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Mathematica > Mathematics and Algorithms > Polynomial Algebra >

Built-in Mathematica Symbol

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.

Exponent[expr, {form₁, form₂, ...}] gives the list of exponents for each of the form_i.

Find the highest exponent of

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:

The degree of a polynomial over the integers modulo 2:

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

Compute the leading coefficient:

Compute the leading term:

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:

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