begin shift to nim code base

py/m.py

@@ -0,0 +1,107 @@
+#!/usr/bin/env python3
+import sys
+import readline
+
+from noether.math import *
+from noether.cli import *
+
+
+PROMPT = '[n]: '
+
+'''
+Pairwise orbit cumulative summation (cum orb) 
+'''
+def orb_cum(cum, orb):
+    for i in range(len(cum)):
+        cum[i] += orb[i]
+
+def main():
+    while True:
+        n = None
+        strlen_n = None
+        try:
+            uprint(PROMPT, color=Color.Blue, end='')
+            n = input()
+            strlen_n = len(n)
+            n = int(n)
+        except ValueError:
+            continue
+
+        # calculate phi of n
+        phi = totient(n)
+        # determine if n is prime
+        prime = n - 1 == phi
+        if prime:
+            uprint('', moveup=1, end='', flush=False)
+            column = len(PROMPT) + strlen_n + 1
+            sys.stdout.write(f'\033[{column}C')
+            uprint('[PRIME]', color=Color.Magenta, style=Color.Bold, flush=True)
+        # primitive root values
+        proot_v = []
+        # primitive root count
+        proot_c = 0
+        # cumulative sum of primitive root orbits
+        prorb_cum = []
+        
+        # calculate left padding to align i values
+        # lpadded = strlen_n
+        # calculate right padding to align len(orb) values
+        rpadded = len(str(phi))
+    
+        # find all invertible elements (skipped for now)
+        for a in range(n):
+            orb, ord, periodic = orbit(a, n)
+
+            # check if `a` is a primitive root
+            # NOTE: this should actually be `proot = (ord == phi(n))`
+            # proot = (ord + 1 == n)
+            proot = (ord == phi)
+            proot_c += proot 
+
+            # calculate padding
+            lpad = ' ' * (strlen_n - len(str(a)))
+            rpad = ' ' * (rpadded - len(str(ord)))
+            # calculate coloring
+            color_a = Color.Red
+            color_ord = None
+            color_orb = None
+            style_ord = None
+            style_orb = None                
+            if proot:
+                color_a = Color.Green
+                color_ord = Color.Yellow
+                color_orb = Color.Green
+                style_ord = Color.Bold
+                style_orb = Color.Bold
+                proot_v.append(a)
+                if not prorb_cum:
+                    prorb_cum = orb
+                else:
+                    orb_cum(prorb_cum, orb)
+            elif gcd(a, n) == 1:
+                color_a = Color.Yellow
+            
+            uprint(f'{lpad}{a}', color=color_a, style=Color.Bold, end=' ', flush=False)
+            uprint('->', end=' ', flush=False)
+            uprint(f'{ord}{rpad}', color=color_ord, style=style_ord, end=' ', flush=False)
+            uprint('|', end=' ', flush=False)
+            uprint(f'{orb}', color=color_orb, style=style_orb, flush=True)
+        uprint('Cum Orb:   ', end='', color=Color.Cyan)
+        uprint(f'{prorb_cum}', flush=True)
+        prorb_cum_mod = [x % n for x in prorb_cum]
+        uprint(f'           {prorb_cum_mod}', flush=True)
+
+        uprint('Roots:     ', end='', color=Color.Cyan)
+        uprint(proot_v, flush=True)
+        root_delta = [proot_v[i+1] - proot_v[i] for i in range(proot_c - 1)]
+        uprint('Delta:     ', end='', color=Color.Cyan)
+        uprint(root_delta, flush=True)
+        
+        uprint('Roots/Phi: ', end='', color=Color.Cyan)
+        uprint(f'{proot_c}/{phi}\n', flush=True)
+
+if __name__ == '__main__':
+    try:
+        main()
+    except (KeyboardInterrupt, EOFError):
+        pass