Nth term of a polynomial
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nthterm(p
,n
) nthterm(f
, <vars
>,n
)
nthterm(p, n)
returns the n
th
nonzero term of the polynomialp
.
nthterm
returns the n
th
nonzero term with respect to the lexicographical ordering.
The "first" term is the leading term as returned
by lterm
.
A zero polynomial has no terms: nthterm
returns FAIL
.
The identity nthterm(p, n) nthcoeff(p, n) = nthmonomial(p, n) holds.
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.
We give some self explaining examples:
p := poly(100*x^100 + 49*x^49 + 7*x^7, [x]): nthterm(p, 1), nthterm(p, 2), nthterm(p, 3)
nthterm(p, 4)
nthterm(poly(0, [x]), 1)
delete p:
The nth monomial is the product of the nth coefficient and the nth term:
p := poly(2*x^2*y + 3*x*y^2 + 6, [x, y]): mapcoeffs(nthterm(p, 2), nthcoeff(p, 2)) = nthmonomial(p, 2)
delete p:

A polynomial of
type 
 

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

A positive integer 
Polynomial of the same type as p
. An expression
is returned if a polynomial expression is given as input. FAIL
is
returned if n
is larger than the actual number
of terms of the polynomial.
p