Documentation

# isequal

Test equality of symbolic inputs

## Syntax

``isequal(a,b)``
``isequal(a1,a2,...,aN)``

## Description

example

````isequal(a,b)` returns logical `1` (`true`) if `A` and `B` are the same size and their contents are of equal value. Otherwise, `isequal` returns logical `0` (`false`). `isequal` does not consider `NaN` (not a number) values equal. `isequal` recursively compares the contents of symbolic data structures and the properties of objects. If all contents in the respective locations are equal, `isequal` returns logical `1` (`true`).```

example

````isequal(a1,a2,...,aN)` returns logical `1` (`true`) if all the inputs `a1,a2,...,aN` are equal.```

## Examples

### Test Numbers for Equality

Test numeric or symbolic inputs for equality using `isequal`. If you compare numeric inputs against symbolic inputs, `isequal` returns `0` (`false`) because double and symbolic are distinct data types.

Test if `2` and `5` are equal. Because you are comparing doubles, the MATLAB® `isequal` function is called. `isequal` returns `0` (`false`) as expected.

`isequal(2,5)`
```ans = logical 0```

Test if the solution of the equation `cos(x) == -1` is `pi`. The `isequal` function returns `1` (`true`) meaning the solution is equal to `pi`.

```syms x sol = solve(cos(x) == -1, x); isequal(sol,sym(pi))```
```ans = logical 1```

Compare the double and symbolic representations of `1`. `isequal` returns `0` (`false`) because double and symbolic are distinct data types. To return `1` (`true`) in this case, use `logical` instead.

```usingIsEqual = isequal(pi,sym(pi)) usingLogical = logical(pi == sym(pi))```
```usingIsEqual = logical 0 usingLogical = logical 1```

### Test Symbolic Expressions for Equality

Test if `rewrite` correctly rewrites `tan(x)` as `sin(x)/cos(x)`. The `isequal` function returns `1` (`true`) meaning the rewritten result equals the test expression.

```syms x f = rewrite(tan(x),'sincos'); testf = sin(x)/cos(x); isequal(f,testf)```
```ans = logical 1```

### Test Symbolic Vectors and Matrices for Equality

Test vectors and matrices for equality using `isequal`.

Test if solutions of the quadratic equation found by `solve` are equal to the expected solutions. `isequal` function returns `1` (`true`) meaning the inputs are equal.

```syms a b c x eqn = a*x^2 + b*x + c; Sol = solve(eqn, x); testSol = [-(b+(b^2-4*a*c)^(1/2))/(2*a); -(b-(b^2-4*a*c)^(1/2))/(2*a)]; isequal(Sol,testSol)```
```ans = logical 1```

The Hilbert matrix is a special matrix that is difficult to invert accurately. If the inverse is accurately computed, then multiplying the inverse by the original Hilbert matrix returns the identity matrix.

Use this condition to symbolically test if the inverse of `hilb(20)` is correctly calculated. `isequal` returns `1` (`true`) meaning that the product of the inverse and the original Hilbert matrix is equal to the identity matrix.

```H = sym(hilb(20)); prod = H*inv(H); eye20 = sym(eye(20)); isequal(prod,eye20)```
```ans = logical 1```

### Compare Inputs Containing `NaN`

Compare three vectors containing `NaN` (not a number). `isequal` returns logical `0` (`false`) because `isequal` does not treat `NaN` values as equal to each other.

```syms x A1 = [x NaN NaN]; A2 = [x NaN NaN]; A3 = [x NaN NaN]; isequal(A1, A2, A3)```
```ans = logical 0```

## Input Arguments

collapse all

Inputs to compare, specified as numbers, vectors, matrices, or multidimensional arrays or symbolic numbers, variables, vectors, matrices, multidimensional arrays, functions, or expressions.

Several inputs to compare, specified as numbers, vectors, matrices, or multidimensional arrays or symbolic numbers, variables, vectors, matrices, multidimensional arrays, functions, or expressions.

## Tips

• When your inputs are not symbolic objects, the MATLAB `isequal` function is called. If one of the arguments is symbolic, then all other arguments are converted to symbolic objects before comparison, and the symbolic `isequal` function is called.