How to change from matrix to polynomial using SYM? Mine results in ERROR - Error using symengine (line 59)

Here's my code:

% initializing values
D = sym('D');
g1 = [1 0 1 1];
g2 = [1 1 0 1];
g = [g1;g2];      % 4 by 2 matrix, g1 will be transformed to g_D(1) and g2 => g_D(2) as below
[no_of_g, size_of_g] = size(g);

% setting all g_D = 0
for i=1:no_of_g
    g_D(i)=0;
end

for i=1:no_of_g
    for j=1:size_of_g
        g_D(i)=g_D(i)+ g(i,j)*D^(j-1);   % expected to have g_D(1)=1+D^2+D^3 but ERROR
    end
end

ERROR shows: The following error occurred converting from sym to double: Error using symengine (line 59) DOUBLE cannot convert the input expression into a double array. If the input expression contains a symbolic variable, use VPA.

Error in test (line 15) g_D(i)=g_D(i)+ g(i,j)*D^(j-1);

Answer 1

[John D'Errico]

Easy enough.

g1 = [1 0 1 1];
syms D
D.^(0:3)*g1.'
ans =
D^3 + D^2 + 1

[smileyz_1990]

You put my code to shame, but at least I learned something new.

I just ran sections by sections, so I see how that works, but not sure what the "." does though...could you please explain for me?

[John D'Errico]

There are two dots there. lol

The first one, in here:

D.^(0:3)

is necessary, because MATLAB cannot raise a scalar to a vector power directly. So this will fail, as you can see what it does:

D^(0:3)

Error using symengine
A square matrix is expected.
Error in sym/privBinaryOp (line 908)
            Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:});
Error in  ^  (line 266)
        B = privBinaryOp(A, p, 'symobj::mpower');

The dot there tells MATLAB to use element-wise exponentiation, raising the scalar D to each element of the vector exponent.

The second dot is the .' operator. This is the non-conjugate transpose. Just in case some of the lements of g1 were complex. I wanted to make g1 a column vector. Alternatively, I could have written it as

D.^(0:3)*g1(:)
ans =
D^3 + D^2 + 1

that would have been equally valid. Some might argue easier to read too.

Finally, if g is a matrix, then we can create the pair of polynomials in one multiply.

g = [1 0 1 1;1 1 0 1];
D.^(0:3)*g.'
ans =
[ D^3 + D^2 + 1, D^3 + D + 1]

[smileyz_1990]

This is a very helpful answer. I appreciate your elaborate answer.

Now, how would you convert that back to matrix, more specifically, taking the coefficient of the D's into matrix? I want to make sure that it's in the form of [D^0, D^1, D^2 ... ] instead of reverse.

This is all for learning purposes, as I will be dealing with converting between polynomials and matrices.

[John D'Errico]

p = D.^(0:3)*g1.';
sym2poly(p)
ans =
     1     1     0     1

As a test...

p = D.^(0:3)*flip(g1).'
p =
D^3 + D + 1
sym2poly(p)
ans =
     1     0     1     1

[smileyz_1990]

Apparently I have so much to learn, I mean I never heard of flip!

I tried using poly2sym and coeffs, but didn't work for some reason or I didn't get the results I want.

Anyhoo, you're awesome thanks!