A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables
in the function 
are 
and 
.
A function having a single variable is said to be univariate, one having two variables is said to be bivariate, and one having two or more variables is said
to be multivariate. In a polynomial,
the variables correspond to the base symbols themselves stripped of coefficients
and any powers or products.
In literature, one often distinguishes between dependent variables and independent variables,
the latter of which usually represents the inputs or quantities whose causality is
being tested experimentally while the former generally represents the output whose
values are altered by causal phenomena. Similar to the multivariate
example mentioned above, the equation 
has 
as a dependent variable
due to the fact that its value depends on what values 
and 
are plugged into 
;
and 
are both independent variables
due to their having no dependences within the equation.
The variables in a polynomial can be extracted using the Wolfram Language command Variables[poly].
In general, mathematical functions may have a number of arguments. Arguments that are typically varied when plotting, performing mathematical operations, etc., are termed "variables," while those that are not explicitly varied in situations of interest are termed "parameters." For example, in the standard equation of an ellipse
 |
and 
are generally considered variables and 
and 
are considered parameters. The decision on which arguments to consider variables and which to consider parameters may be historical or may be based on the application
under consideration. However, the nature of a mathematical function
may change depending on which choice is made. For example, the above equation
has total polynomial degree 2 in 
and 
,
but if 
and 
are instead considered as variables, the resulting equation
 |
has total polynomial degree 4 in 
and 
.
