Get coefficients of complex equation

I am trying to get coefficients of Quadric Surfaces in General Form like here: http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/simple.html

My code is:

args=[1,1,1,0,0,0,0,0,-5,0];
a=args(1);b=args(2);c=args(3);d=args(4);e=args(5);f=args(6);g=args(7);h=args(8);m=args(9);s=args(10); %M=i  , j = s

syms x y z real

Q=[a,d,e,g;
   d,b,f,h;
   e,f,c,m;
   g,h,m,s];
X=[x,y,z,1]';

func(x,y,z)=X'*Q*X;

[A,B]=coeffs(func)

My problem is that I don't get coefficients all those with zeros values my result should be : [1,1,1,0,0,0,0,0,-5,0]

I get : [ 1, 1, 1, -10]

How do I get the zeros as well

Answer 1

[saar beno]

The only solution that I found is:

[parameters,Eqations]=coeffs(funcToConvert)
parameters= sym2poly(parameters(x,y,z));

EqationsCells=arrayfun(@char,Eqations(x,y,z),'Un',0);

SerachRes=Myeq(EqationsCells,{'matrix([[x^2, 1, 1]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    a=0;
else
    a=parameters(index);
end

SerachRes=Myeq(EqationsCells,{'matrix([[x, x, 1]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    d=0;
else
    d=parameters(index)/2;
end

SerachRes=Myeq(EqationsCells,{'matrix([[x, 1, x]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    e=0;
else
    e=parameters(index)/2;
end

SerachRes=Myeq(EqationsCells,{'matrix([[x, 1, 1]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    g=0;
else
    g=parameters(index)/2;
end

SerachRes=Myeq(EqationsCells,{'matrix([[1, x^2, 1]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    b=0;
else
    b=parameters(index);
end

SerachRes=Myeq(EqationsCells,{'matrix([[1, x, x]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    f=0;
else
    f=parameters(index)/2;
end

SerachRes=Myeq(EqationsCells,{'matrix([[1, x, 1]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    h=0;
else
    h=parameters(index)/2;
end

SerachRes=Myeq(EqationsCells,{'matrix([[1, 1, x^2]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    c=0;
else
    c=parameters(index);
end

SerachRes=Myeq(EqationsCells,{'matrix([[1, 1, x]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    m=0;
else
    m=parameters(index)/2;
end

SerachRes=Myeq(EqationsCells,{'matrix([[1, 1, 1]])'});
index= GetSearchIndex( SerachRes );
if 0==index
    s=0;
else
    s=parameters(index);
end

But it seem no so efficient

Answer 2

[Walter Roberson]

By default, coeffs() extracts coefficients with respect to the indeterminates. If a particular symbol has disappeared because its only multiplier was 0, then it is not an indeterminate of the expression and its coefficient will not be extracted by default.

You should possibly use the third form of coeffs