share/pytranslate/cantorr.py

   1 from pytranslate import *
   2
   3 #########################
   4 ### Cantorr2 Function ###
   5 #########################
   6 def block17340(v):
   7     v = Stack({}, v)
   8     if ((v["x"] > 0) and (v["x"] <= (1 / 3))):
   9             v["ret"] = cantorr2((3 * v["x"]), (v["n"] + (-1)))
  10     if (((1 / 3) < v["x"]) and (v["x"] < (2 / 3))):
  11             v["ret"] = 1
  12     if ((v["x"] >= (2 / 3)) and (v["x"] < 1)):
  13             v["ret"] = (1 + cantorr2(((3 * v["x"]) + (-2)), (v["n"] + (-1))))
  14     return((v["ret"] / 2))
  15 def cantorr2(x, n, v = v):
  16     v = Stack({}, v)
  17     v.ins({"x" : x, "n" : n})
  18     v.ins({"ret" : 0, "k" : 0})
  19     if not(f["numberp"](v["x"])):
  20             return(f["cantorr2"](v["x"], v["n"]))
  21     if (v["x"] == 0):
  22             return(0)
  23     if (v["x"] == 1):
  24             return(1)
  25     f["print"](v["x"], v["n"])
  26     return((block17340(v) if (v["n"] > 0) else v["x"]))
  27 f["cantorr2"] = cantorr2
  28
  29
  30 #########################
  31 ### Cantorri Function ###
  32 #########################
  33 def block34784(v):
  34     v = Stack({}, v)
  35     v["ret"] = 0
  36     return(v["ret"])
  37 def cantorri(x, n, v = v):
  38     v = Stack({}, v)
  39     v.ins({"x" : x, "n" : n})
  40     v.ins({"ret" : 1, "q" : None})
  41     if not(f["numberp"](v["x"])):
  42             return(f["cantorri"](v["x"], v["n"]))
  43     if ((v["x"] == 0) or (v["x"] == 1)):
  44             return(1)
  45     v["x"] = f["mod"](v["x"], 1)
  46     for v["i"] in range(1, (v["n"] + 1)):
  47         v["x"] = (3 * v["x"])
  48         v["q"] = math.floor(v["x"])
  49
  50         if (v["q"] == 1):
  51                     return(block34784(v))
  52         v["x"] = (v["x"] + (-v["q"]))
  53     return(v["ret"])
  54 f["cantorri"] = cantorri
  55
  56 #########################
  57 ### Cantorrd Function ###
  58 #########################
  59 def block47665(v):
  60     v = Stack({}, v)
  61     if ((v["x"] > 0) and (v["x"] <= (1 / 3))):
  62             v["ret"] = cantorrd((3 * v["x"]), (v["n"] + (-1)))
  63     if (((1 / 3) < v["x"]) and (v["x"] < (2 / 3))):
  64             v["ret"] = 0
  65     if (((2 / 3) <= v["x"]) and (v["x"] < 1)):
  66             v["ret"] = cantorrd(((3 * v["x"]) + (-2)), (v["n"] + (-1)))
  67     return(v["ret"])
  68 def cantorrd(x, *n, v = v):
  69     v = Stack({}, v)
  70     v.ins({"x" : x, "n" : list(n)})
  71     v.ins({"ret" : 0})
  72     if f["emptyp"](v["n"]):
  73             v["n"] = v["fpprec"]
  74     else:
  75             v["n"] = f["first"](v["n"])
  76     if not(f["numberp"](v["x"])):
  77             return(f["cantorrd"](v["x"], v["n"]))
  78     if (v["x"] == 0):
  79             return(1)
  80     if (v["x"] == 1):
  81             return(1)
  82     v["x"] = f["mod"](v["x"], 1)
  83     return((block47665(v) if (v["n"] > 0) else 1))
  84 f["cantorrd"] = cantorrd
  85
  86 ########################
  87 ## Cantorr_p Function ##
  88 ########################
  89 def block71117(v):
  90     v = Stack({}, v)
  91     v["p"] = f["denom"](v["b"])
  92     v["q"] = f["num"](v["b"])
  93     if ((v["x"] > 0) and (v["x"] < v["b"])):
  94             v["ret"] = cantorr_p((v["p"] * v["x"]), v["b"], (v["n"] + (-1)))
  95     if ((v["b"] <= v["x"]) and (v["x"] <= (1 + (-v["b"])))):
  96             v["ret"] = 1
  97     if ((v["x"] > (1 + (-v["b"]))) and (v["x"] < 1)):
  98             v["ret"] = (1 + cantorr_p(((v["p"] * v["x"]) + (-(v["p"] + (-v["q"])))), v["b"], (v["n"] + (-1))))
  99     return((v["ret"] / 2))
 100 def cantorr_p(x, b, n, v = v):
 101     v = Stack({}, v)
 102     v.ins({"x" : x, "b" : b, "n" : n})
 103     v.ins({"ret" : 0, "p" : None, "q" : None, "d" : None})
 104     if not(f["numberp"](v["x"])):
 105             return(f["cantorr_p"](v["x"], v["b"], v["n"]))
 106     if (v["x"] == 0):
 107             return(0)
 108     if (v["x"] == 1):
 109             return(1)
 110     if (v["b"] > (1 / 2)):
 111             v["b"] = (1 + (-f["mod"](v["b"], 1)))
 112     return((block71117(v) if (v["n"] > 0) else v["x"]))
 113
 114 #########################
 115 ## gcantorseq Function ##
 116 #########################
 117 def block85290(v):
 118     v = Stack({}, v)
 119     v["s"] = f["append"](gcantorseq(v["u"], (v["q"] + (-(v["p"] / 2))), (v["p"] * v["r"]), v["r"], (v["n"] + (-1))), gcantorseq((v["q"] + (v["p"] / 2)), v["w"], (v["p"] * v["r"]), v["r"], (v["n"] + (-1))))
 120     return(v["s"])
 121 def gcantorseq(u, w, p, r, n, v = v):
 122     v = Stack({}, v)
 123     v.ins({"u" : u, "w" : w, "p" : p, "r" : r, "n" : n})
 124     v.ins({"s" : None, "q" : None})
 125
 126     if not(f["integerp"](v["n"])):
 127             return(None)
 128     v["q"] = ((v["u"] + v["w"]) / 2)
 129     v["s"] = [v["u"], v["w"]]
 130     return((block85290(v) if (v["n"] > 1) else v["s"]))
 131
 132 ########################
 133 ## cantorseq Function ##
 134 ########################
 135 def cantorseq(n, v = v):
 136     v = Stack({}, v)
 137     v.ins({"n" : n})
 138     v.ins({"seq" : [0, 1], "l" : [], "r" : []})
 139     if not(f["integerp"](v["n"])):
 140             return(f["cantorseq"](v["n"]))
 141     for v["k"] in range(1, ((v["n"] + (-1)) + 1)):
 142         v["r"] = v["seq"]
 143         # Map divide using Lambda in the following
 144         v["l"] = (v["r"] / 3)
 145         v["r"] = f["reverse"]((1 + (-v["l"])))
 146         v["seq"] = f["append"](v["l"], v["r"])
 147     return(v["seq"])
 148
 149 f["plot2d"](lambda x, v = Stack({}, v): f["cantorr2"](x, 10), ['x', 0, 1])
 150 f["plot2d"](lambda x, v = Stack({}, v): f["cantorrd"](x, 10), ['x', 0, 1])
 151 f["plot2d"](lambda x, v = Stack({}, v): f["cantorri"](x, 10), ['x', 0, 1])