@@ -425,9 +425,9 @@ g += line([(x1, y2), (x2, y1)], color='black', linestyle=':') + line([(x1, y3),
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g += line ([(0 , y1 ), (x2 , y1 )], color = 'black' , linestyle = ':' )+ line ([(0 , y2 ), (x2 , y2 )], color = 'black' , linestyle = ':' )+ line ([(0 , y3 ), (x2 , y3 )], color = 'black' , linestyle = ':' )+ line ([(0 , yn1 ), (x2 , yn1 )], color = 'black' , linestyle = ':' )+ line ([(0 , yn ), (x2 , yn )], color = 'black' , linestyle = ':' )+ line ([(x1 , 0 ), (x1 , yn )], color = 'black' , linestyle = ':' )+ line ([(x2 , 0 ), (x2 , yn )], color = 'black' , linestyle = ':' )
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g += point ([(u ,v ),(x1 ,y2 ),(x2 ,y1 ),(x1 ,y3 ),(x2 ,y2 ),(x1 ,yn ),(x2 ,yn1 )], color = 'black' ,size = 30 ,zorder = 10 )
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ticks = [[u , x1 , x2 , u + delta , u + eta ], [v , y1 , y2 , y3 , yn1 , yn , v + eta ]]
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- tick_formatter = [["$u$" , "$x$" , "$x'$" , "" , "$u+\eta$" ],["$v$" ,"$y_1$" ,"$y_2$" ,"$y_3$" ,"$y_{N-1}$" ,"$y_N$" ,"$v+\eta$" ]]
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+ tick_formatter = [["$u$" , "$x$" , "$x'$" , "" , r "$u+\eta$" ],["$v$" ,"$y_1$" ,"$y_2$" ,"$y_3$" ,"$y_{N-1}$" ,"$y_N$" ,r "$v+\eta$" ]]
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g += text ("$(u,v)$" , (u - 0.01 ,v - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )
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- g += text ("$u+\delta$" , (u + delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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+ g += text (r "$u+\delta$" , (u + delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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g .fontsize (20 )
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g .show (ticks = ticks , tick_formatter = tick_formatter )
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g .save (destdir + "proof_uniform_cont_case_1.png" , ticks = ticks , tick_formatter = tick_formatter )
@@ -449,10 +449,10 @@ g += line([(x1, y2), (x2, y1)], color='black', linestyle=':') + line([(x1, y3),
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g += line ([(0 , y1 ), (x2 , y1 )], color = 'black' , linestyle = ':' )+ line ([(0 , y2 ), (x2 , y2 )], color = 'black' , linestyle = ':' )+ line ([(0 , y3 ), (x2 , y3 )], color = 'black' , linestyle = ':' )+ line ([(0 , yn1 ), (x2 , yn1 )], color = 'black' , linestyle = ':' )+ line ([(0 , yn ), (x2 , yn )], color = 'black' , linestyle = ':' )+ line ([(x1 , 0 ), (x1 , yn )], color = 'black' , linestyle = ':' )+ line ([(x2 , 0 ), (x2 , yn )], color = 'black' , linestyle = ':' )
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g += point ([(u ,v ),(x1 ,y2 ),(x2 ,y1 ),(x1 ,y3 ),(x2 ,y2 ),(x1 ,yn ),(x2 ,yn1 )], color = 'black' ,size = 30 ,zorder = 10 )
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ticks = [[u , x1 , x2 , u - delta , u - eta , u + delta , u + eta ], [v , y1 , y2 , y3 , yn1 , yn , v + eta ]]
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- tick_formatter = [["$u$" , "$x$" , "" , "" , "$u-\eta$" , "" , "$u+\eta$" ],["$v$" ,"$y_1$" ,"$y_2$" ,"$y_3$" ,"$y_{N-1}$" ,"$y_N$" ,"$v+\eta$" ]]
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+ tick_formatter = [["$u$" , "$x$" , "" , "" , r "$u-\eta$" , "" , r "$u+\eta$" ],["$v$" ,"$y_1$" ,"$y_2$" ,"$y_3$" ,"$y_{N-1}$" ,"$y_N$" ,r "$v+\eta$" ]]
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g += text ("$(u,v)$" , (u - 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )
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- g += text ("$u-\delta$" , (u - delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )
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- g += text ("$u+\delta$" , (u + delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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+ g += text (r "$u-\delta$" , (u - delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )
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+ g += text (r "$u+\delta$" , (u + delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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g += text ("$x'$" , (x2 , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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g .fontsize (20 )
