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| ツール:mathjax [2019/06/12 12:27] – mumeiyamibito | ツール:mathjax [2020/11/11 11:53] (現在) – [総和や総乗などで、上限や下限を真上および真下に付ける] mumeiyamibito | ||
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| ===== 数式の記法 ===== | ===== 数式の記法 ===== | ||
| - | ==== 数 (Numbe)r ==== | + | ==== 数 (Number) ==== |
| * 分数 (fraction) | * 分数 (fraction) | ||
| - | * '' | + | * < |
| * $\frac{ 1 }{ 2 }$ | * $\frac{ 1 }{ 2 }$ | ||
| * 分数 (大) (fraction large) | * 分数 (大) (fraction large) | ||
| - | * '' | + | * < |
| * $\displaystyle \frac{ 1 }{ 2 }$ | * $\displaystyle \frac{ 1 }{ 2 }$ | ||
| * 分数と括弧 (fraction and parentheses) | * 分数と括弧 (fraction and parentheses) | ||
| - | * '' | + | * < |
| * $\left( - \frac{ 1 }{ 2 } \right )^2$ | * $\left( - \frac{ 1 }{ 2 } \right )^2$ | ||
| * 連分数 (continued fraction) | * 連分数 (continued fraction) | ||
| - | * '' | + | * < |
| * $\frac{ a + b }{ c + \frac{ d }{ e } }$ | * $\frac{ a + b }{ c + \frac{ d }{ e } }$ | ||
| + | * 無限連分数 (infinite continued fraction) | ||
| + | * < | ||
| + | $ | ||
| + | \begin{eqnarray} | ||
| + | 1 + \frac{ 1 }{ 1 + \frac{ 1 }{ 1 + \frac{ 1 }{ 1 + \ddots } } } = \frac{ 1 }{ 2 } \left( 1 + \sqrt{ 5 } \right) | ||
| + | \end{eqnarray} | ||
| + | $ | ||
| + | </ | ||
| + | * $\begin{eqnarray} 1 + \frac{ 1 }{ 1 + \frac{ 1 }{ 1 + \frac{ 1 }{ 1 + \ddots } } } = \frac{ 1 }{ 2 } \left( 1 + \sqrt{ 5 } \right) \end{eqnarray}$ | ||
| + | * 小数 (decimal) | ||
| + | * < | ||
| + | * $0.123$ | ||
| + | * 循環小数 (repeating decimal) | ||
| + | * < | ||
| + | * $\frac{ 1 }{ 11 } = 0.\dot{ 0 } \dot{ 9 }$ | ||
| + | * 無限小数 (infinite decimal) | ||
| + | * < | ||
| + | * $3.14 \ldots$ | ||
| + | * 無理数サンプル (irrational number sample) | ||
| + | * < | ||
| + | * $\sqrt{ 2 } = 1.4142 \ldots$ | ||
| + | * 無限大 (infinity) | ||
| + | * < | ||
| + | * $\infty$ | ||
| + | * 絶対値 (absolute value) | ||
| + | * < | ||
| + | * $| x |$ | ||
| + | * 絶対値2 (absolute value 2) | ||
| + | * < | ||
| + | * $\vert x \vert$ | ||
| + | * 分数と絶対値 (fraction and absolute value) | ||
| + | * < | ||
| + | * $\left| \frac{ x }{ 2 } \right|$ | ||
| + | * ガウス記号 (Gauss brackets) | ||
| + | * < | ||
| + | * $[ x ]$ | ||
| + | * ガウス記号 (Gauss brackets 2) | ||
| + | * < | ||
| + | * $\lbrack x \rbrack$ | ||
| + | * 床関数 (floor function) | ||
| + | * < | ||
| + | * $\lfloor x \rfloor$ | ||
| + | * 天井関数 (ceiling function) | ||
| + | * < | ||
| + | * $\lceil x \rceil$ | ||
| + | |||
| + | ==== 四則演算 (Arithmetic Operation) ==== | ||
| + | * 加算 (plus) | ||
| + | * < | ||
| + | * $1 + 2$ | ||
| + | * 減算 (minus) | ||
| + | * < | ||
| + | * $3 - 1$ | ||
| + | * 乗算 (times) | ||
| + | * < | ||
| + | * $2 \times 3$ | ||
| + | * 割る (divide) | ||
| + | * < | ||
| + | * $6 \div 3$ | ||
| + | * プラスマイナス (plus minus) | ||
| + | * < | ||
| + | * $\pm 1$ | ||
| + | * マイナスプラス (minus plus) | ||
| + | * < | ||
| + | * $\mp 1$ | ||
| + | * 乗算 (簡略) (times dot) | ||
| + | * < | ||
| + | * $a \cdot b = ab$ | ||
| + | * 除算 (分数) (divide fraction) | ||
| + | * < | ||
| + | * $a / b = \frac{a}{b}$ | ||
| + | * 合同式 (modular equivalence) | ||
