Add better interaction with and export to sympy, and uses sympy to implement more Hessian functions

.github/workflows/windows-tests.yml

@@ -11,7 +11,7 @@ on:
 jobs:
   build:
     name: "py${{ matrix.python-version }} on ${{ matrix.os }}"
-    if: "!contains(github.event.head_commit.message, 'skip ci')"
+    if: "!contains(toJSON(github.event.commits.*.message), '[skip ci]') && !contains(toJSON(github.event.commits.*.message), '[ci skip]')"
     runs-on: ${{ matrix.os }}
     strategy:
       fail-fast: false

CHANGES.rst

@@ -4,13 +4,21 @@
 New Features
 ------------
 
+- Added a new ``.to_sympy()`` classmethod for the ``Potential`` classes to
+  return a sympy expression and variables.
+
 Bug fixes
 ---------
 
 - Fixed a bug with ``Potential`` classes ``.replace_units()`` so that classes
   with dimensionless unit systems cannot be replaced with physical unit systems,
   and vice versa.
 
+- Implemented Hessian functions for most potentials.
+
+- Fixed ``.to_latex()`` to properly return a latex representation of the
+  potential. This uses the new ``.to_sympy()`` method under the hood.
+
 API changes
 -----------
 

docs/potential/index.rst

@@ -237,6 +237,40 @@ and method::
     >>> load("potential.yml")
     <NFWPotential: m=6.00e+11, r_s=20.00, a=1.00, b=1.00, c=1.00 (kpc,Myr,solMass,rad)>
 
+Exporting potentials as ``sympy`` expressions
+=============================================
+
+Most of the potential classes can be exported to a ``sympy`` expression that can
+be used to manipulate or evaluate the form of the potential. To access this
+functionality, the potential classes have a ``.to_sympy()`` classmethod (note:
+this requires that ``sympy`` is installed):
+
+    >>> expr, vars_, pars = gp.LogarithmicPotential.to_sympy()
+    >>> str(expr)
+    '0.5*v_c**2*log(r_h**2 + z**2/q3**2 + y**2/q2**2 + x**2/q1**2)'
+
+This method also returns a dictionary containing the coordinate variables used
+in the expression as ``sympy`` symbols, here defined as ``vars_``:
+
+    >>> vars_
+    {'x': x, 'y': y, 'z': z}
+
+A second dictionary containing the potential parameters as ``sympy`` symbols is
+also returned, here defined as ``pars``:
+
+    >>> pars
+    {'v_c': v_c, 'r_h': r_h, 'q1': q1, 'q2': q2, 'q3': q3, 'phi': phi, 'G': G}
+
+The expressions and variables returned can be used to perform operations on the
+potential expression. For example, to create a ``sympy`` expression for the
+gradient of the potential:
+
+    >>> import sympy as sy
+    >>> grad = sy.derive_by_array(expr, list(vars_.values()))
+    >>> grad[0]  # dPhi/dx
+    1.0*v_c**2*x/(q1**2*(r_h**2 + z**2/q3**2 + y**2/q2**2 + x**2/q1**2))
+
+
 Using gala.potential
 ====================
 More details are provided in the linked pages below: