1,
last1 = true;
elseif P(j,1)==-1,
% only print the '-'
last1 = true;
str = [str,'-'];
else
last1 = false;
str = [str,sprintf('%g',P(j,1))]; % include coefficient
end;
deg = P(j,2:end);
for k=1:length(deg),
if deg(k)>0,
if last1,
last1 = false;
else
str = [str,'*'];
end;
str = [str,varnames{k}]; % print variable name
end;
if deg(k)>1,
str = [str,sprintf('^%d',deg(k))]; % print exponent
end;
end;
if last1,
% this must be a constant term 1, so print the 1
str = [str,'1'];
end;
end;
end;
strcell{i}=str;
end;
end % main function poly2str(...)