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g .show (ticks = ticks , tick_formatter = tick_formatter )
@@ -475,10 +475,10 @@ g += line([(x1, y2), (x2, y1)], color='black', linestyle=':') + line([(x1, y3),
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g += line ([(0 , y1 ), (x2 , y1 )], color = 'black' , linestyle = ':' )+ line ([(0 , y2 ), (x2 , y2 )], color = 'black' , linestyle = ':' )+ line ([(0 , y3 ), (x2 , y3 )], color = 'black' , linestyle = ':' )+ line ([(0 , yn1 ), (x2 , yn1 )], color = 'black' , linestyle = ':' )+ line ([(0 , yn ), (x2 , yn )], color = 'black' , linestyle = ':' )+ line ([(x1 , 0 ), (x1 , yn )], color = 'black' , linestyle = ':' )+ line ([(x2 , 0 ), (x2 , yn )], color = 'black' , linestyle = ':' )
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g += point ([(u ,v ),(x1 ,y2 ),(x2 ,y1 ),(x1 ,y3 ),(x2 ,y2 ),(x1 ,yn ),(x2 ,yn1 )], color = 'black' ,size = 30 ,zorder = 10 )
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ticks = [[u , x1 , x2 , u - delta , u - eta ], [v , y1 , y2 , y3 , yn1 , yn , v + eta ]]
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- tick_formatter = [["$u$" , "$x$" , "$x'$" , "" , "$u-\eta$" ],["$v$" ,"$y_1$" ,"$y_2$" ,"$y_3$" ,"$y_{N-1}$" ,"$y_N$" ,"$v+\eta$" ]]
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+ tick_formatter = [["$u$" , "$x$" , "$x'$" , "" , r "$u-\eta$" ],["$v$" ,"$y_1$" ,"$y_2$" ,"$y_3$" ,"$y_{N-1}$" ,"$y_N$" ,r "$v+\eta$" ]]
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#g += text("$v$", (-0.01,v), axis_coords=False, vertical_alignment='center', horizontal_alignment='right',color='black',fontsize=20)
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g += text ("$(u,v)$" , (u ,v ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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- g += text ("$u-\delta$" , (u - delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )
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+ g += text (r "$u-\delta$" , (u - delta , - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )
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g .fontsize (20 )
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g .show (ticks = ticks , tick_formatter = tick_formatter )
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g .save (destdir + "proof_uniform_cont_case_3.png" , ticks = ticks , tick_formatter = tick_formatter )
@@ -505,7 +505,7 @@ g += line([(0, y1), (x1, y1)], color='black', linestyle=':')+line([(0, y2), (x2,
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g += point ([(u ,v ),(x1 ,y1 ),(x2 ,y2 )], color = 'black' ,size = 30 ,zorder = 10 )
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g += text ("$(u,v)$" , (u - 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )
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ticks = [[u , x1 , x2 , u - delta , u + delta ], [v , y1 , y2 , v + delta ]]
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- tick_formatter = [["$u$" , "$x$" , "$x'$" , "$u-\delta$" , "$u+\delta$" ],["$v$" ,"$y$" ,"$y'$" ,"$v+\delta$" ]]
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+ tick_formatter = [["$u$" , "$x$" , "$x'$" , r "$u-\delta$" , r "$u+\delta$" ],["$v$" ,"$y$" ,"$y'$" ,r "$v+\delta$" ]]
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g .fontsize (20 )
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g .show (ticks = ticks , tick_formatter = tick_formatter )
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g .save (destdir + "proof_uniform_V_case12.png" , ticks = ticks , tick_formatter = tick_formatter )
@@ -522,7 +522,7 @@ g += line([(x1, y1), (x2, y2)], color='black', linestyle=':')
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g += line ([(0 , y1 ), (u , y1 )], color = 'black' , linestyle = ':' )+ line ([(0 , y2 ), (x2 , y2 )], color = 'black' , linestyle = ':' )+ line ([(x1 , 0 ), (x1 , y1 )], color = 'black' , linestyle = ':' )+ line ([(x2 , 0 ), (x2 , y2 )], color = 'black' , linestyle = ':' )
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g += point ([(u ,v ),(x1 ,y1 ),(x2 ,y2 )], color = 'black' ,size = 30 ,zorder = 10 )