| + | * < | ||
| + | * $a \equiv b \bmod n$ | ||
| + | * 合同式 (括弧付) (modular equivalence with parentheses) | ||
| + | * < | ||
| + | * $a \equiv b \pmod n$ | ||
| + | * 比例 (proportional) | ||
| + | * < | ||
| + | * $x \propto y$ | ||
| + | |||
| + | ==== 大小 (Greater or Less) ==== | ||
| + | * 大なり (greater than) | ||
| + | * < | ||
| + | * $a \gt b$ | ||
| + | * 大なりイコール (greater than or equal) | ||
| + | * < | ||
| + | * $a \geq b$ | ||
| + | * 大なりイコール2 (greater than or equal 2) | ||
| + | * < | ||
| + | * $a \geqq b$ | ||
| + | * 小なり (less than) | ||
| + | * < | ||
| + | * $a \lt b$ | ||
| + | * 小なりイコール (less than or equal) | ||
| + | * < | ||
| + | * $a \leq b$ | ||
| + | * 小なりイコール2 (less than or equal 2) | ||
| + | * < | ||
| + | * $a \leqq b$ | ||
| + | * 等しい (equal) | ||
| + | * < | ||
| + | * $a = b$ | ||
| + | * 等しくない (not equal) | ||
| + | * < | ||
| + | * $a \neq b$ | ||
| + | * ほぼ等しい (nearly equal) | ||
| + | * < | ||
| + | * $a \fallingdotseq b$ | ||
| + | * ほぼ等しい2 (nearly equal 2) | ||
| + | * < | ||
| + | * $a \sim b$ | ||
| + | * ほぼ等しい3 (nearly equal 3) | ||
| + | * < | ||
| + | * $a \simeq b$ | ||
| + | * ほぼ等しい4 (nearly equal 4) | ||
| + | * < | ||
| + | * $a \approx b$ | ||
| + | * 十分大きい (much greater than) | ||
| + | * < | ||
| + | * $a \gg b$ | ||
| + | * 十分小さい (much less than) | ||
| + | * < | ||
| + | * $a \ll b$ | ||
| + | * 最大 (maximum) | ||
| + | * < | ||
| + | * $\max f(x)$ | ||
| + | * 最小 (minimum) | ||
| + | * < | ||
| + | * $\min f(x)$ | ||
| + | * 最大サンプル (max sample) | ||
| + | * < | ||
| + | $\begin{eqnarray} | ||
| + | \max ( a, b ) = | ||
| + | \begin{cases} | ||
| + | a & ( a \geqq b ) \\ | ||
| + | b & ( a \lt b ) | ||
| + | \end{cases} | ||
| + | \end{eqnarray}$ | ||
| + | </ | ||
| + | * $\begin{eqnarray} \max ( a, b ) = \begin{cases} a & ( a \geqq b ) \\ b & ( a \lt b ) \end{cases} \end{eqnarray}$ | ||
| + | |||
| + | ==== 複数行数式 (Multiple Line Equations) ==== | ||
| + | * 改行 (line break) | ||
| + | * < | ||
| + | $\begin{eqnarray} | ||
| + | aaa \\ | ||
| + | bbb | ||
| + | \end{eqnarray}$ | ||
| + | </ | ||
| + | * $\begin{eqnarray} aaa \\ bbb \end{eqnarray}$ | ||
| + | * 改行 (サイズ指定) (big line break) | ||
| + | * < | ||
| + | $\begin{eqnarray} | ||
| + | aaa \\[ 5pt ] | ||
| + | bbb | ||
| + | \end{eqnarray}$ | ||
| + | </ | ||
| + | * $\begin{eqnarray} aaa \\[ 5pt ] bbb \end{eqnarray}$ | ||
| + | * 位置合わせ (alignment) | ||
| + | * < | ||
| + | $\begin{eqnarray} | ||
| + | x + 2x &=& 3 \\ | ||
| + | x &=& 1 | ||
| + | \end{eqnarray}$ | ||
| + | </ | ||
| + | * $\begin{eqnarray} x + 2x &=& 3 \\ x &=& 1 \end{eqnarray}$ | ||
| + | * 連立方程式 (simultaneous equations) | ||
| + | * < | ||
| + | $\begin{eqnarray} | ||
| + | \left\{ | ||
| + | \begin{array}{l} | ||
| + | x + y = 10 \\ | ||
| + | 2x + 4y = 32 | ||
| + | \end{array} | ||
| + | \right. | ||
| + | \end{eqnarray}$ | ||
| + | </ | ||
| + | * $\begin{eqnarray} \left\{ \begin{array}{l} x + y = 10 \\ 2x + 4y = 32 \end{array} \right. \end{eqnarray}$ | ||
| + | * 場合分け (case) | ||
| + | * < | ||
| + | $\begin{eqnarray} | ||
| + | | x | = \begin{cases} | ||
