Source Word
complex projective line
Noun
analytic
(analytic
geometry,
projective
geometry)
A
complex
line
(especially,
the
set
of
complex
numbers
regarded
as
such)
endowed
with
a
point
at
infinity
(thus
becoming
a
projective
line);
(more
formally)
the
set
of
equivalence
classes
of
ordered
pairs
(α,
β)
of
complex
numbers,
not
both
zero,
with
respect
to
the
equivalence
relation
"(α,
β)
≡
(λα,
λβ)
for
all
nonzero
complex
λ".
Japanese Meaning
複素射影直線とは、解析幾何学や射影幾何学において、複素数全体（特に複素平面）に無限遠点を追加して得られる射影直線の意味を持つ。より厳密には、(α, β)（ただしα, βは複素数で、両方がゼロでない）の順序つき組に対し、任意の非零複素数λによる拡大（(α, β) ≡ (λα, λβ)）という同値関係によって定義される同値類の集合として捉えられる。
Sense（1）
(analytic
geometry,
projective
geometry)
A
complex
line
(especially,
the
set
of
complex
numbers
regarded
as
such)
endowed
with
a
point
at
infinity
(thus
becoming
a
projective
line);
(more
formally)
the
set
of
equivalence
classes
of
ordered
pairs
(α,
β)
of
complex
numbers,
not
both
zero,
with
respect
to
the
equivalence
relation
"(α,
β)
≡
(λα,
λβ)
for
all
nonzero
complex
λ".
（ plural ）