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ticks = [[u , x1 , x2 , u - delta ], [v , y1 , y2 , v + delta ]]
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- tick_formatter = [["$u$" , "$x$" , "$x'$" ,"$u-\delta$" ],["$v$" ,"$y$" ,"$y'$" ,"$v+\delta$" ]]
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+ tick_formatter = [["$u$" , "$x$" , "$x'$" ,r "$u-\delta$" ],["$v$" ,"$y$" ,"$y'$" ,r "$v+\delta$" ]]
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g += text ("$(u,v)$" , (u ,v ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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g += text ("=" ,(u - t1 / 4 ,v + t1 + 0.01 ), rotation = "vertical" , axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'center' ,color = 'blue' , fontsize = 15 )+ text ("=" ,(u - t1 * 3 / 4 ,v + t1 + 0.01 ), rotation = "vertical" ,axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'center' ,color = 'blue' , fontsize = 15 )
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g .fontsize (20 )
@@ -542,11 +542,11 @@ g += line([(u,v), (u-eta, v+eta)], color='black')+line([(u,v), (u+eta, v)], colo
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g += line ([(u , y ), (x2 , y )], color = 'black' , linestyle = ':' )
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g += line ([(u , v ), (u + v , 0 )], color = 'black' , linestyle = ':' )+ line ([(u , v + t1 ), (z1 , 0 )], color = 'black' , linestyle = ':' )+ line ([(x2 , y ), (z2 , 0 )], color = 'black' , linestyle = ':' )+ line ([(u + delta , v ), (u + v + delta , 0 )], color = 'black' , linestyle = ':' )
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g += point ([(u ,v ),(x1 ,y ),(x2 ,y )], color = 'black' ,size = 30 ,zorder = 10 ) #(u+delta,v),(u, v+delta)
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- g += text ("$(u,v)$" , (u - 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )+ text ("$(u+\delta,v)$" , (u + delta + 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )+ text ("$(u,v+\delta)$" , (u ,v + delta + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )+ text ("$(x,y)$" , (x1 + 0.02 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )+ text ("$(x',y)$" , (x2 + 0.02 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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+ g += text ("$(u,v)$" , (u - 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )+ text (r "$(u+\delta,v)$" , (u + delta + 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )+ text (r "$(u,v+\delta)$" , (u ,v + delta + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )+ text (r "$(x,y)$" , (x1 + 0.02 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )+ text ("$(x',y)$" , (x2 + 0.02 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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g += arrow ((0.3 ,0 ), (u + v + delta + 0.4 ,0 ), color = 'black' ,width = 1 )
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zticks = [u + v , z1 , z2 , u + v + delta + 0.05 ]
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zlocs = [u + v , z1 , z2 , u + v + delta ]
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- ztick_formatter = ["$u+v$" , "$z$" , "$z'$" , "$u+v+\delta$" ]
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+ ztick_formatter = ["$u+v$" , "$z$" , "$z'$" , r "$u+v+\delta$" ]
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for i in range (4 ):
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g += text (ztick_formatter [i ], (zticks [i ], - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )
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g += line ([(zlocs [i ],0 ),(zlocs [i ],0.03 )],color = 'black' ,thickness = 0.5 )
@@ -570,11 +570,11 @@ g += line([(u, y), (0, y)], color='black', linestyle=':')
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g += line ([(u , v ), (u + v , 0 )], color = 'black' , linestyle = ':' )+ line ([(x1 , y ), (z1 , 0 )], color = 'black' , linestyle = ':' )+ line ([(x2 , y ), (z2 , 0 )], color = 'black' , linestyle = ':' )+ line ([(u , y ), (u + v + delta , 0 )], color = 'black' , linestyle = ':' )
