res=myrese(exprz,z)

function res=myrese(exprz,z)
% myres   figure out residues of a function of complex variables
%
% Input  changeable1exprz = The expression of the function and specified variable
%                      2z = The singular point which residue you want to know
%                      (Enter when you just want that point
% Output   The singular points and corresponding residuessymbolic object
% formatin a matrix with two rows,the first row is singular points,the
% seceond row is correspoind residues.
% Example:   res=myrese('1/(z*(z+1)),z');res=myrese('cot(z),z');res=myres('1/z,z','0');res=myres('cos(z),z');
%            res=myrese('z,z');
% Note  Every argument must be character!
% Physical Science and technology College of Central China Normal
% University  Grade 2005 Pu Ke  Nov.4th.2006 
if nargin==0
    error('No argument!');
elseif nargin==1
    maple('interface(warnlevel=0);myresidue := proc (ex, z) Sing := singular(ex, z); n := nops({Sing}); if n = 0 then ERROR("No singular point!") elif n = 1 then resi := residue(ex, Sing[1]) elif 1 < n then resi := [seq(r[I], I = 1 .. n)]; for k to n do resi[k] := residue(ex, Sing[k][1]) end do end if; return Sing, resi end proc:');
    [cha,chan,chay]=command(exprz);
    num=str2double(maple(chan));
    try  
        inter=maple(cha);
        if isempty(strfind(inter,'residue'))%The'residue'appears imply that maple can't find the residue
            if isempty(strfind(inter,'_Z1'))==0
                error('problem');  
            else
                res=condition1(inter,num);
            end
        elseif isempty(strfind(inter,'residue'))==0&&isempty(strfind(inter,'_Z1'))
            disp('Cant figure out the residue. The singular points are:');
            maple(chay)
            res=[];
        else
            error('problem');%Throw a exception
        end
    catch%Deal with the situation that there are infinite singular points.
        res=condition2(chay,num,exprz); 
    end
    elseif nargin==2
        com=['residue(',exprz,'=',z,')'];
        res=[simple(sym(z));sym(maple(com))];
end
maple('restart');%clear the memory of the worksheet
end
function [cha,chan,chay]=command(exprz)%Call maple function
     cha=['myresidue(',exprz,')'];
     chan=['nops({singular(',exprz,')})'];%The number of singular point
     chay=['singular(',exprz,')'];%singular point
end
function res=condition1(inter,num)
indexe=strfind(inter,'=');
indexh=strfind(inter,'}');
index=max(strfind(inter,'}'));
sing=sym(zeros(1,num));
for k=1:length(indexe)
    sing(k)=simple(sym(inter(indexe(k)+1:indexh(k)-1)));
end
res=[sing;simple(sym(inter(index+3:length(inter))))];%convert charater to MATLAB symbolic object. 
end
function res=condition2(chay,num,exprz)
if num==0
    disp('There is no singular point finite area!');
    res=sym('0');
else
    disp('This function have infinite singular point. they are:')
    maple(chay)
    z=input('Please choose a singular point:z=');
    z=num2str(z);%conver it to charater
    com=['residue(',exprz,'=',z,')'];
    res=[sym(z);simple(sym(maple(com)))];%convert charater to MATLAB symbolic object. 
end
end