P-Adic numbers, basic: Difference between revisions

Content added Content deleted

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@@ Line 822: / Line 822: @@
 var data = [
-    /* rational reconstruction limits are relative to the precision */
+    /* rational reconstruction depends on the precision
+       until the dsum-loop overflows */
     [2, 1, 2, 4, 1, 1],
     [4, 1, 2, 4, 3, 1],
     [4, 1, 2, 5, 3, 1],
     [4, 9, 5, 4, 8, 9],
-    [-7, 5, 7, 4, 99, 70],
     [26, 25, 5, 4, -109, 125],
     [49, 2, 7, 6, -4851, 2],
     [-9, 5, 3, 8, 27, 7],
     [5, 19, 2, 12, -101, 384],
-    /* three decadic pairs */
+    /* two decadic pairs */
-    [6, 7, 10, 7, -5, 7],
+    [2, 7, 10, 7, -1, 7],
-    [2, 7, 10, 7, -3, 7],
     [34, 21, 10, 9, -39034, 791],
-    /*familiar digits*/
+    /* familiar digits */
     [11, 4, 2, 43, 679001, 207],
-    [11, 4, 3, 27, 679001, 207],
+    [-8, 9, 23, 9, 302113, 92],
-    [11, 4, 11, 13, 679001, 207],
-    [-22, 7, 2, 37, 46071, 379],
     [-22, 7, 3, 23, 46071, 379],
-    [-22, 7, 7, 13, 46071, 379],
+    [-22, 7, 32749, 3, 46071, 379],
-    [-101, 109, 2, 40, 583376, 6649],
+    [35, 61, 5, 20, 9400, 109],
     [-101, 109, 61, 7, 583376, 6649],
-    [-101, 109, 32749, 3, 583376, 6649]
+    [-25, 26, 7, 13, 5571, 137],
+    [1, 4, 7, 11, 9263, 2837],
+    [122, 407, 7, 11, -517, 1477],
+    /* more subtle */
+    [5, 8, 7, 11, 353, 30809]
 ]
@@ Line 905: / Line 906: @@
 1 3 3
 /3
--7/5 + 0(7^4)
-5 4 0
-/70 + 0(7^4)
-5 0. 5
-+ =
-2 0. 5
-/70
 /25 + 0(5^4)
@@ Line 946: / Line 939: @@
 /7296
 /7 + 0(10^7)
-1 4 2 8 5 8
+7 1 4 2 8 6
--5/7 + 0(10^7)
+-1/7 + 0(10^7)
-7 1 4 2 8 5
+1 4 2 8 5 7
 + =
 8 5 7 1 4 3
 /7
-/7 + 0(10^7)
-7 1 4 2 8 6
--3/7 + 0(10^7)
-4 2 8 5 7 1
-+ =
-1 4 2 8 5 7
--1/7
 /21 + 0(10^9)
@@ Line 978: / Line 963: @@
 2718281/828
-/4 + 0(3^27)
+-8/9 + 0(23^9)
+12 17 20 10 5 2 12 17
-0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 1 2
-/207 + 0(3^27)
+/92 + 0(23^9)
+17 5 17 6 0 10 12. 2
-1 0 2 2 0 1 2 2 1 2 1 1 0 2 2 1 0 1 1 0 0 2 2 2. 0 1
 + =
+12 3 4 11 3 0 6. 2
-2 0 0 1 1 1 0 1 2 1 2 0 1 2 0 0 1 0 1 2 1 2 1 1. 0 1
 2718281/828
-/4 + 0(11^13)
-2 8 2 8 2 8 2 8 2 8 3 0
-/207 + 0(11^13)
-7 9 5 6 10 6 3 6 4 2 10 9
-+ =
-10 6 8 4 2 3 6 3 7 0 2 9
-2718281/828
--22/7 + 0(2^37)
-0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0
-/379 + 0(2^37)
-1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1
-+ =
-0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1
-/2653
 -22/7 + 0(3^23)
@@ Line 1,010: / Line 979: @@
 /2653
--22/7 + 0(7^13)
+-22/7 + 0(32749^3)
+18713 23389
-6 6 6 6 6 6 6 6 6 6 3. 6
-/379 + 0(7^13)
+/379 + 0(32749^3)
+8727 10145
-4 1 6 6 5 1 2 2 1 3 2 4
 + =
+27441 785
-1 6 6 5 1 2 2 1 3 2 0. 6
 /2653
--101/109 + 0(2^40)
+/61 + 0(5^20)
-1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1
+3 2 3 0 2 4 1 3 3 0 0 4 0 2 2 1 2 2 0
-/6649 + 0(2^40)
+/109 + 0(5^20)
-0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0
+1 4 4 1 2 3 4 4 3 4 1 1 3 1 1 2 4 0 0
 + =
-0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1
+0 2 2 2 0 3 1 3 1 4 2 0 3 3 3 4 1 2 0
 /6649
@@ Line 1,034: / Line 1,003: @@
 /6649
--101/109 + 0(32749^3)
+-25/26 + 0(7^13)
+6 5 0 5 4 4 0 1 6 1 2 2
-21031 15322
-/6649 + 0(32749^3)
+/137 + 0(7^13)
+2 4 1 4 5 4 2 2 5 5 3 5
-13766 16445
 + =
+2 2 2 3 3 1 2 4 4 6 6 0
-2048 31767
+/3562
-/6649
+/4 + 0(7^11)
+5 1 5 1 5 1 5 1 5 2
+/2837 + 0(7^11)
+5 6 6 0 3 2 0 4 4 1
++ =
+4 1 4 2 1 3 5 6 2 3
+/11348
+/407 + 0(7^11)
+2 0 3 0 6 2 4 4 4 3
+-517/1477 + 0(7^11)
+2 3 4 3 5 4 6 4 1. 1
++ =
+2 6 5 3 1 2 4 1 4. 1
+-27584/90671
+/8 + 0(7^11)
+2 4 2 4 2 4 2 4 2 5
+/30809 + 0(7^11)
+3 6 6 3 6 4 3 4 5 5
++ =
+6 4 2 1 2 1 6 2 1 3
+/10977
 </pre>