Tue Oct 19 11:32:47 2021 diophantine_nd_test(): Python version: 3.6.9 Test diophantine_nd() diophantine_nd_nonnegative_test diophantine_nd_nonnegative returns nonnegative solutions of a Diophantine equation in N variables. 2 * x 1 + 3 * x 2 = 18 4 solutions found. 0 : 2 * 9.0 + 3 * 0.0 = 18 1 : 2 * 6.0 + 3 * 2.0 = 18 2 : 2 * 3.0 + 3 * 4.0 = 18 3 : 2 * 0.0 + 3 * 6.0 = 18 6 * x 1 + 3 * x 2 + 13 * x 3 = 16 1 solutions found. 0 : 6 * 0.0 + 3 * 1.0 + 13 * 1.0 = 16 12 * x 1 + 9 * x 2 + 7 * x 3 = 60 4 solutions found. 0 : 12 * 5.0 + 9 * 0.0 + 7 * 0.0 = 60 1 : 12 * 2.0 + 9 * 4.0 + 7 * 0.0 = 60 2 : 12 * 1.0 + 9 * 3.0 + 7 * 3.0 = 60 3 : 12 * 0.0 + 9 * 2.0 + 7 * 6.0 = 60 2 * x 1 + 3 * x 2 + 5 * x 3 + 6 * x 4 = 24 31 solutions found. 0 : 2 * 12.0 + 3 * 0.0 + 5 * 0.0 + 6 * 0.0 = 24 1 : 2 * 9.0 + 3 * 2.0 + 5 * 0.0 + 6 * 0.0 = 24 2 : 2 * 9.0 + 3 * 0.0 + 5 * 0.0 + 6 * 1.0 = 24 3 : 2 * 8.0 + 3 * 1.0 + 5 * 1.0 + 6 * 0.0 = 24 4 : 2 * 7.0 + 3 * 0.0 + 5 * 2.0 + 6 * 0.0 = 24 5 : 2 * 6.0 + 3 * 4.0 + 5 * 0.0 + 6 * 0.0 = 24 6 : 2 * 6.0 + 3 * 2.0 + 5 * 0.0 + 6 * 1.0 = 24 7 : 2 * 6.0 + 3 * 0.0 + 5 * 0.0 + 6 * 2.0 = 24 8 : 2 * 5.0 + 3 * 3.0 + 5 * 1.0 + 6 * 0.0 = 24 9 : 2 * 5.0 + 3 * 1.0 + 5 * 1.0 + 6 * 1.0 = 24 10 : 2 * 4.0 + 3 * 2.0 + 5 * 2.0 + 6 * 0.0 = 24 11 : 2 * 4.0 + 3 * 0.0 + 5 * 2.0 + 6 * 1.0 = 24 12 : 2 * 3.0 + 3 * 6.0 + 5 * 0.0 + 6 * 0.0 = 24 13 : 2 * 3.0 + 3 * 4.0 + 5 * 0.0 + 6 * 1.0 = 24 14 : 2 * 3.0 + 3 * 2.0 + 5 * 0.0 + 6 * 2.0 = 24 15 : 2 * 3.0 + 3 * 1.0 + 5 * 3.0 + 6 * 0.0 = 24 16 : 2 * 3.0 + 3 * 0.0 + 5 * 0.0 + 6 * 3.0 = 24 17 : 2 * 2.0 + 3 * 5.0 + 5 * 1.0 + 6 * 0.0 = 24 18 : 2 * 2.0 + 3 * 3.0 + 5 * 1.0 + 6 * 1.0 = 24 19 : 2 * 2.0 + 3 * 1.0 + 5 * 1.0 + 6 * 2.0 = 24 20 : 2 * 2.0 + 3 * 0.0 + 5 * 