Neaten up Sage code

main.tex

@@ -141,16 +141,18 @@ def charact_curves(v):
     alpha = stability.Tilt().alpha
     beta = stability.Tilt().beta
     coords_range = (beta, -4, 5), (alpha, 0, 4)
+    text_args = {"fontsize":"x-large", "clip":True}
+    black_text_args = {"rgbcolor": "black", **text_args}
     p = (
       implicit_plot(stability.Tilt().degree(v), *coords_range )
       + line([(mu(v),0),(mu(v),5)], linestyle = "dashed")
-      + text(r"$ch_2^{\alpha, \beta}(v)=0$",[3.5, 2], rotation=45, fontsize="x-large", clip=True)
-      + text(r"$ch_1^{\alpha, \beta}(v)=0$", [0.45, 1.5], rotation=90, fontsize="x-large", clip=True)
-      + text(r"$ch_2^{\alpha, \beta}(v)=0$", [-2, 2], rotation=-45, fontsize="x-large", clip=True)
-      + text(r"$\nu_{\alpha, \beta}(v)>0$", [-3, 1], rgbcolor="black", fontsize="x-large", clip=True)
-      + text(r"$\nu_{\alpha, \beta}(v)<0$", [-1, 3], rgbcolor="black", fontsize="x-large", clip=True)
-      + text(r"$\nu_{\alpha, \beta}(-v)>0$", [2, 3], rgbcolor="black", fontsize="x-large", clip=True)
-      + text(r"$\nu_{\alpha, \beta}(-v)<0$", [4, 1], rgbcolor="black", fontsize="x-large", clip=True)
+      + text(r"$ch_2^{\alpha, \beta}(v)=0$",[3.5, 2], rotation=45, **text_args)
+      + text(r"$ch_1^{\alpha, \beta}(v)=0$", [0.45, 1.5], rotation=90, **text_args)
+      + text(r"$ch_2^{\alpha, \beta}(v)=0$", [-2, 2], rotation=-45, **text_args)
+      + text(r"$\nu_{\alpha, \beta}(v)>0$", [-3, 1], **black_text_args)
+      + text(r"$\nu_{\alpha, \beta}(v)<0$", [-1, 3], **black_text_args)
+      + text(r"$\nu_{\alpha, \beta}(-v)>0$", [2, 3], **black_text_args)
+      + text(r"$\nu_{\alpha, \beta}(-v)<0$", [4, 1], **black_text_args)
     )
     p.xmax(5)
     p.xmin(-4)
@@ -287,24 +289,30 @@ Recalling how the sign of $\nu_{\alpha,\beta}(\pm u)$ changes
 def hyperbola_intersection_plot():
   var("alpha beta", domain="real")
   coords_range = (beta, -3, -1/2), (alpha, 0, 2.5)
-  
   delta1 = -sqrt(2)+1/100
   delta2 = 1/2
   pbeta=-1.5
-  
+  text_args = {"fontsize":"large", "clip":True}
+  black_text_args = {"rgbcolor":"black", **text_args}
   p = (
-    implicit_plot(beta^2 - alpha^2 == 2, *coords_range , rgbcolor = "black", legend_label=r"a")
-    + implicit_plot((beta+4)^2 - (alpha)^2 == 2, *coords_range , rgbcolor = "red")
-    + implicit_plot((beta+delta1)^2 - alpha^2 == (delta1-2)^2-2, *coords_range , rgbcolor = "blue")
-    + implicit_plot((beta+delta2)^2 - alpha^2 == (delta2-2)^2-2, *coords_range , rgbcolor = "green")
+    implicit_plot( beta^2 - alpha^2 == 2,
+        *coords_range , rgbcolor = "black", legend_label=r"a")
+    + implicit_plot( (beta+4)^2 - (alpha)^2 == 2,
+        *coords_range , rgbcolor = "red")
+    + implicit_plot( (beta+delta1)^2 - alpha^2 == (delta1-2)^2-2,
+        *coords_range , rgbcolor = "blue")
+    + implicit_plot( (beta+delta2)^2 - alpha^2 == (delta2-2)^2-2,
+        *coords_range , rgbcolor = "green")
     + point([-2, sqrt(2)], size=50, rgbcolor="black", zorder=50)
-    + text("Q",[-2, sqrt(2)+0.1], rgbcolor="black", fontsize="large", clip=true)
+    + text("Q",[-2, sqrt(2)+0.1], **black_text_args)
     + point([pbeta, sqrt(pbeta^2-2)], size=50, rgbcolor="black", zorder=50)
-    + text("P",[pbeta+0.1, sqrt(pbeta^2-2)], rgbcolor="black", fontsize="large", clip=true)
+    + text("P",[pbeta+0.1, sqrt(pbeta^2-2)], **black_text_args)
     + circle((-2,0),sqrt(2), linestyle="dashed", rgbcolor="purple")
     # dummy lines to add legends (circumvent bug in implicit_plot)
-    + line([(2,0),(2,0)] , rgbcolor = "purple", linestyle="dotted", legend_label=r"pseudo-wall")
-    + line([(2,0),(2,0)] , rgbcolor = "black", legend_label=r"$ch_2^{\alpha,\beta}(v)=0$")
+    + line([(2,0),(2,0)] , rgbcolor = "purple", linestyle="dotted",
+        legend_label=r"pseudo-wall")
+    + line([(2,0),(2,0)] , rgbcolor = "black",
+        legend_label=r"$ch_2^{\alpha,\beta}(v)=0$")
     + line([(2,0),(2,0)] , rgbcolor = "red", legend_label=r"case 1")
     + line([(2,0),(2,0)] , rgbcolor = "blue", legend_label=r"case 2")
     + line([(2,0),(2,0)] , rgbcolor = "green", legend_label=r"case 3")
@@ -313,36 +321,46 @@ def hyperbola_intersection_plot():
   p.xmin(coords_range[0][1])
   p.ymax(coords_range[1][2])
   p.ymin(coords_range[1][1])
-  p.axes_labels([r"$\beta$",
-  r"$\alpha$"])
-  
+  p.axes_labels([r"$\beta$", r"$\alpha$"])
   return p
 
