so i thought i’d Update everything on the admin panel, and set about doing some tests
[details="deriving the formula for cartesian curl"]
[grid]
$$
\nabla \times \mathbf{A} = \left| \begin{matrix}
\hat{i} & \hat{j} & \hat{k} \\
\partial_x & \partial_y & \partial_z \\
A_x & A_y & A_z
\end{matrix} \right|
$$
$$
\nabla \times \mathbf{A} = \left| \begin{matrix}
\hat{i} & \hat{j} & \hat{k} \\
\partial_x & \partial_y & \partial_z \\
A_x & A_y & A_z
\end{matrix} \right|
$$
[/grid]
[grid]
$$
\begin{align*}
\nabla \times \mathbf{A} =\
&\hat{i} \left| \begin{matrix}
\partial_y & \partial_z \\
A_y & A_z
\end{matrix} \right|
- \hat{j} \left| \begin{matrix}
\partial_x & \partial_z \\
A_x & A_z
\end{matrix} \right| \\
&+ \hat{k} \left| \begin{matrix}
\partial_x & \partial_y \\
A_x & A_y
\end{matrix} \right|
\end{align*}
$$
$$
\begin{align*}
\nabla \times \mathbf{A} =\
&\hat{i} \left| \begin{matrix}
\partial_y & \partial_z \\
A_y & A_z
\end{matrix} \right|
+ \hat{j} \left| \begin{matrix}
A_z & A_x \\
\partial_z & \partial_x
\end{matrix} \right| \\
&+ \hat{k} \left| \begin{matrix}
\partial_x & \partial_y \\
A_x & A_y
\end{matrix} \right|
\end{align*}
$$
[/grid]
[/details]
pass ![]()
AI being daft by putting excessive whitespace between two $...$ in grid
[details="deriving the formula for cartesian curl"]
[grid]
$\nabla \times \mathbf{A} = \left| \begin{matrix}
\hat{i} & \hat{j} & \hat{k} \\
\partial_x & \partial_y & \partial_z \\
A_x & A_y & A_z
\end{matrix} \right|$
$\nabla \times \mathbf{A} = \left| \begin{matrix}
\hat{i} & \hat{j} & \hat{k} \\
\partial_x & \partial_y & \partial_z \\
A_x & A_y & A_z
\end{matrix} \right|$
[/grid]
[grid]
$\begin{aligned}
\nabla \times \mathbf{A} =\
&\hat{i} \left| \begin{matrix}
\partial_y & \partial_z \\
A_y & A_z
\end{matrix} \right|
- \hat{j} \left| \begin{matrix}
\partial_x & \partial_z \\
A_x & A_z
\end{matrix} \right| \\
&+ \hat{k} \left| \begin{matrix}
\partial_x & \partial_y \\
A_x & A_y
\end{matrix} \right|
\end{aligned}$
$\begin{aligned}
\nabla \times \mathbf{A} =\
&\hat{i} \left| \begin{matrix}
\partial_y & \partial_z \\
A_y & A_z
\end{matrix} \right|
+ \hat{j} \left| \begin{matrix}
A_z & A_x \\
\partial_z & \partial_x
\end{matrix} \right| \\
&+ \hat{k} \left| \begin{matrix}
\partial_x & \partial_y \\
A_x & A_y
\end{matrix} \right|
\end{aligned}$
[/grid]
[/details]
fail ![]()
[details="deriving the formula for spherical curl"]
[grid]
$$
\nabla \times \mathbf{A} =
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & r\hat{\theta} & r\sin\theta\,\hat{\phi} \\
\partial_r & \partial_\theta & \partial_\phi \\
A_r & r A_\theta & r\sin\theta\, A_\phi
\end{matrix} \right|
$$
$$
= \frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & \hat{\theta} & \hat{\phi} \\
\partial_\theta & \partial_\phi & \partial_r \\
r A_\theta & r \sin\theta A_\phi & A_r
\end{matrix} \right|
$$
[/grid]
[grid]
$$
\begin{align*}
= \frac{1}{r^2 \sin\theta} \Big(
&\hat{r} \left| \begin{matrix} \partial_\theta & \partial_\phi \\ r A_\theta & r \sin\theta A_\phi \end{matrix} \right|
\ \\&- \hat{\theta} \left| \begin{matrix} \partial_r & \partial_\phi \\ A_r & r \sin\theta A_\phi \end{matrix} \right| \\
&+ \hat{\phi} \left| \begin{matrix} \partial_r & \partial_\theta \\ A_r & r A_\theta \end{matrix} \right|
\Big)
\end{align*}
$$
$$
