This file is indexed.

/usr/lib/open-axiom/input/cdraw.input is in open-axiom-test 1.4.1+svn~2626-2ubuntu2.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
--Copyright The Numerical Algorithms Group Limited 1994.

-- complex surface and vector field drawing by SCM
-- complex surface vector field drawing
 
C := Complex DoubleFloat
S := Segment DoubleFloat
PC := Record(rr:DoubleFloat, th:DoubleFloat)
 
realSteps: PI := 25    -- the number of steps in the real direction
imagSteps: PI := 25    -- the number of steps in the imaginary direction
clipValue: DoubleFloat := 10    -- the maximum length of a vector to draw
 

-- Draw a complex function as a height field
-- uses the complex norm as the height and the complex argument as the color
-- optionally it will draw arrows on the surface indicating the direction
-- of the complex argument

-- sample call:
--   f: C -> C
--   f z == exp(1/z)
--   drawComplex(f, 0.3..3, 0..2*%pi, false)

-- parameter descriptions:
--   f:  the function to draw
--   rRange: the range of the real values
--   imagRange: the range of imaginary values
drawComplex(f: C -> C, realRange: S, imagRange: S): VIEW3D ==
  free realSteps, imagSteps
  delReal := (hi(realRange) - lo(realRange))/realSteps
  delImag := (hi(imagRange) - lo(imagRange))/imagSteps
  funTable: ARRAY2(PC) := new(realSteps+1, imagSteps+1, [0,0]$PC)
  real := lo(realRange)
  for i in 1..realSteps+1 repeat
    imag := lo(imagRange)
    for j in 1..imagSteps+1 repeat
      z := f complex(real, imag)
      funTable(i,j) := [clipFun(sqrt norm z), argument(z)]$PC
      imag := imag + delImag
    real := real + delReal
  llp:List List Point DoubleFloat := []
  real := lo(realRange)
  for i in 1..realSteps+1 repeat
    imag := lo(imagRange)
    lp:List Point DoubleFloat := []
    for j in 1..imagSteps+1 repeat
      lp := cons(point [real,imag, funTable(i,j).rr, 
                                    funTable(i,j).th] ,lp)
      imag := imag + delImag
    real := real + delReal
    llp := cons(reverse! lp, llp)
  llp := reverse! llp
  space := mesh(llp)$ThreeSpace(DoubleFloat)
  makeViewport3D(space, "Complex Function")$VIEW3D

-- draw a complex vector field
-- these vector fields should be viewed from the top by pressing the
-- "XY" translate button on the VIEW3D control panel
 
-- parameters:
--   f: the mapping from C to C which we will draw
--   realRange: the range of the reals
--   tRange: the range of the imaginaries
 
-- sample call:
--    f z == sin z
--    drawComplexVectorField(f, -2..2, -2..2)
-- call the functions 'setRealSteps' and 'setImagSteps' to change the
-- number of arrows drawn in each direction.
 
drawComplexVectorField(f: C -> C, realRange: S, imagRange: S): VIEW3D ==
  -- compute the steps size of the grid
  delReal := (hi(realRange) - lo(realRange))/realSteps
  delImag := (hi(imagRange) - lo(imagRange))/imagSteps
  -- create the space to hold the arrows
  space := create3Space()$ThreeSpace DoubleFloat
  real := lo(realRange)
  for i in 1..realSteps+1 repeat
    imag := lo(imagRange)
    for j in 1..imagSteps+1 repeat
      -- compute the function
      z := f complex(real, imag)
      -- get the direction of the arrow
      arg := argument z
      -- get the length of the arrow
      len := clipFun(sqrt norm z)
      -- create point at the base of the arrow
      p1 :=  point [real, imag, 0.0@DoubleFloat, arg]
      -- scale the arrow length so it isn't too long
      scaleLen := delReal * len
      -- create the point at the top of the arrow
      p2 := point [p1.1 + scaleLen*cos(arg), p1.2 + scaleLen*sin(arg), 
                   0.0@DoubleFloat, arg]
      -- make the pointer at the top of the arrow
      arrow := makeArrow(p1, p2, scaleLen, arg)
      -- add the line segments in the arrow to the space
      for a in arrow repeat curve(space, a)$ThreeSpace DoubleFloat
      imag := imag + delImag
    real := real + delReal
  -- draw the vector feild
  makeViewport3D(space, "Complex Vector Field")$VIEW3D
 
-- relative size of the arrow head compared to the length of the arrow
arrowScale := 0.25@DoubleFloat
 
-- angle of the arrow head
arrowAngle := %pi-%pi/10.0@DoubleFloat
 
-- Add an arrow head to a line segment, which starts at 'p1', ends at 'p2',
-- has length 'len', and and angle 'arg'.  We pass 'len' and 'arg' as
-- arguments since thet were already computed by the calling program
makeArrow(p1, p2, len, arg) ==
  c1 := cos(arg + arrowAngle) 
  s1 := sin(arg + arrowAngle)
  c2 := cos(arg - arrowAngle) 
  s2 := sin(arg - arrowAngle)
  p3 := point [p2.1 + c1*arrowScale*len, p2.2 + s1*arrowScale*len, 
               p2.3, p2.4]
  p4 := point [p2.1 + c2*arrowScale*len, p2.2 + s2*arrowScale*len, 
               p2.3, p2.4]
  [[p1, p2, p3], [p2, p4]]
 
-- set the number of steps to use in the real direction
setRealSteps(n) ==
  free realSteps
  realSteps := n
 
-- set the number of steps to use in the imaginary direction
setImagSteps(n) ==
  free imagSteps
  imagSteps := n
 
-- set the maximum length of a vector 
setClipValue clip ==
  free clipValue
  clipValue := clip

-- clip a value in the interval (-clip...clip)
clipFun(x:DoubleFloat):DoubleFloat == 
  min(max(x, -clipValue), clipValue)