From 29ddd77be0430a48ebe02216b03c41e306fa1ec6 Mon Sep 17 00:00:00 2001
From: Philip-Lynch <phil.lynch25@gmail.com>
Date: Wed, 2 Aug 2023 11:57:42 +0200
Subject: [PATCH] Using ?PossibleZeroQ and closing secitons #50

---
 Kernel/FourVelocity.m       | 18 +++++++++---------
 Kernel/KerrGeoOrbit.m       |  2 +-
 Kernel/OrbitalFrequencies.m | 10 +++++-----
 Kernel/SpecialOrbits.m      |  4 ++--
 4 files changed, 17 insertions(+), 17 deletions(-)

diff --git a/Kernel/FourVelocity.m b/Kernel/FourVelocity.m
index dad7e0e..94a4d9d 100644
--- a/Kernel/FourVelocity.m
+++ b/Kernel/FourVelocity.m
@@ -17,14 +17,14 @@
 Begin["`Private`"];
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Error messages*)
 
 
 KerrGeoFourVelocity::parametrization = "Parameterization error: `1`"
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Schwarzschild*)
 
 
@@ -32,7 +32,7 @@
 (*Circular, Equatorial*)
 
 
-KerrGeoVelocityMino[(0|0.),p_,(0|0.),x_,initPhases_ ]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr,zp,zm,kz, \[CapitalUpsilon]r, \[CapitalUpsilon]z, 
+KerrGeoVelocityMino[a_?PossibleZeroQ,p_,e_?PossibleZeroQ,x_,initPhases_ ]:= Module[{En,L,Q,r,z,r1,r2,r3,r4,kr,zp,zm,kz, \[CapitalUpsilon]r, \[CapitalUpsilon]z, 
 qr, qz, \[Lambda]local ,qr0, qz0, rprime, zprime, \[CapitalDelta], \[CapitalSigma], \[Omega], utContra,urContra,u\[Theta]Contra,uzContra,u\[Phi]Contra, utCo, urCo, u\[Theta]Co, u\[Phi]Co},
 
 (*Constants of Motion*)
@@ -64,7 +64,7 @@
 ] 
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Kerr*)
 
 
@@ -130,7 +130,7 @@
 
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Equatorial (Darwin)*)
 
 
@@ -138,10 +138,10 @@
 (*Circular Case*)
 
 
-KerrGeoVelocityDarwin[a_,p_,(0|0.),x_,initPhases_]:= Module[{ut,ur,u\[Theta],u\[Phi], MinoVelocities,utContra,urContra,u\[Theta]Contra,u\[Phi]Contra,
+KerrGeoVelocityDarwin[a_,p_,e_?PossibleZeroQ,x_,initPhases_]:= Module[{ut,ur,u\[Theta],u\[Phi], MinoVelocities,utContra,urContra,u\[Theta]Contra,u\[Phi]Contra,
 utCo,urCo,u\[Theta]Co,u\[Phi]Co,utUp,urUp,u\[Theta]Up,u\[Phi]Up, utDown,urDown,u\[Theta]Down,u\[Phi]Down},
 
-MinoVelocities = KerrGeoVelocityMino[a,p,0,x,{0,0}];
+MinoVelocities = KerrGeoVelocityMino[a,p,e,x,{0,0}];
 
 utUp="\!\(\*SuperscriptBox[\(u\), \(t\)]\)"; urUp="\!\(\*SuperscriptBox[\(u\), \(r\)]\)"; 
 u\[Theta]Up="\!\(\*SuperscriptBox[\(u\), \(\[Theta]\)]\)"; u\[Phi]Up="\!\(\*SuperscriptBox[\(u\), \(\[Phi]\)]\)";
@@ -167,7 +167,7 @@
 ]
 
 
-(* ::Subsubsection::Closed:: *)
+(* ::Subsubsection:: *)
 (*Eccentric Case*)
 
 
@@ -227,7 +227,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*KerrGeoFourVelocity Wrapper*)
 
 
diff --git a/Kernel/KerrGeoOrbit.m b/Kernel/KerrGeoOrbit.m
index b4e3880..1b9926c 100644
--- a/Kernel/KerrGeoOrbit.m
+++ b/Kernel/KerrGeoOrbit.m
@@ -136,7 +136,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Kerr*)
 
 
diff --git a/Kernel/OrbitalFrequencies.m b/Kernel/OrbitalFrequencies.m
index cadffb5..d0e6ee6 100644
--- a/Kernel/OrbitalFrequencies.m
+++ b/Kernel/OrbitalFrequencies.m
@@ -16,7 +16,7 @@
 Begin["`Private`"];
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Roots of the radial and polar equations*)
 
 
@@ -70,7 +70,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Orbital Frequencies*)
 
 
@@ -121,11 +121,11 @@
 KerrGeoProperFrequencyFactor[a_?PossibleZeroQ ,p_,e_,x_]:=(p^2 ((1+e) (28+4 e^2+(-12+p) p)-((1+e) (-4+p) (-6+2 e+p) EllipticE[(4 e)/(-6+2 e+p)]+2 (6+2 e-p) (3+e^2-p) EllipticPi[(2 e (-4+p))/((1+e) (-6+2 e+p)),(4 e)/(-6+2 e+p)])/EllipticK[(4 e)/(-6+2 e+p)]))/(2 (-1+e) (1+e)^2 (-4+p)^2)
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Kerr*)
 
 
-(* ::Subsubsection:: *)
+(* ::Subsubsection::Closed:: *)
 (*KerrGeoMinoFrequencyr*)
 
 
@@ -147,7 +147,7 @@
 		
 
 
-(* ::Subsubsection:: *)
+(* ::Subsubsection::Closed:: *)
 (*KerrGeoMinoFrequency\[Theta]*)
 
 
diff --git a/Kernel/SpecialOrbits.m b/Kernel/SpecialOrbits.m
index cb4c3f4..82f5c72 100644
--- a/Kernel/SpecialOrbits.m
+++ b/Kernel/SpecialOrbits.m
@@ -8,7 +8,7 @@
 (*Define usage for public functions*)
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Create Package*)
 
 
@@ -602,7 +602,7 @@
 ]
 
 
-(* ::Section:: *)
+(* ::Section::Closed:: *)
 (*Close the package*)