Leading monomial of a polynomial
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order>, <Rem>) lmonomial(
lmonomial(p) returns the leading monomial
of the polynomial
The returned monomial is “leading” with respect
to the lexicographical ordering, unless a different ordering is specified
via the argument
order. Cf. Example 1.
The leading monomial of the zero polynomial is the zero polynomial.
A polynomial expression
f is first converted
to a polynomial with the variables given by
If no variables are given, they are searched for in
details of the conversion. The result is returned as polynomial expression.
f cannot be converted to a polynomial.
Cf. Example 4.
We demonstrate how various orderings influence the result:
p := poly(5*x^4 + 4*x^3*y*z^2 + 3*x^2*y^3*z + 2, [x, y, z]): lmonomial(p), lmonomial(p, DegreeOrder), lmonomial(p, DegInvLexOrder)
The following call uses the reverse lexicographical order on 3 indeterminates:
We compute the reductum of a polynomial:
p := poly(2*x^2*y + 3*x*y^2 + 6, [x, y]): q := lmonomial(p, Rem)
The leading monomial and the reductum add up to the polynomial
p = q + q
delete p, q:
We demonstrate the evaluation strategy of
p := poly(6*x^6*y^2 + x^2 + 2, [x]): y := 4: lmonomial(p)
Evaluation is enforced by
delete p, y:
1/x may not be regarded as
The term ordering: either
Polynomial of the same type as
p. An expression
is returned if an expression is given as input.
FAIL is returned if
the input cannot be converted to a polynomial. With
a list of two polynomials is returned.