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g += point ([(u ,v ),(x1 ,y ),(x2 ,y )], color = 'black' ,size = 30 ,zorder = 10 ) #(u+delta,v),(u, v+delta)
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g += text ("$(u,v)$" , (u - 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'right' ,color = 'black' ,fontsize = 20 )+ text ("$(x,y)$" , (x1 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )+ text ("$(x',y)$" , (x2 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )
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- g += text ("$y=v+\delta$" , (u + 0.02 ,v + delta ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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+ g += text (r "$y=v+\delta$" , (u + 0.02 ,v + delta ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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g += arrow ((0.3 ,0 ), (u + v + delta + 0.4 ,0 ), color = 'black' ,width = 1 )
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zticks = [u + v , z1 , z2 , u + v + delta + 0.05 ]
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zlocs = [u + v , z1 , z2 , u + v + delta ]
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- ztick_formatter = ["$u+v$" , "$z$" , "$z'$" , "$u+v+\delta$" ]
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+ ztick_formatter = ["$u+v$" , "$z$" , "$z'$" , r "$u+v+\delta$" ]
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for i in range (4 ):
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g += text (ztick_formatter [i ], (zticks [i ], - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )
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g += line ([(zlocs [i ],0 ),(zlocs [i ],0.03 )],color = 'black' ,thickness = 0.5 )
@@ -596,11 +596,11 @@ g += line([(u-delta, y), (u, y)], color='black', linestyle=':')
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g += line ([(u , v ), (u + v , 0 )], color = 'black' , linestyle = ':' )+ line ([(x1 , y ), (z1 , 0 )], color = 'black' , linestyle = ':' )+ line ([(x2 , y ), (z2 , 0 )], color = 'black' , linestyle = ':' )+ line ([(u , y ), (u + y , 0 )], color = 'black' , linestyle = ':' )+ line ([(u - delta , y ), (u - delta + y , 0 )], color = 'black' , linestyle = ':' )
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g += point ([(u ,v ),(x1 ,y ),(x2 ,y )], color = 'black' ,size = 30 ,zorder = 10 ) #(u+delta,v),(u, v+delta)
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g += text ("$(u,v)$" , (u + 0.02 ,v ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )+ text ("$(x,y)$" , (x1 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )+ text ("$(x',y)$" , (x2 ,y + 0.02 ), axis_coords = False , vertical_alignment = 'bottom' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )
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- g += text ("$y=v+\ \ frac{\delta}{2}$" , (u + 0.02 ,y ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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+ g += text (r "$y=v+\frac{\delta}{2}$" , (u + 0.02 ,y ), axis_coords = False , vertical_alignment = 'center' , horizontal_alignment = 'left' ,color = 'black' ,fontsize = 20 )
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g += arrow ((0.3 ,0 ), (u + y + 0.4 ,0 ), color = 'black' ,width = 1 )
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zticks = [u + y - delta - 0.05 ,u + v , z1 , z2 , u + y + 0.05 ]
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zlocs = [u + y - delta , u + v , z1 , z2 , u + y ]
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- ztick_formatter = ["$u+v-\\ frac{\delta}{2}$" , "$u+v$" , "$z$" , "$z'$" , "$u+v+\ \ frac{\delta}{2}$" ]
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+ ztick_formatter = [r "$u+v-\frac{\delta}{2}$" , "$u+v$" , "$z$" , "$z'$" , r "$u+v+\frac{\delta}{2}$" ]
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for i in range (5 ):
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g += text (ztick_formatter [i ], (zticks [i ], - 0.01 ), axis_coords = False , vertical_alignment = 'top' , horizontal_alignment = 'center' ,color = 'black' ,fontsize = 20 )
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g += line ([(zlocs [i ],0 ),(zlocs [i ],0.03 )],color = 'black' ,thickness = 0.5 )
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