Leading coefficient of a polynomial
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lcoeff(p) returns the leading coefficient
of the polynomial
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
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 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]): lcoeff(p), lcoeff(p, DegreeOrder), lcoeff(p, DegInvLexOrder)
The following call uses the reverse lexicographical order on 3 indeterminates:
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:
1/x may not be regarded as
The term ordering: either
Element of the coefficient domain of the polynomial or