4.0 + 6 * 0.0 = 24 21 : 2 * 1.0 + 3 * 4.0 + 5 * 2.0 + 6 * 0.0 = 24 22 : 2 * 1.0 + 3 * 2.0 + 5 * 2.0 + 6 * 1.0 = 24 23 : 2 * 1.0 + 3 * 0.0 + 5 * 2.0 + 6 * 2.0 = 24 24 : 2 * 0.0 + 3 * 8.0 + 5 * 0.0 + 6 * 0.0 = 24 25 : 2 * 0.0 + 3 * 6.0 + 5 * 0.0 + 6 * 1.0 = 24 26 : 2 * 0.0 + 3 * 4.0 + 5 * 0.0 + 6 * 2.0 = 24 27 : 2 * 0.0 + 3 * 3.0 + 5 * 3.0 + 6 * 0.0 = 24 28 : 2 * 0.0 + 3 * 2.0 + 5 * 0.0 + 6 * 3.0 = 24 29 : 2 * 0.0 + 3 * 1.0 + 5 * 3.0 + 6 * 1.0 = 24 30 : 2 * 0.0 + 3 * 0.0 + 5 * 0.0 + 6 * 4.0 = 24 2 * x 1 + 3 * x 2 + 5 * x 3 + 6 * x 4 + 7 * x 5 = 35 150 solutions found. 0 : 2 * 16.0 + 3 * 1.0 + 5 * 0.0 + 6 * 0.0 + 7 * 0.0 = 35 1 : 2 * 15.0 + 3 * 0.0 + 5 * 1.0 + 6 * 0.0 + 7 * 0.0 = 35 2 : 2 * 14.0 + 3 * 0.0 + 5 * 0.0 + 6 * 0.0 + 7 * 1.0 = 35 3 : 2 * 13.0 + 3 * 3.0 + 5 * 0.0 + 6 * 0.0 + 7 * 0.0 = 35 4 : 2 * 13.0 + 3 * 1.0 + 5 * 0.0 + 6 * 1.0 + 7 * 0.0 = 35 5 : 2 * 12.0 + 3 * 2.0 + 5 * 1.0 + 6 * 0.0 + 7 * 0.0 = 35 6 : 2 * 12.0 + 3 * 0.0 + 5 * 1.0 + 6 * 1.0 + 7 * 0.0 = 35 7 : 2 * 11.0 + 3 * 2.0 + 5 * 0.0 + 6 * 0.0 + 7 * 1.0 = 35 8 : 2 * 11.0 + 3 * 1.0 + 5 * 2.0 + 6 * 0.0 + 7 * 0.0 = 35 9 : 2 * 11.0 + 3 * 0.0 + 5 * 0.0 + 6 * 1.0 + 7 * 1.0 = 35 10 : 2 * 10.0 + 3 * 5.0 + 5 * 0.0 + 6 * 0.0 + 7 * 0.0 = 35 11 : 2 * 10.0 + 3 * 3.0 + 5 * 0.0 + 6 * 1.0 + 7 * 0.0 = 35 12 : 2 * 10.0 + 3 * 1.0 + 5 * 1.0 + 6 * 0.0 + 7 * 1.0 = 35 13 : 2 * 10.0 + 3 * 1.0 + 5 * 0.0 + 6 * 2.0 + 7 * 0.0 = 35 14 : 2 * 10.0 + 3 * 0.0 + 5 * 3.0 + 6 * 0.0 + 7 * 0.0 = 35 15 : 2 * 9.0 + 3 * 4.0 + 5 * 1.0 + 6 * 0.0 + 7 * 0.0 = 35 16 : 2 * 9.0 + 3 * 2.0 + 5 * 1.0 + 6 * 1.0 + 7 * 0.0 = 35 17 : 2 * 9.0 + 3 * 1.0 + 5 * 0.0 + 6 * 0.0 + 7 * 2.0 = 35 18 : 2 * 9.0 + 3 * 0.0 + 5 * 2.0 + 6 * 0.0 + 7 * 1.0 = 35 19 : 2 * 9.0 + 3 * 0.0 + 5 * 1.0 + 6 * 2.0 + 7 * 0.0 = 35 20 : 2 * 8.0 + 3 * 4.0 + 5 * 0.0 + 6 * 0.0 + 7 * 1.0 = 35 21 : 2 * 8.0 + 3 * 3.0 + 5 * 2.0 + 6 * 0.0 + 7 * 0.0 = 35 22 : 2 * 8.0 + 3 * 2.0 + 5 * 0.0 + 6 * 1.0 + 7 * 1.0 = 35 23 : 2 * 8.0 + 3 * 1.0 + 5 * 2.0 + 6 * 1.0 + 7 * 0.0 = 35 24 : 2 * 8.0 + 3 * 0.0 + 5 * 1.0 + 6 * 0.0 + 7 * 2.0 = 35 25 : 2 * 8.0 + 3 * 0.0 + 5 * 0.0 + 6 * 2.0 + 7 * 1.0 = 35 26 : 2 * 7.0 + 3 * 7.0 + 5 * 0.0 + 6 * 0.0 + 7 * 0.0 = 35 27 : 2 * 7.0 + 3 * 5.0 + 5 * 0.0 + 6 * 1.0 + 7 * 0.0 = 35 28 : 2 * 7.0 + 3 * 3.0 + 5 * 1.0 + 6 * 0.0 + 7 * 1.0 = 35 29 : 2 * 7.0 + 3 * 3.0 + 5 * 0.0 + 6 * 2.0 + 7 * 0.0 = 35 30 : 2 * 7.0 + 3 * 2.0 + 5 * 3.0 + 6 * 0.0 + 7 * 0.0 = 35 31 : 2 * 7.0 + 3 * 1.0 + 5 * 1.0 + 6 * 1.0 + 7 * 1.0 = 35 32 : 2 * 7.0 + 3 * 1.0 + 5 * 0.0 + 6 * 3.0 + 7 * 0.0 = 35 33 : 2 * 7.0 + 3 * 0.0 + 5 * 3.0 + 6 * 1.0 + 7 * 0.0 = 35 34 : 2 * 7.0 + 3 * 0.0 + 5 * 0.0 + 6 * 0.0 + 7 * 3.0 = 35 35 : 2 * 6.0 + 3 * 6.0 + 5 * 1.0 + 6 * 0.0 + 7 * 0.0 = 35 36 : 2 * 6.0 + 3 * 4.0 + 5 * 1.0 + 6 * 1.0 + 7 * 0.0 = 35 37 : 2 * 6.0 + 3 * 3.0 + 5 * 0.0 + 6 * 0.0 + 7 * 2.0 = 35 38 : 2 * 6.0 + 3 * 2.0 + 5 * 2.0 + 6 * 0.0 + 7 * 1.0 = 35 39 : 2 * 6.0 + 3 * 2.0 + 5 * 1.0 + 6 * 2.0 + 7 * 0.0 = 35 40 : 2 * 6.0 + 3 * 1.0 + 5 * 4.0 + 6 * 0.0 + 7 * 0.0 = 35 41 : 2 * 6.0 + 3 * 1.0 + 5 * 0.0 + 6 * 1.0 + 7 * 2.0 = 35 42 : 2 * 6.0 + 3 * 0.0 + 5 * 2.0 + 6 * 1.0 + 7 * 1.0 = 35 43 : 2 * 6.0 + 3 * 0.0 + 5 * 1.0 + 6 * 3.0 + 7 * 0.0 = 35 44 : 2 * 5.0 + 3 * 6.0 + 5 * 0.0 + 6 * 0.0 + 7 * 1.0 = 35 45 : 2 * 5.0 + 3 * 5.0 + 5 * 2.0 + 6 * 0.0 + 7 * 0.0 = 35 46 : 2 * 5.0 + 3 * 4.0 + 5 * 0.0 + 6 * 1.0 + 7 * 1.0 = 35 47 : 2 * 5.0 + 3 * 3.0 + 5 * 2.0 + 6 * 1.0 + 7 * 0.0 = 35 48 : 2 * 5.0 + 3 * 2.0 + 5 * 1.0 + 6 * 0.0 + 7 * 2.0 = 35 49 : 2 * 5.0 + 3 * 2.0 + 5 * 0.0 + 6 * 2.0 + 7 * 1.0 = 35 50 : 2 * 5.0 + 3 * 1.0 + 5 * 3.0 + 6 * 0.0 + 7 * 1.0 = 35 51 : 2 * 5.0 + 3 * 1.0 + 5 * 2.0 + 6 * 2.0 + 7 * 0.0 = 35 52 : 2 * 5.0 + 3 * 0.0 + 5 * 5.0 + 6 * 0.0 + 7 * 0.0 = 35 53 : 2 * 5.0 + 3 * 0.0 + 5 * 1.0 + 6 * 1.0 + 7 * 2.0 = 35 54 : 2 * 5.0 + 3 * 0.0 + 5 * 0.0 + 6 * 3.0 + 7 * 1.0 = 35 55 : 2 * 4.0 + 3 * 9.0 + 5 * 0.0 + 6 * 0.0 + 7 * 0.0 = 35 56 : 2 * 4.0 + 3 * 7.0 + 5 * 0.0 + 6 * 1.0 + 7 * 0.0 = 35 57 : 2 * 4.0 + 3 * 5.0 + 5 * 1.0 + 6 * 0.0 + 7 * 1.0 = 35 58 : 2 * 4.0 + 3 * 5.0 + 5 * 0.0 + 6 * 2.0 + 7 * 0.0 = 35 59 : 2 * 4.0 + 3 * 4.0 + 5 * 3.0 + 6 * 0.0 + 7 * 0.0 = 35 60 : 2 * 4.0 + 3 * 3.0 + 5 * 1.0 + 6 * 1.0 + 7 * 1.0 = 35 61 : 2 * 4.0 + 3 * 3.0 + 5 * 0.0 + 6 * 3.0 + 7 * 0.0 = 35 62 : 2 * 4.0 + 3 * 2.0 + 5 * 3.0 + 6 * 1.0 + 7 * 0.0 = 35 63 : 2 * 4.0 + 3 * 2.0 + 5 * 0.0 + 6 * 0.0 + 7 * 3.0 = 35 64 : 2 * 4.0 + 3 * 1.0 + 5 * 2.0 + 6 * 0.0 + 7 * 2.0 = 35 65 : 2 * 4.0 + 3 * 1.0 + 5 * 1.0 + 6 * 2.0 + 7 * 1.0 = 35 66 : 2 * 4.0 + 3 * 1.0 + 5 * 0.0 + 6 * 4.0 + 7 * 0.0 = 35 67 : 2 * 4.0 + 3 * 0.0 + 5 * 4.0 + 6 * 0.0 + 7 * 1.0 = 35 68 : 2 * 4.0 + 3 * 0.0 + 5 * 3.0 + 6 * 2.0 + 7 * 0.0 = 35 69 : 2 * 4.0 + 3 * 0.0 + 5 * 0.0 + 6 * 1.0 + 7 * 3.0 = 35 70 : 2 * 3.0 + 3 * 8.0 + 5 * 1.0 + 6 * 0.0 + 7 * 0.0 = 35 71 : 2 * 3.0 + 3 * 6.0 + 5 * 1.0 + 6 * 1.0 + 7 * 0.0 = 35 72 : 2 * 3.0 + 3 * 5.0 + 5 * 0.0 + 6 * 0.0 + 7 * 2.0 = 35 73 : 2 * 3.0 + 3 * 4.0 + 5 * 2.0 + 6 * 0.0 + 7 * 1.0 = 35 74 : 2 * 3.0 + 3 * 4.0 + 5 * 1.0 + 6 * 2.0 + 7 * 0.0 = 35 75 : 2 * 3.0 + 3 * 3.0 + 5 * 4.0 + 6 * 0.0 + 7 * 0.0 = 35 76 : 2 * 3.0 + 3 * 3.0 + 5 * 0.0 + 6 * 1.0 + 7 * 2.0 = 35 77 : 2 * 3.0 + 3 * 2.0 + 5 * 2.0 + 6 * 1.0 + 7 * 1.0 = 35 78 : 2 * 3.0 + 3 * 2.0 + 5 * 1.0 + 6 * 3.0 + 7 * 0.0 = 35 79 : 2 * 3.0 + 3 * 1.0 + 5 * 4.0 + 6 * 1.0 + 7 * 0.0 = 35 80 : 2 * 3.0 + 3 * 1.0 + 5 * 1.0 + 6 * 0.0 + 7 * 3.0 = 35 81 : 2 * 3.0 + 3 * 1.0 + 5 * 0.0 + 6 * 2.0 + 7 * 2.0 = 35 82 : 2 * 3.0 + 3 * 0.0 + 5 * 3.0 + 6 * 0.0 + 7 * 2.0 = 35 83 : 2 * 3.0 + 3 * 0.0 + 5 * 2.0 + 6 * 2.0 + 7 * 1.0 = 35 84 : 2 * 3.0 + 3 * 0.0 + 5 * 1.0 + 6 * 4.0 + 7 * 0.0 = 35 85 : 2 * 2.0 + 3 * 8.0 + 5 * 0.0 + 6 * 0.0 + 7 * 1.0 = 35 86 : 2 * 2.0 + 3 * 7.0 + 5 * 2.0 + 6 * 0.0 + 7 * 0.0 = 35 87 : 2 * 2.0 + 3 * 6.0 + 5 * 0.0 + 6 * 1.0 + 7 * 1.0 = 35 88 : 2 * 2.0 + 3 * 5.0 + 5 * 2.0 + 6 * 1.0 + 7 * 0.0 = 35 89 : 2 * 2.0 + 3 * 4.0 + 5 * 1.0 + 6 * 0.0 + 7 * 2.0 = 35 90 : 2 * 2.0 + 3 * 4.0 + 5 * 0.0 + 6 * 2.0 + 7 * 1.0 = 35 91 : 2 * 2.0 + 3 * 3.0 + 5 * 3.0 + 6 * 0.0 + 7 * 1.0 = 35 92 : 2 * 2.0 + 3 * 3.0 + 5 * 2.0 + 6 * 2.0 + 7 * 0.0 = 35 93 : 2 * 2.0 + 3 * 2.0 + 5 * 5.0 + 6 * 0.0 + 7 * 0.0 = 35 94 : 2 * 2.0 + 3 * 2.0 + 5 * 1.0 + 6 * 1.0 + 7 * 2.0 = 35 95 : 2 * 2.0 + 3 * 2.0 + 5 * 0.0 + 6 * 3.0 + 7 * 1.0 = 35 96 : 2 * 2.0 + 3 * 1.0 + 5 * 3.0 + 6 * 1.0 + 7 * 1.0 = 35 97 : 2 * 2.0 + 3 * 1.0 + 5 * 2.0 + 6 * 3.0 + 7 * 0.0 = 35 98 : 2 * 2.0 + 3 * 1.0 + 5 * 0.0 + 6 * 0.0 + 7 * 4.0 = 35 99 : 2 * 2.0 + 3 * 0.0 + 5 * 5.0 + 6 * 1.0 + 7 * 0.0 = 35 100 : 2 * 2.0 + 3 * 0.0 + 5 * 2.0 + 6 * 0.0 + 7 * 3.0 = 35 101 : 2 * 2.0 + 3 * 0.0 + 5 * 1.0 + 6 * 2.0 + 7 * 2.0 = 35 102 : 2 * 2.0 + 3 * 0.0 + 5 * 0.0 + 6 * 4.0 + 7 * 1.0 = 35 103 : 2 * 1.0 + 3 * 11.0 + 5 * 0.0 + 6 * 0.0 + 7 * 0.0 = 35 104 : 2 * 1.0 + 3 * 9.0 + 5 * 0.0 + 6 * 1.0 + 7 * 0.0 = 35 105 : 2 * 1.0 + 3 * 7.0 + 5 * 1.0 + 6 * 0.0 + 7 * 1.0 = 35 106 : 2 * 1.0 + 3 * 7.0 + 5 * 0.0 + 6 * 2.0 + 7 * 0.0 = 35 107 : 2 * 1.0 + 3 * 6.0 + 5 * 3.0 + 6 * 0.0 + 7 * 0.0 = 35 108 : 2 * 1.0 + 3 * 5.0 + 5 * 1.0 + 6 * 1.0 + 7 * 1.0 = 35 109 : 2 * 1.0 + 3 * 5.0 + 5 * 0.0 + 6 * 3.0 + 7 * 0.0 = 35 110 : 2 * 1.0 + 3 * 4.0 + 5 * 3.0 + 6 * 1.0 + 7 * 0.0 = 35 111 : 2 * 1.0 + 3 * 4.0 + 5 * 0.0 + 6 * 0.0 + 7 * 3.0 = 35 112 : 2 * 1.0 + 3 * 3.0 + 5 * 2.0 + 6 * 0.0 + 7 * 2.0 = 35 113 : 2 * 1.0 + 3 * 3.0 + 5 * 1.0 + 6 * 2.0 + 7 * 1.0 = 35 114 : 2 * 1.0 + 3 * 3.0 + 5 * 0.0 + 6 * 4.0 + 7 * 0.0 = 35 115 : 2 * 1.0 + 3 * 2.0 + 5 * 4.0 + 6 * 0.0 + 7 * 1.0 = 35 116 : 2 * 1.0 + 3 * 2.0 + 5 * 3.0 + 6 * 2.0 + 7 * 0.0 = 35 117 : 2 * 1.0 + 3 * 2.0 + 5 * 0.0 + 6 * 1.0 + 7 * 3.0 = 35 118 : 2 * 1.0 + 3 * 1.0 + 5 * 6.0 + 6 * 0.0 + 7 * 0.0 = 35 119 : 2 * 1.0 + 3 * 1.0 + 5 * 2.0 + 6 * 1.0 + 7 * 2.0 = 35 120 : 2 * 1.0 + 3 * 1.0 + 5 * 1.0 + 6 * 3.0 + 7 * 1.0 = 35 121 : 2 * 1.0 + 3 * 1.0 + 5 * 0.0 + 6 * 5.0 + 7 * 0.0 = 35 122 : 2 * 1.0 + 3 * 0.0 + 5 * 4.0 + 6 * 1.0 + 7 * 1.0 = 35 123 : 2 * 1.0 + 3 * 0.0 + 5 * 3.0 + 6 * 3.0 + 7 * 0.0 = 35 124 : 2 * 1.0 + 3 * 0.0 + 5 * 1.0 + 6 * 0.0 + 7 * 4.0 = 35 125 : 2 * 1.0 + 3 * 0.0 + 5 * 0.0 + 6 * 2.0 + 7 * 3.0 = 35 126 : 2 * 0.0 + 3 * 10.0 + 5 * 1.0 + 6 * 0.0 + 7 * 0.0 = 35 127 : 2 * 0.0 + 3 * 8.0 + 5 * 1.0 + 6 * 1.0 + 7 * 0.0 = 35 128 : 2 * 0.0 + 3 * 7.0 + 5 * 0.0 + 6 * 0.0 + 7 * 2.0 = 35 129 : 2 * 0.0 + 3 * 6.0 + 5 * 2.0 + 6 * 0.0 + 7 * 1.0 = 35 130 : 2 * 0.0 + 3 * 6.0 + 5 * 1.0 + 6 * 2.0 + 7 * 0.0 = 35 131 : 2 * 0.0 + 3 * 5.0 + 5 * 4.0 + 6 * 0.0 + 7 * 0.0 = 35 132 : 2 * 0.0 + 3 * 5.0 + 5 * 0.0 + 6 * 1.0 + 7 * 2.0 = 35 133 : 2 * 0.0 + 3 * 4.0 + 5 * 2.0 + 6 * 1.0 + 7 * 1.0 = 35 134 : 2 * 0.0 + 3 * 4.0 + 5 * 1.0 + 6 * 3.0 + 7 * 0.0 = 35 135 : 2 * 0.0 + 3 * 3.0 + 5 * 4.0 + 6 * 1.0 + 7 * 0.0 = 35 136 : 2 * 0.0 + 3 * 3.0 + 5 * 1.0 + 6 * 0.0 + 7 * 3.0 = 35 137 : 2 * 0.0 + 3 * 3.0 + 5 * 0.0 + 6 * 2.0 + 7 * 2.0 = 35 138 : 2 * 0.0 + 3 * 2.0 + 5 * 3.0 + 6 * 0.0 + 7 * 2.0 = 35 139 : 2 * 0.0 + 3 * 2.0 + 5 * 2.0 + 6 * 2.0 + 7 * 1.0 = 35 140 : 2 * 0.0 + 3 * 2.0 + 5 * 1.0 + 6 * 4.0 + 7 * 0.0 = 35 141 : 2 * 0.0 + 3 * 1.0 + 5 * 5.0 + 6 * 0.0 + 7 * 1.0 = 35 142 : 2 * 0.0 + 3 * 1.0 + 5 * 4.0 + 6 * 2.0 + 7 * 0.0 = 35 143 : 2 * 0.0 + 3 * 1.0 + 5 * 1.0 + 6 * 1.0 + 7 * 3.0 = 35 144 : 2 * 0.0 + 3 * 1.0 + 5 * 0.0 + 6 * 3.0 + 7 * 2.0 = 35 145 : 2 * 0.0 + 3 * 0.0 + 5 * 7.0 + 6 * 0.0 + 7 * 0.0 = 35 146 : 2 * 0.0 + 3 * 0.0 + 5 * 3.0 + 6 * 1.0 + 7 * 2.0 = 35 147 : 2 * 0.0 + 3 * 0.0 + 5 * 2.0 + 6 * 3.0 + 7 * 1.0 = 35 148 : 2 * 0.0 + 3 * 0.0 + 5 * 1.0 + 6 * 5.0 + 7 * 0.0 = 35 149 : 2 * 0.0 + 3 * 0.0 + 5 * 0.0 + 6 * 0.0 + 7 * 5.0 = 35 diophantine_nd_nonnegative_bounded_test diophantine_nd_nonnegative_bounded returns solutions of a Diophantine equation in N variables which are nonnegative, and bounded by x(i) <= m(i). 2 * x 1 + 3 * x 2 = 18 Bounds imposed on Diophantine equation solutions: 0 <= x(0) <= 10 0 <= x(1) <= 10 4 solutions found. 0 : 2 * 9.0 + 3 * 0.0 = 18 1 : 2 * 6.0 + 3 * 2.0 = 18 2 : 2 * 3.0 + 3 * 4.0 = 18 3 : 2 * 0.0 + 3 * 6.0 = 18 2 * x 1 + 3 * x 2 = 18 Bounds imposed on Diophantine equation solutions: 0 <= x(0) <= 5 0 <= x(1) <= 4 1 solutions found. 0 : 2 * 3.0 + 3 * 4.0 = 18 2 * x 1 + 3 * x 2 = 18 Bounds imposed on Diophantine equation solutions: 0 <= x(0) <= 1 0 <= x(1) <= 1 0 solutions found. 2 * x 1 + 3 * x 2 + 5 * x 3 + 6 * x 4 = 24 Bounds imposed on Diophantine equation solutions: 0 <= x(0) <= 6 0 <= x(1) <= 6 0 <= x(2) <= 3 0 <= x(3) <= 3 23 solutions found. 