Initial data commit

Task/Multiplicative-order/11l/multiplicative-order.11l

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+T PExp
+   BigInt prime
+   Int exp
+   F (prime, exp)
+      .prime = prime
+      .exp = exp
+
+F isqrt(self)
+   V b = self
+   L
+      V a = b
+      b = (self I/ a + a) I/ 2
+      I b >= a
+         R a
+
+F factor(BigInt n)
+   [PExp] pf
+   V nn = n
+   V b = 0
+   L ((nn % 2) == 0)
+      nn I/= 2
+      b++
+
+   I b > 0
+      pf [+]= PExp(BigInt(2), b)
+
+   V s = isqrt(nn)
+   V d = BigInt(3)
+   L nn > 1
+      I d > s
+         d = nn
+      V e = 0
+      L
+         V (div, rem) = divmod(nn, d)
+         I bit_length(rem) > 0
+            L.break
+         nn = div
+         e++
+
+      I e > 0
+         pf [+]= PExp(d, e)
+         s = isqrt(nn)
+
+      d += 2
+
+   R pf
+
+F moBachShallit58(BigInt a, BigInt n; pf)
+   V n1 = n - 1
+   V mo = BigInt(1)
+   L(pe) pf
+      V y = n1 I/ pow(pe.prime, BigInt(pe.exp))
+      V o = 0
+      V x = pow(a, y, n)
+      L x > 1
+         x = pow(x, pe.prime, n)
+         o++
+      V o1 = pow(pe.prime, BigInt(o))
+      o1 I/= gcd(mo, o1)
+      mo *= o1
+   R mo
+
+F moTest(a, n)
+   I bit_length(a) < 100
+      print(‘ord(’a‘)’, end' ‘’)
+   E
+      print(‘ord([big])’, end' ‘’)
+   print(‘ mod ’n‘ = ’moBachShallit58(a, n, factor(n - 1)))
+
+moTest(37, 3343)
+
+moTest(pow(BigInt(10), 100) + 1, 7919)
+moTest(pow(BigInt(10), 1000) + 1, 15485863)
+moTest(pow(BigInt(10), 10000) - 1, BigInt(22801763489))
+
+moTest(1511678068, 7379191741)
+moTest(BigInt(‘3047753288’), BigInt(‘2257683301’))