Add section titles to curvi_linear_latex.py (#416)

Author: utensil

examples/LaTeX/curvi_linear_latex.py

@@ -15,6 +15,8 @@ def derivatives_in_spherical_coordinates():
     A = sp3d.mv('A','vector',f=True)
     B = sp3d.mv('B','bivector',f=True)
 
+    print('#Derivatives in Spherical Coordinates')
+
     print('f =',f)
     print('A =',A)
     print('B =',B)
@@ -69,6 +71,8 @@ def derivatives_in_elliptic_cylindrical_coordinates():
     A = elip3d.mv('A','vector',f=True)
     B = elip3d.mv('B','bivector',f=True)
 
+    print('#Derivatives in Elliptic Cylindrical Coordinates')
+
     print('f =',f)
     print('A =',A)
     print('B =',B)
@@ -92,6 +96,8 @@ def derivatives_in_prolate_spheroidal_coordinates():
     A = ps3d.mv('A','vector',f=True)
     B = ps3d.mv('B','bivector',f=True)
 
+    print('#Derivatives in Prolate Spheroidal Coordinates')
+
     print('f =',f)
     print('A =',A)
     print('B =',B)

examples/ipython/LaTeX.ipynb

@@ -143,6 +143,7 @@
        "\\lstloadlanguages{Python}\n",
        "\n",
        "\\begin{document}\n",
+       "Derivatives in Spherical Coordinates\n",
        "\\begin{equation*} f = f \\end{equation*}\n",
        "\\begin{equation*} A = A^{r}  \\boldsymbol{e}_{r} + A^{\\theta }  \\boldsymbol{e}_{\\theta } + A^{\\phi }  \\boldsymbol{e}_{\\phi } \\end{equation*}\n",
        "\\begin{equation*} B = B^{r\\theta }  \\boldsymbol{e}_{r}\\wedge \\boldsymbol{e}_{\\theta } + B^{r\\phi }  \\boldsymbol{e}_{r}\\wedge \\boldsymbol{e}_{\\phi } + B^{\\theta \\phi }  \\boldsymbol{e}_{\\theta }\\wedge \\boldsymbol{e}_{\\phi } \\end{equation*}\n",
@@ -158,6 +159,7 @@
        "\\begin{equation*} \\boldsymbol{\\nabla}  f = \\frac{\\partial_{u} f }{\\sqrt{u^{2} + v^{2}}} \\boldsymbol{e}_{u} + \\frac{\\partial_{v} f }{\\sqrt{u^{2} + v^{2}}} \\boldsymbol{e}_{v} + \\frac{\\partial_{\\phi } f }{u v} \\boldsymbol{e}_{\\phi } \\end{equation*}\n",
        "\\begin{equation*} \\boldsymbol{\\nabla} \\cdot A = \\frac{u A^{u} }{\\left(u^{2} + v^{2}\\right)^{\\frac{3}{2}}} + \\frac{v A^{v} }{\\left(u^{2} + v^{2}\\right)^{\\frac{3}{2}}} + \\frac{\\partial_{u} A^{u} }{\\sqrt{u^{2} + v^{2}}} + \\frac{\\partial_{v} A^{v} }{\\sqrt{u^{2} + v^{2}}} + \\frac{A^{v} }{v \\sqrt{u^{2} + v^{2}}} + \\frac{A^{u} }{u \\sqrt{u^{2} + v^{2}}} + \\frac{\\partial_{\\phi } A^{\\phi } }{u v} \\end{equation*}\n",
        "\\begin{equation*} \\boldsymbol{\\nabla} \\W B = \\left ( \\frac{u B^{v\\phi } }{\\left(u^{2} + v^{2}\\right)^{\\frac{3}{2}}} - \\frac{v B^{u\\phi } }{\\left(u^{2} + v^{2}\\right)^{\\frac{3}{2}}} - \\frac{\\partial_{v} B^{u\\phi } }{\\sqrt{u^{2} + v^{2}}} + \\frac{\\partial_{u} B^{v\\phi } }{\\sqrt{u^{2} + v^{2}}} - \\frac{B^{u\\phi } }{v \\sqrt{u^{2} + v^{2}}} + \\frac{B^{v\\phi } }{u \\sqrt{u^{2} + v^{2}}} + \\frac{\\partial_{\\phi } B^{uv} }{u v}\\right ) \\boldsymbol{e}_{u}\\wedge \\boldsymbol{e}_{v}\\wedge \\boldsymbol{e}_{\\phi } \\end{equation*}\n",
+       "Derivatives in Prolate Spheroidal Coordinates\n",
        "\\begin{equation*} f = f \\end{equation*}\n",
        "\\begin{equation*} A = A^{\\xi }  \\boldsymbol{e}_{\\xi } + A^{\\eta }  \\boldsymbol{e}_{\\eta } + A^{\\phi }  \\boldsymbol{e}_{\\phi } \\end{equation*}\n",
        "\\begin{equation*} B = B^{\\xi \\eta }  \\boldsymbol{e}_{\\xi }\\wedge \\boldsymbol{e}_{\\eta } + B^{\\xi \\phi }  \\boldsymbol{e}_{\\xi }\\wedge \\boldsymbol{e}_{\\phi } + B^{\\eta \\phi }  \\boldsymbol{e}_{\\eta }\\wedge \\boldsymbol{e}_{\\phi } \\end{equation*}\n",