Use a substitution that sympy 1.3.0 understands (#169)

The original substitution does not seem to work in sympy 1.3.0, but works in 1.5.0.
The modified one is equivalent, but works in both versions.
A direct substitution is easier to understand here anyway.

Part of the work to migrate to a newer sympy

Author: eric-wieser

examples/LaTeX/latex_check.py

@@ -231,7 +231,7 @@ def noneuclidian_distance_calculation():
     W = W.subs(c**2,(C+1)/2)
     W = W.subs(s**2,(C-1)/2)
     W = simplify(W)
-    W = W.subs(1/Binv,Bmag)
+    W = W.subs(Binv,1/Bmag)
     W = expand(W)
 
     print('#%S = \\f{\\sinh}{\\alpha} \\text{ and } C = \\f{\\cosh}{\\alpha}')

examples/Old Format/latex_check.py

@@ -219,7 +219,7 @@ def noneuclidian_distance_calculation():
     W = W.subs(c**2,(C+1)/2)
     W = W.subs(s**2,(C-1)/2)
     W = simplify(W)
-    W = W.subs(1/Binv,Bmag)
+    W = W.subs(Binv,1/Bmag)
     W = expand(W)
 
     print('#%S = \\f{\\sinh}{\\alpha} \\text{ and } C = \\f{\\cosh}{\\alpha}')

examples/ipython/LaTeX.ipynb

@@ -1131,7 +1131,7 @@
        "    W = W.subs(c**2,(C+1)/2)\n",
        "    W = W.subs(s**2,(C-1)/2)\n",
        "    W = simplify(W)\n",
-       "    W = W.subs(1/Binv,Bmag)\n",
+       "    W = W.subs(Binv,1/Bmag)\n",
        "    W = expand(W)\n",
        "    print('#%S = \\\\f{\\\\sinh}{\\\\alpha} \\\\text{ and } C = \\\\f{\\\\cosh}{\\\\alpha}')\n",
        "    print('W =',W)\n",
@@ -1179,9 +1179,9 @@
        "\\begin{equation*} e^{\\alpha B/{2\\abs{B}}} = c  + (1/B) s \\boldsymbol{X}\\wedge \\boldsymbol{Y} - (1/B) \\left ( Y\\cdot e\\right )  s \\boldsymbol{X}\\wedge \\boldsymbol{e} + (1/B) \\left ( X\\cdot e\\right )  s \\boldsymbol{Y}\\wedge \\boldsymbol{e} \\end{equation*}\n",
        "\\begin{equation*} W = Z\\cdot Y = (1/B)^{2} \\left ( X\\cdot Y\\right ) ^{3} s^{2} - 4 (1/B)^{2} \\left ( X\\cdot Y\\right ) ^{2} \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  s^{2} + 4 (1/B)^{2} \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right ) ^{2} \\left ( Y\\cdot e\\right ) ^{2} s^{2} + 2 (1/B) \\left ( X\\cdot Y\\right ) ^{2} c s - 4 (1/B) \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  c s + \\left ( X\\cdot Y\\right )  c^{2} \\end{equation*}\n",
        "\\begin{equation*} S = \\f{\\sinh}{\\alpha} \\text{ and } C = \\f{\\cosh}{\\alpha} \\end{equation*}\n",
-       "\\begin{equation*} W = (1/B) \\left ( X\\cdot Y\\right )  C \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } - (1/B) \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  C \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } + (1/B) \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } + S \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } \\end{equation*}\n",
-       "\\begin{equation*} \\text{Scalar Coefficient} = (1/B) \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } \\end{equation*}\n",
-       "\\begin{equation*} \\text{Cosh Coefficient} = (1/B) \\left ( X\\cdot Y\\right )  \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } - (1/B) \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } \\end{equation*}\n",
+       "\\begin{equation*} W = \\left ( X\\cdot Y\\right )  C - \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  C + \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right )  + S \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } \\end{equation*}\n",
+       "\\begin{equation*} \\text{Scalar Coefficient} = \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) \\end{equation*}\n",
+       "\\begin{equation*} \\text{Cosh Coefficient} = \\left ( X\\cdot Y\\right )  - \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) \\end{equation*}\n",
        "\\begin{equation*} \\text{Sinh Coefficient} = \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } \\end{equation*}\n",
        "\\begin{equation*} \\abs{B} = \\sqrt{\\left ( X\\cdot Y\\right ) ^{2} - 2 \\left ( X\\cdot Y\\right )  \\left ( X\\cdot e\\right )  \\left ( Y\\cdot e\\right ) } \\end{equation*}\n",
        "\\begin{equation*} \\text{Require } aC^{2}+bC+c = 0 \\end{equation*}\n",