Cat::Polynomial
-- the
category of multivariate polynomials
represents the category
of multivariate polynomials over Cat::Polynomial
(R)R
.
Cat::Polynomial(R)
R |
- | A domain which must be from the category Cat::CommutativeRing . |
Cat::PartialDifferentialRing
, Cat::Algebra(R)
Cat::Polynomial
(R)
is a multivariate
polynomial over a commutative coefficient ring R
.The coefficient ring R
.
The characteristic of this domain, which is is the same as that of
the ring R
.
coeff(dom p)
p
.coeff(dom p, indeterminate x, Type::NonNegInt
n)
x^n
of p
,
which is a polynomial in the remaining indeterminates.coeff(dom p, Type::NonNegInt n)
x^n
of p
,
where x
is the main variable of p
.degree(dom p)
p
.degree(dom p, indeterminate x)
p
with respect to the
indeterminate x
.degreevec(dom p)
p
. The order of the exponents corresponds to the order of
the indeterminates as given by the method "indets"
.evalp(dom p, indeterminate x = R v...)
p
at the point x
=
v
where x
is an indeterminate and
v
an element of R
.R
.indets(dom p)
p
.lcoeff(dom p)
p
.lmonomial(dom p)
p
.lterm(dom p)
p
.mainvar(dom p)
p
, which is the first
of the indeterminates as given by the method
"indets"
.mapcoeffs(dom p, function f <, a...>)
c_i
of p
by
the results of the function calls f(c_i, a...)
.multcoeffs(dom p, R
c)
p
by
c
.nterms(dom p)
p
.nthcoeff(dom p, Type::PosInt n)
n
-th coefficient of
p
.nthmonomial(dom p, Type::PosInt n)
n
-th monomial of p
.nthterm(dom p, Type::PosInt n)
n
-th term of p
.tcoeff(dom p)
p
.unitNormal(dom p)
p
.R
has the axiom
Ax::canonicalUnitNormal
: In
this case p
is multiplied by an unit of R
such that the leading coefficient has unit normal representation in
R
.unitNormalRep(dom p)
p
and
the factors needed to bring p
into unit normal form (see
Cat::IntegralDomain
for the
return value expected).R
has the axiom
Ax::canonicalUnitNormal
.content(dom p)
p
if R
is a
Cat::GcdDomain
.isUnit(dom p)
TRUE
iff
p
is a unit.primpart(dom p)
p
if R
is a
Cat::GcdDomain
: The
content of p
is removed and the unit normal of the result
is returned.solve(dom p, indeterminate x <, opt...>)
p = 0
with respect to
x
over the domain R
. See the function
solve
for details about
the optional arguments opt
....solve(dom p, indeterminate x = DOM_DOMAIN T <,
opt...>)
p = 0
with respect to
x
over the domain T
. See the function
solve
for details about
the optional arguments opt
....solve(dom p)
p
must be univariate. Solves the
polynomial equation p = 0
with respect to the
indeterminate of p
over the domain R
.Cat::PolynomialCat
.