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Degree of a polynomial

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degree(p, x)
degree(f, <vars>)
degree(f, <vars>, x)


degree(p) returns the total degree of the polynomial p.

degree(p, x) returns the degree of p with respect to the variable x.

If the first argument f is not element of a polynomial domain, then degree converts the expression internally to a polynomial of type DOM_POLY via poly(f). If a list of indeterminates is specified, the polynomial poly(f, vars) is considered.

degree(f, vars, x) returns 0 if x is not an element of the list vars.

The degree of the zero polynomial is defined as 0.


Example 1

The total degree of the terms in the following polynomial expression is computed:

degree(x^3 + x^2*y^2 + 2)

Example 2

degree may be applied to polynomials of type DOM_POLY:

degree(poly(x^2*z + x*z^3 + 1, [x, z]))

Example 3

The next expression is regarded as a bi-variate polynomial in x and z. The degree with respect to z is computed:

degree(x^2*z + x*z^3 + 1, [x, z], z)

Example 4

The degree of the zero polynomial is defined as 0:

degree(0, [x, y])



A polynomial of type DOM_POLY


A polynomial expression


A list of indeterminates of the polynomial: typically, identifiers or indexed identifiers


An indeterminate

Return Values

Nonnegative number. FAIL is returned if the input cannot be converted to a polynomial.

Overloaded By

f, p

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