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Signature

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Signature[list]

標準的な順序で list の要素を置換するのに必要な符号を与える．

詳細

  • 置換の符号は(-1)nである．n は，この転置を組み立てるのに合成しなければならない要素のペアの互換の数である．
  • list の任意の2つの要素が同じ場合，Signature[list]は，0を与える．
  • Signatureは，Listに限らず任意の頭部の式に使うことができる．

例題

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例  (1)基本的な使用例

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-n3h
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0bil61gi-o1r
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Out[2]=2

アプリケーション  (3)この関数で解くことのできる問題の例

偶数の置換を求める：

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-b8svmz
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Out[1]=1

階数3で完全に反対称(Levi-Civita)のテンソル：

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-70e5ol
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Out[1]=1

Levi-Civitaテンソルの収縮：

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-ipux2g
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Out[1]=1

特性と関係  (2)この関数の特性および他の関数との関係

3Dの外積の要素を求める：

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-f9bt6y
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0bil61gi-b86q90
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Out[2]=2

行列式を計算する：

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-bobw1u
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Out[1]=1

組込みのDetと比較する：

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In[2]:=2
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https://wolfram.com/xid/0bil61gi-j6ko2q
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Out[2]=2

考えられる問題  (2)よく起る問題と予期しない動作

数の精度が数の順序に影響する：

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-c46r8w
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0bil61gi-t20s4
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Out[2]=2

Signatureは記号的な引数についても評価する：

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-ojdl8v
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Out[1]=1

Unevaluatedを使って未評価のSignatureを挿入する：

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In[2]:=2
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https://wolfram.com/xid/0bil61gi-dwonqb
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Out[2]=2

Signatureを直接Table内で使う：

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In[3]:=3
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https://wolfram.com/xid/0bil61gi-lpy80x
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Out[3]=3

おもしろい例題  (1)驚くような使用例や興味深い使用例

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In[1]:=1
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https://wolfram.com/xid/0bil61gi-quf
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Out[1]=1
Wolfram Research (1988), Signature, Wolfram言語関数， https://reference.wolfram.com/language/ref/Signature.html.
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Wolfram Research (1988), Signature, Wolfram言語関数， https://reference.wolfram.com/language/ref/Signature.html.

テキスト

Wolfram Research (1988), Signature, Wolfram言語関数， https://reference.wolfram.com/language/ref/Signature.html.

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Wolfram Research (1988), Signature, Wolfram言語関数， https://reference.wolfram.com/language/ref/Signature.html.

CMS

Wolfram Language. 1988. "Signature." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Signature.html.

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Wolfram Language. 1988. "Signature." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Signature.html.

APA

Wolfram Language. (1988). Signature. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Signature.html

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Wolfram Language. (1988). Signature. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Signature.html

BibTeX

@misc{reference.wolfram_2025_signature, author="Wolfram Research", title="{Signature}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Signature.html}", note=[Accessed: 07-April-2025 ]}

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@misc{reference.wolfram_2025_signature, author="Wolfram Research", title="{Signature}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Signature.html}", note=[Accessed: 07-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_signature, organization={Wolfram Research}, title={Signature}, year={1988}, url={https://reference.wolfram.com/language/ref/Signature.html}, note=[Accessed: 07-April-2025 ]}

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@online{reference.wolfram_2025_signature, organization={Wolfram Research}, title={Signature}, year={1988}, url={https://reference.wolfram.com/language/ref/Signature.html}, note=[Accessed: 07-April-2025 ]}