 def correct_hyperbola_intersection_plot():
   var("alpha beta", domain="real")
   coords_range = (beta, -2.5, 0.5), (alpha, 0, 3)
-  
   delta2 = 1/2
   pbeta=-1.5
-  
+  text_args = {"fontsize":"large", "clip":True}
+  black_text_args = {"rgbcolor":"black", **text_args}
   p = (
-    implicit_plot(beta^2 - alpha^2 == 2, *coords_range , rgbcolor = "black", legend_label=r"a")
-    + implicit_plot((beta+delta2)^2 - alpha^2 == (delta2-2)^2-2, *coords_range , rgbcolor = "green")
+    implicit_plot( beta^2 - alpha^2 == 2,
+        *coords_range , rgbcolor = "black", legend_label=r"a")
+    + implicit_plot((beta+delta2)^2 - alpha^2 == (delta2-2)^2-2,
+        *coords_range , rgbcolor = "green")
     + point([-2, sqrt(2)], size=50, rgbcolor="black", zorder=50)
-    + text("Q",[-2, sqrt(2)+0.1], rgbcolor="black", fontsize="large", clip=true)
+    + text("Q",[-2, sqrt(2)+0.1], **black_text_args)
     + point([pbeta, sqrt(pbeta^2-2)], size=50, rgbcolor="black", zorder=50)
-    + text("P",[pbeta+0.1, sqrt(pbeta^2-2)], rgbcolor="black", fontsize="large", clip=true)
+    + text("P",[pbeta+0.1, sqrt(pbeta^2-2)], **black_text_args)
     + circle((-2,0),sqrt(2), linestyle="dashed", rgbcolor="purple")
     # dummy lines to add legends (circumvent bug in implicit_plot)
-    + line([(2,0),(2,0)] , rgbcolor = "purple", linestyle="dotted", legend_label=r"pseudo-wall")
-    + line([(2,0),(2,0)] , rgbcolor = "black", legend_label=r"$ch_2^{\alpha,\beta}(v)=0$")
-    + line([(2,0),(2,0)] , rgbcolor = "green", legend_label=r"$ch_2^{\alpha,\beta}(u)=0$")
+    + line([(2,0),(2,0)] , rgbcolor = "purple", linestyle="dotted",
+        legend_label=r"pseudo-wall")
+    + line([(2,0),(2,0)] , rgbcolor = "black",
+        legend_label=r"$ch_2^{\alpha,\beta}(v)=0$")
+    + line([(2,0),(2,0)] , rgbcolor = "green",
+        legend_label=r"$ch_2^{\alpha,\beta}(u)=0$")
     # vertical characteristic lines
-    +line([(0,0),(0,coords_range[1][2])], rgbcolor="black", linestyle="dashed", legend_label=r"$ch_1^{\alpha,\beta}(v)=0$")
-    +line([(-delta2,0),(-delta2,coords_range[1][2])], rgbcolor="green", linestyle="dashed", legend_label=r"$ch_1^{\alpha,\beta}(u)=0$")
-    +line([(0,0),(-coords_range[1][2],coords_range[1][2])], rgbcolor="black", linestyle="dotted", legend_label=r"assymptote for $ch_2^{\alpha,\beta}(v)=0$")
-    +line([(-delta2,0),(-delta2-coords_range[1][2],coords_range[1][2])], rgbcolor="green", linestyle="dotted", legend_label=r"assymptote for $ch_1^{\alpha,\beta}(u)=0$")
-    
+    + line([(0,0),(0,coords_range[1][2])],
+        rgbcolor="black", linestyle="dashed",
+        legend_label=r"$ch_1^{\alpha,\beta}(v)=0$")
+    + line([(-delta2,0),(-delta2,coords_range[1][2])],
+        rgbcolor="green", linestyle="dashed",
+        legend_label=r"$ch_1^{\alpha,\beta}(u)=0$")
+    + line([(0,0),(-coords_range[1][2],coords_range[1][2])],
+        rgbcolor="black", linestyle="dotted",
+        legend_label=r"assymptote for $ch_2^{\alpha,\beta}(v)=0$")
+    + line([(-delta2,0),(-delta2-coords_range[1][2],coords_range[1][2])],
+        rgbcolor="green", linestyle="dotted",
+        legend_label=r"assymptote for $ch_1^{\alpha,\beta}(u)=0$")
   )
   p.set_legend_options(loc="upper right")
   p.xmax(coords_range[0][2])