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## Remarks
## https://rosettacode.org/wiki/Imaginary_base_numbers#Python
import math
import re
def inv(c):
denom = c.real * c.real + c.imag * c.imag
return complex(c.real / denom, -c.imag / denom)
class QuaterImaginary:
twoI = complex(0, 2)
invTwoI = inv(twoI)
def __init__(self, str):
if not re.match("^[0123.]+$", str) or str.count(".") > 1:
raise Exception('Invalid base 2i number')
self.b2i = str
def toComplex(self):
pointPos = self.b2i.find(".")
posLen = len(self.b2i) if (pointPos < 0) else pointPos
sum = complex(0, 0)
prod = complex(1, 0)
for j in range(0, posLen):
k = int(self.b2i[posLen - 1 - j])
if k > 0:
sum = sum + prod * k
prod = prod * QuaterImaginary.twoI
if pointPos != -1:
prod = QuaterImaginary.invTwoI
for j in range(posLen + 1, len(self.b2i)):
k = int(self.b2i[j])
if k > 0:
sum = sum + prod * k
prod = prod * QuaterImaginary.invTwoI
return sum
def __str__(self):
return str(self.b2i)
def toQuaterImaginary(c):
if c.real == 0.0 and c.imag == 0.0:
return QuaterImaginary("0")
re = int(c.real)
im = int(c.imag)
fi = -1
ss = ""
while re != 0:
re, rem = divmod(re, -4)
if rem < 0:
rem = rem + 4
re = re + 1
ss = ss + str(rem) + "0"
if im != 0:
f = c.imag / 2
im = int(math.ceil(f))
f = -4 * (f - im)
index = 1
while im != 0:
im, rem = divmod(im, -4)
if rem < 0:
rem += 4
im += 1
if index < len(ss):
ss[index] = str(rem)
else:
ss = ss + "0" + str(rem)
index = index + 2
fi = int(f)
ss = ss[::-1]
if fi != -1:
ss = ss + "." + str(fi)
ss = ss.lstrip("0")
if ss[0] == ".":
ss = "0" + ss
return QuaterImaginary(ss)
def formatComplex(cInput):
strC = str(cInput)
strC = strC.replace("+", " + ")
strC = strC.replace("-", " - ")
return strC
for i in range(1, 17):
c1 = complex(i, 0)
q1 = toQuaterImaginary(c1)
c2 = q1.toComplex()
print (formatComplex(c1) + " <--> " + formatComplex(q1) + " <--> " + formatComplex(c2))
c1 = -c1
q1 = toQuaterImaginary(c1)
c2 = q1.toComplex()
print (formatComplex(c1) + " <--> " + formatComplex(q1) + " <--> " + formatComplex(c2))
print ()
print ()
for i in range(1, 17):
c1 = complex(0, i)
q1 = toQuaterImaginary(c1)
c2 = q1.toComplex()
print (formatComplex(c1) + " <--> " + formatComplex(q1) + " <--> " + formatComplex(c2))
c1 = -c1
q1 = toQuaterImaginary(c1)
c2 = q1.toComplex()
print (formatComplex(c1) + " <--> " + formatComplex(q1) + " <--> " + formatComplex(c2))
print ()
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