Leading term of a polynomial
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lterm(p
, <order
>) lterm(f
, <vars
>, <order
>)
lterm(p)
returns the leading term of the
polynomial p
.
The returned term is "leading" with respect to
the lexicographical ordering, unless a different ordering is specified
via the argument order
. Cf. Example 1.
The identity lterm(p)*lcoeff(p) = lmonomial(p)
holds.
The leading term of the zero polynomial is the zero polynomial.
A polynomial expression f
is first converted
to a polynomial with the variables given by vars
.
If no variables are given, they are searched for in f
.
See poly
about
details of the conversion. The result is returned as polynomial expression. FAIL
is
returned if f
cannot be converted to a polynomial.
Cf. Example 3.
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]): lterm(p), lterm(p, DegreeOrder), lterm(p, DegInvLexOrder)
The following call uses the reverse lexicographical order on 3 indeterminates:
lterm(p, Dom::MonomOrdering(RevLex(3)))
delete p:
The leading monomial is the product of the leading coefficient and the leading term:
p := poly(2*x^2*y + 3*x*y^2 + 6, [x, y]): mapcoeffs(lterm(p),lcoeff(p)) = lmonomial(p)
delete p:
The expression 1/x
may not be regarded as
polynomial:
lterm(1/x)

A polynomial of
type 
 

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

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.
p