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