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Merge pull request #503 from pygae/svg-bg-switch
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Replace SVGs of LaTeX to just LaTeX
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utensil authored Mar 30, 2024
2 parents 28ad58c + ddf95fb commit e96f8d1
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47 changes: 44 additions & 3 deletions README.md
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Expand Up @@ -48,7 +48,18 @@ Features

Overloaded Python operators for basic GA operations:

![](https://raw.githubusercontent.com/pygae/galgebra/master/doc/images/basic_op.svg?sanitize=true)
```math
\begin{split}\begin{aligned}
A+B &= \texttt{A+B} \\
A-B &= \texttt{A-B} \\
AB &= \texttt{A*B} \\
A \wedge B &= \mathtt{A \verb!^! 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 @@ -59,7 +70,35 @@ Overloaded Python operators for basic GA operations:

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

![](https://raw.githubusercontent.com/pygae/galgebra/master/doc/images/grad.svg?sanitize=true) ![](https://raw.githubusercontent.com/pygae/galgebra/master/doc/images/grad_cmp.svg?sanitize=true)
```math
\begin{aligned}
\nabla F &= \texttt{grad*F} \\
F \bar{\nabla} &= \texttt{F*rgrad} \\
\nabla {\wedge}F &= \mathtt{grad \verb!^! F} \\
F {\wedge}\bar{\nabla} &= \mathtt{F \verb!^! 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 &= \mathtt{F \verb!^! grad} \\
\bar{\nabla} {\wedge}F &= \mathtt{rgrad \verb!^! 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 @@ -106,7 +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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4 changes: 1 addition & 3 deletions doc/conf.py
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Expand Up @@ -54,9 +54,7 @@
'releases',
'sphinxcontrib.bibtex',
'sphinx_rtd_theme',

# local extensions
'md_include',
'sphinx_mdinclude'
]

# This is not actually used as we have a template overload to render this with
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2 changes: 0 additions & 2 deletions doc/getting-started.rst
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@@ -1,3 +1 @@
.. mdinclude:: ../README.md
:start-after: <!-- begin: getting-started -->
:end-before: <!-- end: getting-started -->
1 change: 0 additions & 1 deletion doc/index.rst
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@@ -1,5 +1,4 @@
.. mdinclude:: ../README.md
:end-before: <!-- begin:

.. these are all hidden, because they render more clearly in the sidebar.
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1 change: 1 addition & 0 deletions doc/readthedocs-pip-requirements.txt
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Expand Up @@ -11,6 +11,7 @@ ipykernel
nbsphinx
numba
sphinx-rtd-theme
sphinx_mdinclude

sphinx-markdown-tables
notedown
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