Using solve and/or linsolve with the symbolic toolbox in R2010b

Question

I asked a question a few days ago here and got an answer that seems like it would work- it involves using linsolve to find the solutions to a system of equations that are all modulo p, where p is a non-prime integer.

However, when I try to run the commands from the provided answer, or the linsolve help page, I get an error saying linsolve doesn't support arguments of type 'sym'. Is using linsolve with sym variables only possible in R2013b? I've also tried it with my school's copy, which is R2012b. Here is the code I'm attempting to execute (from the answer at the above link):

A = [0 5 4 1;1 7 0 2;8 1 0 2;10 5 1 0];
b = [2946321;5851213;2563617;10670279];
s = mod(linsolve(sym(A),sym(b)),8)

And the output is:

??? Undefined function or method linsolve' for input arguments of type 'sym'.

I've also tried to use the function solve for this, however even if I construct the equations represented by the matrices A and b above, I'm having issues. Here's what I'm attempting:

syms x y z q;
solve(5*y + 4*z + q == 2946321, x + 7*y + 2*q == 5851213, 8*x + y + 2*q == 2563617, 10*x + 5*y + z == 10670279,x,y,z,q)

And the output is:

??? Error using ==> char
Conversion to char from logical is not possible.

Error in ==> solve>getEqns at 169
vc = char(v);

Error in ==> solve at 67
[eqns,vars] = getEqns(varargin{:});

Am I using solve wrong? Should I just try to execute my code in R2013b to use linsolve with symbolic data types?

Answer 1

The Symbolic Math toolbox math toolbox has changed a lot (for the better) over the years. You might not have sym/linsolve, but does this work?:

s = mod(sym(A)\sym(b),8)

That will basically do the same thing. sym/linsolve just does some extra input checking and and rank calculation to mirror the capabilities of linsolve.

You're using solve correctly for current versions, but it looks like R2010b may not understand the == operator (sym/eq) in this context. You can use the old string format to specify your equations:

eqs = {'5*y + 4*z + q = 2946321',...
       'x + 7*y + 2*q = 5851213',...
       '8*x + y + 2*q = 2563617',...
       '10*x + 5*y + z = 10670279'};
vars = {'x','y','z','q'};
[x,y,z,q] = solve(eqs{:},vars{:})