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 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 is quadratic in 
and 
,
but if 
and 
are instead considered as variables, the resulting equation
 |
is quartic in 
and 
.
