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Use math code blocks instead
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utensil authored Mar 30, 2024
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Expand Up @@ -48,18 +48,18 @@ Features

Overloaded Python operators for basic GA operations:

$$
```math
\begin{split}\begin{aligned}
A+B &= \texttt{A+B} \\
A-B &= \texttt{A-B} \\
AB &= \texttt{A*B} \\
A \wedge B &= \texttt{A \\^{} B} \\
A \wedge B &= \texttt{A \^{} B} \\
A \cdot B &= \texttt{A|B} \\
A \rfloor B &= \texttt{A<B} \\
A \lfloor B &= \texttt{A>B} \\
A/B &= \texttt{A/B} \\
\end{aligned}\end{split}
$$
```

### Geometric Calculus

Expand All @@ -70,35 +70,35 @@ $$

The various derivatives of a multivector function is accomplished by multiplying the gradient operator vector with the function:

$$
```math
\begin{aligned}
\nabla F &= \texttt{grad\*F} \\
F \bar{\nabla} &= \texttt{F\*rgrad} \\
\nabla {\wedge}F &= \texttt{grad \\^{} F} \\
F {\wedge}\bar{\nabla} &= \texttt{F \\^{} rgrad} \\
\nabla F &= \texttt{grad*F} \\
F \bar{\nabla} &= \texttt{F*rgrad} \\
\nabla {\wedge}F &= \texttt{grad \^{} F} \\
F {\wedge}\bar{\nabla} &= \texttt{F \^{} rgrad} \\
\nabla \cdot F &= \texttt{grad|F} \\
F \cdot \bar{\nabla} &= \texttt{F|rgrad} \\
\nabla \rfloor F &= \texttt{grad<F} \\
F \rfloor \bar{\nabla} &= \texttt{F<rgrad} \\
\nabla \lfloor F &= \texttt{grad>F} \\
F \lfloor \bar{\nabla} &= \texttt{F>rgrad}
\end{aligned}
$$
```

$$
```math
\begin{aligned}
F \nabla &= \texttt{F\*grad} \\
\bar{\nabla} F &= \texttt{rgrad\*F} \\
F {\wedge}\nabla &= \texttt{F \\^{} grad} \\
\bar{\nabla} {\wedge}F &= \texttt{rgrad \\^{} F} \\
F \nabla &= \texttt{F*grad} \\
\bar{\nabla} F &= \texttt{rgrad*F} \\
F {\wedge}\nabla &= \texttt{F \^{} grad} \\
\bar{\nabla} {\wedge}F &= \texttt{rgrad \^{} F} \\
F \cdot \nabla &= \texttt{F|grad} \\
\bar{\nabla}\cdot F &= \texttt{rgrad|F} \\
F \rfloor \nabla &= \texttt{F<grad} \\
\bar{\nabla} \rfloor F &= \texttt{rgrad<F} \\
F \lfloor \nabla &= \texttt{F>grad} \\
\bar{\nabla} \lfloor F &= \texttt{rgrad>F}
\end{aligned}
$$
```

Tip: an example for getting `grad` and `rgrad` of a 3-d Euclidean geometric algebra in rectangular coordinates:

Expand Down Expand Up @@ -145,7 +145,9 @@ M.grade(3).Fmt(3,r'\langle \mathbf{M} \rangle _3')

You will see:

![](https://raw.githubusercontent.com/pygae/galgebra/master/doc/images/st4_M3.svg?sanitize=true)
```math
\begin{aligned} \langle \mathbf{M} \rangle _3 =& M^{txy} \boldsymbol{e}_{t}\wedge \boldsymbol{e}_{x}\wedge \boldsymbol{e}_{y} \\ & + M^{txz} \boldsymbol{e}_{t}\wedge \boldsymbol{e}_{x}\wedge \boldsymbol{e}_{z} \\ & + M^{tyz} \boldsymbol{e}_{t}\wedge \boldsymbol{e}_{y}\wedge \boldsymbol{e}_{z} \\ & + M^{xyz} \boldsymbol{e}_{x}\wedge \boldsymbol{e}_{y}\wedge \boldsymbol{e}_{z} \end{aligned}
```

You may also check out more examples [here](https://github.com/pygae/galgebra/blob/master/examples/).

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