Initial data commit

2023-07-01 11:58:00 -04:00 · 2023-07-01 11:58:00 -04:00 · f23f22d71c
commit f23f22d71c
parent 72d218235f
199087 changed files with 3378941 additions and 0 deletions
--- a/Task/Tonelli-Shanks-algorithm/11l/tonelli-shanks-algorithm.11l
+++ b/Task/Tonelli-Shanks-algorithm/11l/tonelli-shanks-algorithm.11l
@ -0,0 +1,45 @@
+F legendre(a, p)
+   R pow(a, (p - 1) I/ 2, p)
+
+F tonelli(n, p)
+   assert(legendre(n, p) == 1, ‘not a square (mod p)’)
+   V q = p - 1
+   V s = 0
+   L q % 2 == 0
+      q I/= 2
+      s++
+   I s == 1
+      R pow(n, (p + 1) I/ 4, p)
+   V z = 2
+   L
+      I p - 1 == legendre(z, p)
+         L.break
+      z++
+   V c = pow(z, q, p)
+   V r = pow(n, (q + 1) I/ 2, p)
+   V t = pow(n, q, p)
+   V m = s
+   V t2 = BigInt(0)
+   L (t - 1) % p != 0
+      t2 = (t * t) % p
+      V i = 1
+      L(ii) 1 .< m
+         I (t2 - 1) % p == 0
+            i = ii
+            L.break
+         t2 = (t2 * t2) % p
+      V b = pow(c, Int64(1 << (m - i - 1)), p)
+      r = (r * b) % p
+      c = (b * b) % p
+      t = (t * c) % p
+      m = i
+   R r
+
+V ttest = [(BigInt(10), BigInt(13)), (BigInt(56), BigInt(101)), (BigInt(1030), BigInt(10009)), (BigInt(44402), BigInt(100049)),
+           (BigInt(665820697), BigInt(1000000009)), (BigInt(881398088036), BigInt(1000000000039)),
+           (BigInt(‘41660815127637347468140745042827704103445750172002’), BigInt(10) ^ 50 + 577)]
+L(n, p) ttest
+   V r = tonelli(n, p)
+   assert((r * r - n) % p == 0)
+   print(‘n = #. p = #.’.format(n, p))
+   print("\t  roots : #. #.".format(r, p - r))