\begin{align*}
= \frac{1}{r^2 \sin\theta} \Big(
&\hat{r} \left| \begin{matrix} \partial_\phi & \partial_r \\ r \sin\theta A_\phi & A_r \end{matrix} \right|
\ \\&+ \hat{\theta} \left| \begin{matrix} A_r & r \sin\theta A_\phi \\ \partial_r & \partial_\phi \end{matrix} \right| \\
&+ \hat{\phi} \left| \begin{matrix} \partial_\theta & \partial_r \\ r A_\theta & A_r \end{matrix} \right|
\Big)
\end{align*}
$$
[/grid]
[/details]
pass ![]()
[details="deriving the formula for spherical curl"]
[grid]
$$
\nabla \times \mathbf{A} =
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & r\hat{\theta} & r\sin\theta\,\hat{\phi} \\
\partial_r & \partial_\theta & \partial_\phi \\
A_r & r A_\theta & r\sin\theta\, A_\phi
\end{matrix} \right|
$$
$$
= \frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & \hat{\theta} & \hat{\phi} \\
\partial_\theta & \partial_\phi & \partial_r \\
r A_\theta & r \sin\theta A_\phi & A_r
\end{matrix} \right|
$$
[/grid]
[grid]
$\begin{align*}
= \frac{1}{r^2 \sin\theta} \Big(
&\hat{r} \left| \begin{matrix} \partial_\theta & \partial_\phi \\ r A_\theta & r \sin\theta A_\phi \end{matrix} \right|
\ \\&- \hat{\theta} \left| \begin{matrix} \partial_r & \partial_\phi \\ A_r & r \sin\theta A_\phi \end{matrix} \right| \\
&+ \hat{\phi} \left| \begin{matrix} \partial_r & \partial_\theta \\ A_r & r A_\theta \end{matrix} \right|
\Big)
\end{align*}$ $\begin{align*}
= \frac{1}{r^2 \sin\theta} \Big(
&\hat{r} \left| \begin{matrix} \partial_\phi & \partial_r \\ r \sin\theta A_\phi & A_r \end{matrix} \right|
\ \\&+ \hat{\theta} \left| \begin{matrix} A_r & r \sin\theta A_\phi \\ \partial_r & \partial_\phi \end{matrix} \right| \\
&+ \hat{\phi} \left| \begin{matrix} \partial_\theta & \partial_r \\ r A_\theta & A_r \end{matrix} \right|
\Big)
\end{align*}$
[/grid]
[/details]
pass ![]()
[details="deriving the formula for spherical curl"]
[grid]
$$
\nabla \times \mathbf{A} =
\frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & r\hat{\theta} & r\sin\theta\,\hat{\phi} \\
\partial_r & \partial_\theta & \partial_\phi \\
A_r & r A_\theta & r\sin\theta\, A_\phi
\end{matrix} \right|
$$
$$
= \frac{1}{r^2 \sin\theta}
\left| \begin{matrix}
\hat{r} & \hat{\theta} & \hat{\phi} \\
\partial_\theta & \partial_\phi & \partial_r \\
r A_\theta & r \sin\theta A_\phi & A_r
\end{matrix} \right|
$$
[/grid]
[grid] $\begin{align}
= \frac{1}{r^2 \sin\theta} \Big(
&\hat{r} \left| \begin{matrix} \partial_\theta & \partial_\phi \\ r A_\theta & r \sin\theta A_\phi \end{matrix} \right|
\ \\&- \hat{\theta} \left| \begin{matrix} \partial_r & \partial_\phi \\ A_r & r \sin\theta A_\phi \end{matrix} \right| \\
&+ \hat{\phi} \left| \begin{matrix} \partial_r & \partial_\theta \\ A_r & r A_\theta \end{matrix} \right|
\Big)
\end{align}$ $\begin{align}
= \frac{1}{r^2 \sin\theta} \Big(
&\hat{r} \left| \begin{matrix} \partial_\phi & \partial_r \\ r \sin\theta A_\phi & A_r \end{matrix} \right|
\ \\&+ \hat{\theta} \left| \begin{matrix} A_r & r \sin\theta A_\phi \\ \partial_r & \partial_\phi \end{matrix} \right| \\
&+ \hat{\phi} \left| \begin{matrix} \partial_\theta & \partial_r \\ r A_\theta & A_r \end{matrix} \right|
\Big)
\end{align}$ [/grid]
[/details]
that’s where it fails
the problem is that i’m putting too few whitespace between [grid] → object and/or object → [/grid]




