最終更新日：2022/12/24
Let us describe in general the subfield generated by a given element. Let K be a given field, F a subfield of K, and c an element of K. Consider those elements of K which are given by polynomial expressions of the form (1) qquad f(c)=a_0+a_1c+a_2c²+...+a_ncⁿ qquad qquad mbox (eacha_i mbox inF mbox ). … If f(c) and g(c) ≠ 0 are polynomial expressions like (1), their quotient f(c)/g(c) is an element of K, called a rational expression in c with coefficients in F. The set of all such quotients is a subfield; it is the field generated by F and c and is conventionally denoted by F(c), with round brackets.
音声機能が動作しない場合はこちらをご確認ください
編集履歴（0）
元となった例文
Let
us
describe
in
general
the
subfield
generated
by
a
given
element.
Let
K
be
a
given
field,
F
a
subfield
of
K,
and
c
an
element
of
K.
Consider
those
elements
of
K
which
are
given
by
polynomial
expressions
of
the
form
If
f(c)
and
g(c)
≠
0
are
polynomial
expressions
like
(1),
their
quotient
f(c)/g(c)
is
an
element
of
K,
called
a
rational
expression
in
c
with
coefficients
in
F.
The
set
of
all
such
quotients
is
a
subfield;
it
is
the
field
generated
by
F
and
c
and
is
conventionally
denoted
by
F(c),
with
round
brackets.
