%% Choose syms or sym Function
% In Symbolic Math Toolbox™, you can declare symbolic objects using either syms or sym. These two functions are conceptually different.
% The syms function creates a symbolic object that is automatically assigned to a MATLAB® variable with the same name.
% The sym function refers to a symbolic object that can be assigned to a MATLAB variable with the same name or a different name.
%
%% Assign Symbolic Variables to MATLAB Variables
% The syms function creates a variable dynamically. For example, the command syms x creates the symbolic variable x and automatically assigns it to a MATLAB variable with the same name.

syms x
x

% The sym function refers to a symbolic variable, which you can then assign to a MATLAB variable with a different name. For example, the command f1 = sym('x') refers to the symbolic variable x and assigns it to the MATLAB variable f1.

f1 = sym('x')

%
%% Create Symbolic Number
% Use the syms function to create a symbolic variable x and automatically assign it to a MATLAB variable x. When you assign a number to the MATLAB variable x, the number is represented in double-precision and this assignment overwrites the previous assignment to a symbolic variable. The class of x becomes double.

syms x
x = 1/33
class(x)

% Use the sym function to refer to an exact symbolic number without floating-point approximation. You can then assign this number to the MATLAB variable x. The class of x is sym.

x = sym('1/33')
class(x)

%
%% Create Symbolic Variable with Assumptions
% When you create a symbolic variable with an assumption, MATLAB stores the symbolic variable and its assumption separately.
% Use syms to create a symbolic variable that is assigned to a MATLAB variable with the same name. You get a fresh symbolic variable with no assumptions. If you declare a variable using syms, existing assumptions are cleared.

syms x positive
syms x
assumptions

% Use sym to refer to an existing symbolic variable. If this symbolic variable was used in your MATLAB session before, then sym refers to it and its current assumption. If it was not used before, then sym creates it with no assumptions.

syms x positive
x = sym('x');
assumptions

%
%% Create Many Symbolic Variables
% To create many symbolic variables simultaneously, using the syms function is more convenient. You can create multiple variables in one line of code.

syms a b c

% When you use sym, you have to declare MATLAB variables one by one and refer them to the corresponding symbolic variables.

a = sym('a');
b = sym('b');
c = sym('c');

%
%% Create Array of Symbolic Variables
% To declare a symbolic array that contains symbolic variables as its elements, you can use either syms or sym.
% The command syms a [1 3] creates a 1-by-3 symbolic array a and the symbolic variables a1, a2, and a3 in the workspace. The symbolic variables a1, a2, and a3 are automatically assigned to the symbolic array a.

clear all
syms a [1 3]
a
whos

% The command a = sym('a',[1 3]) refers to the symbolic variables  a1, a2, and a3, which are assigned to the symbolic array a in the workspace. The elements a1, a2, and a3 are not created in the workspace.

clear all
a = sym('a',[1 3])
whos

%
%% Symbolic Variable in Nested Function
% To declare a symbolic variable within a nested function, use sym. For example, you can explicitly define a MATLAB variable x in the parent function workspace and refer x to a symbolic variable with the same name.

function primaryFx
    x = sym('x')
    function nestedFx
        ...
    end
end

% Nested functions make the workspace static, so you cannot dynamically add variables using syms.
%
% Copyright 2019 The MathWorks, Inc.