User:Just granpa/sandbox

${\phantom {-}}{\frac {8}{2}}={\phantom {-}}4$

and

${\frac {-8}{-2}}={\phantom {-}}4$

If dividend and divisor have different signs, the result is always negative.

${\frac {{\phantom {-}}8}{-2}}=-4$

and

${\frac {-8}{{\phantom {-}}2}}=-4$

and

Failed to parse (unknown function "\begin{array}"): {\displaystyle \begin{array}[l] ({\color{blue} \mathbf{u} \, \lrcorner \, (\alpha \wedge \beta)} &= {\color{red} (\mathbf{u} \, \lrcorner \, \alpha)} \wedge \beta &- \alpha \wedge (\mathbf{u} \, \lrcorner \, \beta) \\ &= ( \mathbf{u} \cdot \alpha ) \cdot \beta &- \alpha \cdot ( \mathbf{u} \cdot \beta ) \\ &= ( \mathbf{u} \cdot \alpha ) \cdot \beta &- ( \mathbf{u} \cdot \beta ) \cdot \alpha \end{array} }

and

Failed to parse (unknown function "\begin{array}"): {\displaystyle \begin{array}[l] \mathbf{u} \, \lrcorner \, (\alpha \wedge \beta \wedge \gamma) &= {\color{blue} (\mathbf{u} \, \lrcorner \, (\alpha \wedge \beta))} \wedge \gamma && +(\alpha \wedge \beta) \wedge (\mathbf{u} \, \lrcorner \, \gamma) \\ &= {\color{blue} ( \, ( \mathbf{u} \, \lrcorner \, \alpha ) \wedge \beta} & {\color{blue} - \alpha \wedge (\mathbf{u} \, \lrcorner \, \beta) \, ) } \wedge \gamma &+ (\alpha \wedge \beta) \wedge (\mathbf{u} \, \lrcorner \, \gamma) \\ &= ( \mathbf{u} \cdot \alpha ) \cdot \beta \wedge \gamma &- \alpha \cdot ( \mathbf{u} \cdot \beta ) \wedge \gamma &+ (\alpha \wedge \beta) \cdot (\mathbf{u} \cdot \gamma) \\ &= ( \mathbf{u} \cdot \alpha ) \cdot \beta \wedge \gamma &+ ( \mathbf{u} \cdot \beta ) \cdot \gamma \wedge \alpha &+ (\mathbf{u} \cdot \gamma) \cdot (\alpha \wedge \beta) \end{array} }