Last Updated：2025/12/03
(algebra) A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.)
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polynomial form
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polynomial form
Noun
(algebra)
A
linear
combination
of
powers
of
an
indeterminate
(or
products
of
powers
of
more
than
one
indeterminate),
with
coefficients
belonging
to
an
integral
domain
or
a
field.
(The
indeterminate
is
thought
of
as
an
element
extraneous
to
the
set
of
coefficients,
instead
of
as
a
variable
element
of
it
(as
in
the
case
of
polynomial
functions),
just
as,
say,
the
square
root
of
negative
one
is
an
element
extraneous
to
the
set
of
integers
when
it
is
adjoined
to
them
to
form
the
domain
of
Gaussian
integers.
The
indeterminate
forms
a
free
commutative
monoid,
to
which
all
powers
of
it
belong,
and
the
unity
of
it
can
also
show
up
implicitly
in
the
constant
term
of
a
polynomial
form.)
Japanese Meaning
代数学において、不定元（または複数の不定元）のべき乗の線形結合、またはその積の形をとる表現。ここで、各項の係数は整域や体に属する。
Sense（1）
(algebra)
A
linear
combination
of
powers
of
an
indeterminate
(or
products
of
powers
of
more
than
one
indeterminate),
with
coefficients
belonging
to
an
integral
domain
or
a
field.
(The
indeterminate
is
thought
of
as
an
element
extraneous
to
the
set
of
coefficients,
instead
of
as
a
variable
element
of
it
(as
in
the
case
of
polynomial
functions),
just
as,
say,
the
square
root
of
negative
one
is
an
element
extraneous
to
the
set
of
integers
when
it
is
adjoined
to
them
to
form
the
domain
of
Gaussian
integers.
The
indeterminate
forms
a
free
commutative
monoid,
to
which
all
powers
of
it
belong,
and
the
unity
of
it
can
also
show
up
implicitly
in
the
constant
term
of
a
polynomial
form.)
（ plural ）
