Leading coefficient of a polynomial
This functionality does not run in MATLAB.
lcoeff(p
, <order
>) lcoeff(f
, <vars
>, <order
>)
lcoeff(p)
returns the leading coefficient
of the polynomial p
.
The returned coefficient is "leading" with respect
to the lexicographical ordering, unless a different ordering is specified
via the argument order
. Cf. Example 1.
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.
The result of lcoeff
is not fully evaluated.
Evaluation can be enforced by the function eval
. Cf. Example 2.
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]): lcoeff(p), lcoeff(p, DegreeOrder), lcoeff(p, DegInvLexOrder)
The following call uses the reverse lexicographical order on 3 indeterminates:
lcoeff(p, Dom::MonomOrdering(RevLex(3)))
delete p:
The result of lcoeff
is not fully evaluated:
p := poly(a*x^2 + 27*x, [x]): a := 5: lcoeff(p), eval(lcoeff(p))
delete p, a:
The expression 1/x
may not be regarded as
polynomial:
lcoeff(1/x)

A polynomial of
type 
 

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

The term ordering: either 
Element of the coefficient domain of the polynomial or FAIL
.
p