# Operators and Elementary Operations

Perform arithmetic, relational, and logical operations on symbolic objects

Symbolic Math Toolbox™ includes functions for arithmetic, relational, and logical operations, as well as modulo and complex number operations, on symbolic objects. You can use these functions to perform simple operations like addition, multiplication, and calculating exponents, as well as other operations like finding the `n`th root, modulus, and finding the quotient and remainder of a division.

## Functions

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 `minus` Symbolic subtraction `plus` Symbolic addition `times` Symbolic array multiplication `ldivide` Symbolic array left division `rdivide` Symbolic array right division `power` Symbolic array power `nthroot` Nth root of symbolic numbers `mtimes` Symbolic matrix multiplication `mldivide` Symbolic matrix left division `mrdivide` Symbolic matrix right division `mpower` Symbolic matrix power `transpose` Symbolic matrix transpose `ctranspose` Symbolic matrix complex conjugate transpose

#### Operators

 `eq` Define symbolic equation `ge` Define greater than or equal to condition `gt` Define greater than relation `le` Define less than or equal to condition `lt` Define less than relation `ne` Define inequality

#### Functions

 `has` Check if expression contains particular subexpression `hasSymType` Determine whether symbolic object contains specific type (Since R2019a) `in` Numeric type of symbolic input `isAlways` Determine if symbolic conditions are true for all values of variables `isequal` Determine if symbolic inputs are equal `isequaln` Test symbolic objects for equality, treating `NaN` values as equal `isSymType` Determine whether symbolic object is specific type (Since R2019a) `max` Maximum elements of symbolic input (Since R2021a) `min` Minimum elements of symbolic input (Since R2021a) `piecewise` Conditionally defined expression or function

#### Operators

 `and` Logical AND for symbolic expressions `not` Logical NOT for symbolic expressions `or` Logical OR for symbolic expressions `xor` Logical XOR for symbolic expressions

#### Functions

 `all` Test whether all equations and inequalities represented as elements of symbolic array are valid `any` Test whether at least one of equations and inequalities represented as elements of symbolic array is valid `has` Check if expression contains particular subexpression `hasSymType` Determine whether symbolic object contains specific type (Since R2019a) `in` Numeric type of symbolic input `isAlways` Determine if symbolic conditions are true for all values of variables `isequaln` Test symbolic objects for equality, treating `NaN` values as equal `isfinite` Check whether symbolic array elements are finite `isinf` Check whether symbolic array elements are infinite `isnan` Check whether symbolic array elements are `NaN`s `isSymType` Determine whether symbolic object is specific type (Since R2019a) `logical` Determine if symbolic equation, inequality, or condition is true `symtrue` Symbolic logical constant true (Since R2020a) `symfalse` Symbolic logical constant false (Since R2020a)
 `mod` Symbolic modulus after division `powermod` Modular exponentiation `quorem` Quotient and remainder `rem` Remainder after division
 `abs` Symbolic absolute value (complex modulus or magnitude) `angle` Symbolic polar angle `conj` Complex conjugate of symbolic input `imag` Imaginary part of complex number `real` Real part of complex number