Update Starmath examples

Some corrections and addition to examples to show more different uses:
- Circumference: add spaces for a better readibility
- Pytahorean: use sqrt function
- Newton: use times for multiplication and vec
- special relativity: 't' instead of 'T'
- Euler-Lagrange: right parenthesis misplaced
- FTC: inversion of border value
- Chaos: use bold r and double vertical lines
- Taylor series: use fact function instead of exclamation mark
and remove extra {}
- Gauss distribution: more logical repartition of spaces

Change-Id: I4563a8c031de2c8db1b1c674a29e7b1d843d57e1
Reviewed-on: https://gerrit.libreoffice.org/c/core/+/107050
Tested-by: Jenkins
Reviewed-by: Dante DM <dante19031999@gmail.com>
Reviewed-by: Noel Grandin <noel.grandin@collabora.co.uk>

starmath/source/ElementsDockingWindow.cxx

@@ -252,17 +252,17 @@ const SmElementDescr SmElementsControl::m_aOthersList[] =
 const SmElementDescr SmElementsControl::m_aExamplesList[] =
 {
     {"{func e}^{i %pi} + 1 = 0", RID_EXAMPLE_EULER_IDENTITY_HELP},
-    {"C=%pi cdot d = 2 cdot %pi cdot r", RID_EXAMPLE_CIRCUMFERENCE_HELP},
-    {"a^2 + b^2 = c^2", RID_EXAMPLE_PYTHAGOREAN_THEO_HELP},
-    {"F = m a", RID_EXAMPLE_2NEWTON},
+    {"C = %pi cdot d = 2 cdot %pi cdot r", RID_EXAMPLE_CIRCUMFERENCE_HELP},
+    {"c = sqrt{ a^2 + b^2 }", RID_EXAMPLE_PYTHAGOREAN_THEO_HELP},
+    {"vec F = m times vec a", RID_EXAMPLE_2NEWTON},
     {"E = m c^2", RID_EXAMPLE_MASS_ENERGY_EQUIV_HELP},
     {"G_{%mu %nu} + %LAMBDA g_{%mu %nu}= frac{8 %pi G}{c^4} T_{%mu %nu}", RID_EXAMPLE_GENERAL_RELATIVITY_HELP},
-    {" %DELTA t' = { %DELTA T } over sqrt{ 1 - v^2 over c^2 } ", RID_EXAMPLE_SPECIAL_RELATIVITY_HELP },
-    { "d over dt left( {partial L}over{partial dot q} = {partial L}over{partial q} right)", RID_EXAMPLE_EULER_LAGRANGE_HELP },
-    {"int from a to b f'(x) dx = f(a) - f(b)", RID_EXAMPLE_FTC_HELP},
-    { "abs{ %delta Z(t) } approx e^{%lambda t} abs{ %delta Z(0) }", RID_EXAMPLE_CHAOS_HELP},
-    {"f ( x ) = sum from { { n = 0 } } to { infinity } { {f^{(n)}(x_0)} over {n!} (x-x_0)^n}", RID_EXAMPLE_A_TAYLOR_SERIES_HELP},
-    {"f ( x ) = {1} over {%sigma sqrt{2%pi} }func e^-{{(x-%mu)^2} over {2%sigma^2}}", RID_EXAMPLE_GAUSS_DISTRIBUTION_HELP},
+    {"%DELTA t' = { %DELTA t } over sqrt{ 1 - v^2 over c^2 }", RID_EXAMPLE_SPECIAL_RELATIVITY_HELP },
+    {"d over dt left( {partial L}over{partial dot q} right) = {partial L}over{partial q}", RID_EXAMPLE_EULER_LAGRANGE_HELP },
+    {"int from a to b f'(x) dx = f(b) - f(a)", RID_EXAMPLE_FTC_HELP},
+    {"ldline %delta bold{r}(t) rdline approx e^{%lambda t} ldline %delta { bold{r} }_0 rdline", RID_EXAMPLE_CHAOS_HELP},
+    {"f(x) = sum from { n=0 } to { infinity } { {f^{(n)}(x_0) } over { fact{n} } (x-x_0)^n }", RID_EXAMPLE_A_TAYLOR_SERIES_HELP},
+    {"f(x) = {1} over { %sigma sqrt{2 %pi} } func e^-{ {(x-%mu)^2} over {2 %sigma^2} }", RID_EXAMPLE_GAUSS_DISTRIBUTION_HELP},
 };
 
 #define AS_PAIR(a) a, SAL_N_ELEMENTS(a)