| + | x & ( x \geqq 0 ) \\ | ||
| + | -x & ( x \lt 0 ) | ||
| + | \end{cases} | ||
| + | \end{eqnarray}$ | ||
| + | </ | ||
| + | * $\begin{eqnarray} | x | = \begin{cases} x & ( x \geqq 0 ) \\ -x & ( x \lt 0 ) \end{cases} \end{eqnarray}$ | ||
| + | |||
| + | ==== 集合 (set) ==== | ||
| + | * 帰属関係 (belong to) | ||
| + | * < | ||
| + | * $x \in A$ | ||
| + | * 帰属関係2 (belong to 2) | ||
| + | * < | ||
| + | * $A \ni x$ | ||
| + | * 帰属していない (not belong to) | ||
| + | * < | ||
| + | * $x \notin A$ | ||
| + | * 部分集合 (subset) | ||
| + | * < | ||
| + | * $A \subset B$ | ||
| + | * 部分集合2 (subset 2) | ||
| + | * < | ||
| + | * $A \subseteq B$ | ||
| + | * 部分集合3 (subset 3) | ||
| + | * < | ||
| + | * $A \subseteqq B$ | ||
| + | * 部分集合 (逆向き) (subset reverse) | ||
| + | * < | ||
| + | * $A \supset B$ | ||
| + | * 部分集合 (逆向き) 2 (subset reverse 2) | ||
| + | * < | ||
| + | * $A \supseteq B$ | ||
| + | * 部分集合 (逆向き) 3 (subset reverse 3) | ||
| + | * < | ||
| + | * $A \supseteqq B$ | ||
| + | * 部分集合でない (not subset) | ||
| + | * < | ||
| + | * $A \not \subset B$ | ||
| + | * 真の部分集合 (proper subset) | ||
| + | * < | ||
| + | * $A \subsetneqq B$ | ||
| + | * 集合の交わり; | ||
| + | * < | ||
| + | * $A \cap B$ | ||
| + | * 集合の結び; | ||
| + | * < | ||
| + | * $A \cup B$ | ||
| + | * 空集合 (empty set) | ||
| + | * < | ||
| + | * $\varnothing$ | ||
| + | * 補集合 (complement set) | ||
| + | * < | ||
| + | * $A^c$ | ||
| + | * 補集合2 (complement set 2) | ||
| + | * < | ||
| + | * $\overline{ A }$ | ||
| + | * 差集合 (relative complement) | ||
| + | * < | ||
| + | * $A \setminus B$ | ||
| + | * 差集合サンプル (relative complement sample) | ||
| + | * < | ||
| + | * $A \setminus B = A \cap B^c = \{ x \mid x \in A, x \notin B \}$ | ||
| + | * 自然数全体の集合 (all natural numbers) | ||
| + | * < | ||
| + | * $\mathbb{ N }$ | ||
| + | * 整数全体の集合 (all integers) | ||
| + | * < | ||
| + | * $\mathbb{ Z }$ | ||
| + | * 有理数全体の集合 (all rational numbers) | ||
| + | * < | ||
| + | * $\mathbb{ Q }$ | ||
| + | * 実数全体の集合 (all real numbers) | ||
| + | * < | ||
| + | * $\mathbb{ R }$ | ||
| + | * 複素数全体の集合 (all complex numbers) | ||
| + | * < | ||
| + | * $\mathbb{ C }$ | ||
| + | * 四元数全体の集合 (all quaternions) | ||
| + | * < | ||
| + | * $\mathbb{ H }$ | ||
| + | * 上限 (supremum) | ||
| + | * < | ||
| + | * $\sup A$ | ||
| + | * 下限 (infimum) | ||
| + | * < | ||
| + | * $\inf A$ | ||
| + | * アレフ数 (aleph number) | ||
| + | * < | ||
| + | * $\aleph$ | ||
| + | |||
| + | |||
| + | ==== 数式番号 ==== | ||
| + | * 数式に番号をふる場合、'' | ||
| + | * 例 | ||
| + | * < | ||
| + | * $E = mc^2 \tag{1.2}$ | ||
| + | |||
| + | |||
| + | ==== 総和や総乗などで、上限や下限を真上および真下に付ける ==== | ||
| + | * '' | ||
| + | * 通常: | ||
| + | * $\sum_{i = 1}^{10} x_{i}$ | ||
| + | * < | ||
| + | * '' | ||
| + | * $\displaystyle \sum_{i = 1}^{10} x_{i}$ | ||
| + | * < | ||
| + | * 分数などで文字が小さくなった場合も有効だったりする。 | ||
| + | |||
| + | ==== 斜体をキャンセルする ==== | ||
| + | * '' | ||
| + | * 通常: | ||
| + | * $\Delta G_{Protein} + \Delta G_{DNA}$ | ||
| + | * < | ||
| + | * '' | ||
| + | * $\Delta G_{\rm Protein} + \Delta G_{\rm DNA}$ | ||
| + | * < | ||
| + | * '' | ||