optimize ux

chapter-03/binseq/binseq.py

@@ -0,0 +1,11 @@
+from collections.abc import Callable
+
+class REAL:
+    def __init__(self, f: Callable[[int], str]) -> None:
+        self.binseq = f
+
+    def as_string(self, w: int) -> str:
+        s = ""
+        for n in range(w):
+            s += self.binseq(n)
+        return s

chapter-03/binseq/main.py

@@ -0,0 +1,20 @@
+from binseq import REAL
+from math import isqrt  # integer sqrt
+
+
+def one_third(n):
+    if n == 1: return "."
+    if n % 2 == 0: return "0"
+    return "1"
+
+
+def irrational(n):
+    if n == 1: return "."
+    if n != isqrt(n) * isqrt(n): return "1"
+    return "0"
+
+
+x = REAL(one_third)
+y = REAL(irrational)
+
+print("x: " + x.as_string(50) + "\ny: " + y.as_string(50))

chapter-03/dedekint/dedekint.py

@@ -0,0 +1,6 @@
+from collections.abc import Callable
+from gmpy2 import mpq
+
+
+class REAL:
+    def __init__(self, f: Callable[[mpq], bool]): self.smaller=f

chapter-03/dedekint/main.py

@@ -0,0 +1,26 @@
+from dedekint import REAL
+# mpq for rational numbers
+from gmpy2 import mpq
+
+
+def sqrt_two(q):
+    if q <= 0 or q * q < 2: return True
+    return False
+
+
+x = REAL(sqrt_two)
+
+print("1.41422 is smaller:", x.smaller(mpq(141422, 100000)))
+print("1.41421 is smaller:", x.smaller(mpq(141421, 100000)))
+
+k = 0
+n = 1
+z = 0
+
+for k in range(100):
+    if x.smaller(mpq(z, n)):
+        z = z + 1
+    else:
+        print(z, "/", n)
+        z = (z - 1) * 10
+        n = n * 10