Exponent

Exponent[expr,form]

gives the maximum power with which form appears in the expanded form of expr.

Exponent[expr,form,h]

applies h to the set of exponents with which form appears in expr.

Details and Options

  • The default taken for h is Max.
  • form can be a product of terms.
  • Exponent works whether or not expr is explicitly given in expanded form.
  • Exponent[0,x] is -Infinity.
  • Exponent[expr,{form1,form2,}] gives the list of exponents for each of the formi.

Examples

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Basic Examples  (1)

Find the highest exponent of :

Scope  (4)

The degree of a polynomial:

Exponents may be rational numbers or symbolic expressions:

The lowest exponent in a polynomial:

The list of all exponents with which appears:

Options  (2)

Modulus  (1)

The degree of a polynomial over the integers modulo 2:

Trig  (1)

With Trig->True, Exponent recognizes dependencies between trigonometric functions:

Applications  (1)

Compute the leading coefficient:

Compute the leading term:

Properties & Relations  (2)

The number of complex roots of a polynomial is equal to its degree:

Use Solve to find the roots:

Length of the CoefficientList of a polynomial is one more than its degree:

Possible Issues  (1)

Exponent is purely syntactical; it does not attempt to recognize zero coefficients:

Introduced in 1988
 (1.0)
 |
Updated in 1996
 (3.0)
2003
 (5.0)