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ldegree -- the lowest degree of the terms in a polynomial

Introduction

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.

Call(s)

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

Parameters

p - a polynomial of type DOM_POLY
f - a polynomial expression
vars - a list of indeterminates of the polynomial: typically, identifiers or indexed identifiers
x - an indeterminate

Returns

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

Overloadable:

p, f

Related Functions

coeff, degree, degreevec, ground, lcoeff, lmonomial, lterm, nterms, nthcoeff, nthmonomial, nthterm, poly, poly2list, tcoeff

Details

Example 1

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

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

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

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

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])
                                     3

We compute the low degree with respect to x:

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

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)
                                     0

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