Getting Started (Symbolic Math Toolbox)

Symbolic Math Toolbox

Symbolic Objects

The Symbolic Math Toolbox defines a new MATLAB data type called a symbolic object or sym (see the MATLAB topic Programming and Data Types for an introduction to MATLAB classes and objects). Internally, a symbolic object is a data structure that stores a string representation of the symbol. The Symbolic Math Toolbox uses symbolic objects to represent symbolic variables, expressions, and matrices.

The following example illustrates the difference between a standard MATLAB data type, such as double, and the corresponding symbolic object. The MATLAB command

```
sqrt(2)
```

returns a floating-point decimal number:

```
ans =
1.4142
```

On the other hand, if you convert 2 to a symbolic object using the sym command, and then take its square root by entering

```
a = sqrt(sym(2))
```

the result is

```
a =
2^(1/2)
```

MATLAB gives the result 2^(1/2), which means 2^1/2, or , using symbolic notation for the square root operation, without actually calculating a numerical value. MATLAB records this symbolic expression in the string that represents 2^(1/2). You can always obtain the numerical value of a symbolic object with the double command:

```
double(a)
ans =
1.4142
```

When you create a fraction involving symbolic objects, MATLAB records the numerator and denominator. For example:

```
sym(2)/sym(5)
ans =
2/5
```

MATLAB performs arithmetic on symbolic objects differently than it does on standard data types. If you two fractions that are of data type double, MATLAB gives the answer as a decimal fraction. For example:

```
2/5 + 1/3
ans =
0.7333
```

If you add the same fractions as symbolic objects, MATLAB finds their common denominator and combines them by the usual procedure for adding rational numbers:

sym(2)/sym(5) + sym(1)/sym(3)
ans =
11/15

The Symbolic Math Toolbox enables you to perform a variety of symbolic calculations that arise in mathematics and science. These are described in detail in Using the Symbolic Math Toolbox.

Getting Started Creating Symbolic Variables and Expressions