Lowest degree of the terms in a polynomial

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


ldegree(p) returns the lowest total degree of the terms of the polynomial p.

ldegree(p, x) returns the lowest degree of the terms in p with respect to the variable x.

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

ldegree(f, vars, x) returns 0 if x is not an element of vars.

The low degree of the zero polynomial is defined as 0.


Example 1

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

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

The next call regards the expression as a polynomial in x with a parameter y:

ldegree(x^3 + x^2*y^2, x)

The next expression is regarded as a bi-variate polynomial in x and z with coefficients containing the parameter y. The total degree with respect to x and z is computed:

ldegree(x^3*z^2 + x^2*y^2*z, [x, z])

We compute the low degree with respect to x:

ldegree(x^3*z^2 + x^2*y^2*z, [x, z], x)

A polynomial in x and z is regarded constant with respect to any other variable, i.e., its corresponding degree is 0:

ldegree(poly(x^3*z^2 + x^2*y^2*z, [x, z]), 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