Use more Math markup in documentation #7226
Description
Description of the desired feature
Given that our Restructured Text documentation fully support mathematics, it would be nice to try to use it when we do math. If I cd into the doc source directory and search for things like "raised to the second power" which we do for area units and simple math, I find lots of places that could be improved very simply:
cd doc/rst/source/
find . -type f -exec grep -H '\^2' {} \;
./supplements/gshhg/gshhg.rst:north* is the enclosing rectangle, *area* is the polygon area in km^2
./supplements/mgd77/mgd77list.rst: 7.5038 \* V \* cos(lat) \* sin(az) + 0.004154 \* V^2
./supplements/mgd77/mgd77list.rst:(1) g = 978052.0 \* [1 + 0.005285 \* sin^2(lat) - 7e-6 \* sin^2(2\*lat)
./supplements/mgd77/mgd77list.rst:+ 27e-6 \* cos^2(lat) \* cos^2(lon-18)]
./supplements/mgd77/mgd77list.rst:(2) g = 978049.0 \* [1 + 0.0052884 \* sin^2(lat) - 0.0000059 \*
./supplements/mgd77/mgd77list.rst:sin^2(2\*lat)]
./supplements/mgd77/mgd77list.rst:(3) g = 978031.846 \* [1 + 0.0053024 \* sin^2(lat) - 0.0000058 \*
./supplements/mgd77/mgd77list.rst:sin^2(2\*lat)]
./supplements/mgd77/mgd77list.rst:(4) g = 978032.67714 \* [(1 + 0.00193185138639 \* sin^2(lat)) / sqrt (1
./supplements/mgd77/mgd77list.rst:- 0.00669437999013 \* sin^2(lat))]
./supplements/mgd77/mgd77list.rst:99999999 mag 0.5\*cos(0.5\*(azim-19))^2 1.0\*exp(-1e-3(lat))^1.5
./supplements/potential/gmtflexure.rst: or Young's modulus [7.0e10 N/m^2], respectively.
./supplements/potential/grdflexure.rst: or Young's modulus [7.0e10 N/m^2], respectively.
./supplements/x2sys/x2sys_solve.rst: **g** will fit f(**p**) = *a* + *b* sin(y)^2
./trend2d.rst: z(x,y) = m_1 + m_{2}x + m_{3}y + m_{4}xy + m_{5}x^2 + m_{6}y^2 + m_{7}x^3 +
./trend2d.rst: m_{8}x^{2}y + m_{9}xy^2 + m_{10}y^3.
./trend2d.rst: and create weights as 1/*sigma*\ ^2, or use the weights as read (**+w**)
./tutorial/session-2_jl.rst:#. At *y = 5*, add the sentence :math:`z^2 = x^2 + y^2`.
./tutorial/session-1.rst:ranges from 10^20 to 10^24. One possibility is
./tutorial/session-2.rst:#. At *y = 5*, add the sentence :math:`z^2 = x^2 + y^2`.
./tutorial/session-3_jl.rst: (1-t)\nabla ^2 z - t \nabla z = 0,
./tutorial/session-1_jl.rst:raw *x* data range from 3 to 9613 and that *y* ranges from 10^20 to 10^24. One possibility is
./grdfft.rst:curvature of the field. We can compute these as mGal/m^2 by::
./grd2xyz.rst: For geographic grids we default to a length unit of **k** (hence area is in km^2). Change
./grd2xyz.rst:To write out *lon, lat, topo, area* from the @AFR.nc file, selecting meter^2 as the area unit,
./blockmean.rst: then append **+s** and we compute weight = 1/sigma^2. Otherwise (or
./explain_-A.rst_: Features with an area smaller than *min\_area* in km^2 or of
./grdvolume.rst:To determine area (in km^2), volume (in km^3), and mean height (in km) of all land areas
./grdvolume.rst: in unit^2 * z_unit quantities.
./gmtmath.rst: **D2DT2** 1 1 d^2(A)/dt^2 2nd derivative Calculus
./gmtmath.rst: **HYPOT** 2 1 Hypotenuse of a right triangle of sides A and B (= sqrt (A^2 + B^2)) Calculus
./gmtmath.rst: **R2** 2 1 Hypotenuse squared (= A^2 + B^2) Calculus
./grdtrend.rst: m_1 + m_2x + m_3y + m_4xy + m_5x^2 + m_6y^2 + m_7x^3 + m_8x^2y + m_9xy^2 + m_{10}y^3.
./grdtrend.rst: :math:`m_1 + m_2x + m_3x^2 + m_4x^3` or :math:`m_1 + m_2y + m_3y^2 + m_4y^3`.
./grdtrend.rst: as 1/sigma^2. If the robust option has been selected, the weights used
./grdfill.rst: append a search *radius* in pixels [default radius is :math:`r = \sqrt{n^2 + m^2}`,
./grdmath.rst:| **AREA** | 0 1 | Area of each gridnode cell (in km^2 if geographic) |
./grdmath.rst:| **D2DX2** | 1 1 | d^2(A)/dx^2 2nd derivative |
./grdmath.rst:| **D2DY2** | 1 1 | d^2(A)/dy^2 2nd derivative |
./grdmath.rst:| **D2DXY** | 1 1 | d^2(A)/dxdy 2nd derivative |
./grdmath.rst:| **R2** | 2 1 | R2 = A^2 + B^2 |
./grdmath.rst:| **SQR** | 1 1 | A^2 |
./grdmath.rst: 2^24 or 16,777,216. Any higher result will be masked to fit in the lower
./trend1d.rst: and create weights as 1/*sigma*\ ^2 [Default reads only the first 2 columns].
./trend1d.rst:To fit the model y(x) = a + bx^2 + c * cos(2*pi*3*(x/l) + d * sin(2*pi*3*(x/l), with l the fundamental period (here l = 15), try:
./grdfilter.rst:filter exp (-0.5\*r^2) whose distances r from the center is given by
./grdfilter.rst:(2x^2 + y^2 -2xy)/6, with major axis at an angle of 63 degrees with the
For the uninitiated you can just grep ':math:' * to see how it is done with math. I post this here since it is a very simple thing that new wannabe collaborators could try out for, say, one module at the time and offer a pull request for us to consider. We all have to full on the oars if we want to documentation to shine,