Create symbolic variables, expressions, functions, matrices

**Support of character vectors that are not valid variable names and that do not define a number
has been removed. To create symbolic expressions, first create symbolic variables, and
then use operations on them. For example, use syms x; x + 1 instead
of sym('x + 1'), exp(sym(pi)) instead of
sym('exp(pi)'), and syms f(var1,...varN)
instead of f(var1,...varN) = sym('f(var1,...varN)').**

creates an
`A`

= sym('`a`

',`[n1 ... nM]`

)`n1`

-by-`...`

-by-`nM`

symbolic array filled with automatically generated elements. For example,
`A = sym('a',[1 3])`

creates the row vector ```
A =
[a1 a2 a3]
```

. The generated elements `a1`

,
`a2`

, and `a3`

do not appear in the
MATLAB^{®} workspace. For multidimensional arrays, these elements have the
prefix `a`

followed by the element’s index using
`_`

as a delimiter, such as
`a1_3_2`

.

`sym(___,`

creates a symbolic variable
or array and sets the assumption that the variable or all array elements belong
to a `set`

)`set`

. Here, `set`

can be
`'real'`

, `'positive'`

,
`'integer'`

, or `'rational'`

. You also can
combine multiple assumptions by specifying a string array or cell array of
character vectors. For example, assume a positive rational value by specifying
`set`

as `["positive" "rational"]`

or
`{'positive','rational'}`

.

`sym(`

converts a number or numeric matrix
specified by `num`

)`num`

to a symbolic number or symbolic
matrix.

Statements like

`pi = sym('pi')`

and`delta = sym('1/10')`

create symbolic numbers that avoid the floating-point approximations inherent in the values of`pi`

and`1/10`

. The`pi`

created in this way temporarily replaces the built-in numeric function with the same name.`sym`

always treats`i`

in character vector input as an identifier. To input the imaginary number`i`

, use`1i`

instead.`clear x`

does not clear the symbolic object of its assumptions, such as real, positive, or any assumptions set by`assume`

,`sym`

, or`syms`

. To remove assumptions, use one of these options:`assume(x,'clear')`

removes all assumptions affecting`x`

.`clear all`

clears all objects in the MATLAB workspace and resets the symbolic engine.`assume`

and`assumeAlso`

provide more flexibility for setting assumptions on variable.

When you replace one or more elements of a numeric vector or matrix with a symbolic number, MATLAB converts that number to a double-precision number.

`A = eye(3); A(1,1) = sym('pi')`

A = 3.1416 0 0 0 1.0000 0 0 0 1.0000

You cannot replace elements of a numeric vector or matrix with a symbolic variable, expression, or function because these elements cannot be converted to double-precision numbers. For example,

`A(1,1) = sym('a')`

throws an error.When you use the syntax

`A = sym('a',[n1 ... nM])`

, the`sym`

function assigns only the symbolic array`A`

to the MATLAB workspace. To also assign the automatically generated elements of`A`

, use the`syms`

function instead. For example,`syms a [1 3]`

creates the row vector`a = [a1 a2 a3]`

and the symbolic variables`a1`

,`a2`

, and`a3`

in the MATLAB workspace.

To create several symbolic variables in one function call, use `syms`

.
Using `syms`

also clears assumptions from the named
variables.