最終更新日：2025/12/05
(mathematics) A theorem expressing the number of distinct real roots of p located in an interval in terms of the number of changes of signs of the values of the Sturm sequence at the bounds of the interval. Applied to the interval of all the real numbers, it gives the total number of real roots of p.
音声機能が動作しない場合はこちらをご確認ください
正解を見る
Sturm's theorem
編集履歴（0）
元となった辞書の項目
Sturm's theorem
固有名詞
(mathematics)
A
theorem
expressing
the
number
of
distinct
real
roots
of
p
located
in
an
interval
in
terms
of
the
number
of
changes
of
signs
of
the
values
of
the
Sturm
sequence
at
the
bounds
of
the
interval.
Applied
to
the
interval
of
all
the
real
numbers,
it
gives
the
total
number
of
real
roots
of
p.
日本語の意味
シュトゥームの定理とは、数学における定理で、任意の多項式 p がある区間に持つ異なる実数解の個数が、その区間の両端における（Sturm列の）符号変化の回数によって示されるというものです。全実数を対象とした場合には、p の全ての実数解の個数を与えます。
意味（1）
(mathematics)
A
theorem
expressing
the
number
of
distinct
real
roots
of
p
located
in
an
interval
in
terms
of
the
number
of
changes
of
signs
of
the
values
of
the
Sturm
sequence
at
the
bounds
of
the
interval.
Applied
to
the
interval
of
all
the
real
numbers,
it
gives
the
total
number
of
real
roots
of
p.