0 : 2 * 6.0 + 3 * 4.0 + 5 * 0.0 + 6 * 0.0 = 24 1 : 2 * 6.0 + 3 * 2.0 + 5 * 0.0 + 6 * 1.0 = 24 2 : 2 * 6.0 + 3 * 0.0 + 5 * 0.0 + 6 * 2.0 = 24 3 : 2 * 5.0 + 3 * 3.0 + 5 * 1.0 + 6 * 0.0 = 24 4 : 2 * 5.0 + 3 * 1.0 + 5 * 1.0 + 6 * 1.0 = 24 5 : 2 * 4.0 + 3 * 2.0 + 5 * 2.0 + 6 * 0.0 = 24 6 : 2 * 4.0 + 3 * 0.0 + 5 * 2.0 + 6 * 1.0 = 24 7 : 2 * 3.0 + 3 * 6.0 + 5 * 0.0 + 6 * 0.0 = 24 8 : 2 * 3.0 + 3 * 4.0 + 5 * 0.0 + 6 * 1.0 = 24 9 : 2 * 3.0 + 3 * 2.0 + 5 * 0.0 + 6 * 2.0 = 24 10 : 2 * 3.0 + 3 * 1.0 + 5 * 3.0 + 6 * 0.0 = 24 11 : 2 * 3.0 + 3 * 0.0 + 5 * 0.0 + 6 * 3.0 = 24 12 : 2 * 2.0 + 3 * 5.0 + 5 * 1.0 + 6 * 0.0 = 24 13 : 2 * 2.0 + 3 * 3.0 + 5 * 1.0 + 6 * 1.0 = 24 14 : 2 * 2.0 + 3 * 1.0 + 5 * 1.0 + 6 * 2.0 = 24 15 : 2 * 1.0 + 3 * 4.0 + 5 * 2.0 + 6 * 0.0 = 24 16 : 2 * 1.0 + 3 * 2.0 + 5 * 2.0 + 6 * 1.0 = 24 17 : 2 * 1.0 + 3 * 0.0 + 5 * 2.0 + 6 * 2.0 = 24 18 : 2 * 0.0 + 3 * 6.0 + 5 * 0.0 + 6 * 1.0 = 24 19 : 2 * 0.0 + 3 * 4.0 + 5 * 0.0 + 6 * 2.0 = 24 20 : 2 * 0.0 + 3 * 3.0 + 5 * 3.0 + 6 * 0.0 = 24 21 : 2 * 0.0 + 3 * 2.0 + 5 * 0.0 + 6 * 3.0 = 24 22 : 2 * 0.0 + 3 * 1.0 + 5 * 3.0 + 6 * 1.0 = 24 2 * x 1 + 3 * x 2 + 5 * x 3 + 6 * x 4 + 7 * x 5 = 35 Bounds imposed on Diophantine equation solutions: 0 <= x(0) <= 6 0 <= x(1) <= 2 0 <= x(2) <= 2 0 <= x(3) <= 2 0 <= x(4) <= 2 17 solutions found. 0 : 2 * 6.0 + 3 * 2.0 + 5 * 2.0 + 6 * 0.0 + 7 * 1.0 = 35 1 : 2 * 6.0 + 3 * 2.0 + 5 * 1.0 + 6 * 2.0 + 7 * 0.0 = 35 2 : 2 * 6.0 + 3 * 1.0 + 5 * 0.0 + 6 * 1.0 + 7 * 2.0 = 35 3 : 2 * 6.0 + 3 * 0.0 + 5 * 2.0 + 6 * 1.0 + 7 * 1.0 = 35 4 : 2 * 5.0 + 3 * 2.0 + 5 * 1.0 + 6 * 0.0 + 7 * 2.0 = 35 5 : 2 * 5.0 + 3 * 2.0 + 5 * 0.0 + 6 * 2.0 + 7 * 1.0 = 35 6 : 2 * 5.0 + 3 * 1.0 + 5 * 2.0 + 6 * 2.0 + 7 * 0.0 = 35 7 : 2 * 5.0 + 3 * 0.0 + 5 * 1.0 + 6 * 1.0 + 7 * 2.0 = 35 8 : 2 * 4.0 + 3 * 1.0 + 5 * 2.0 + 6 * 0.0 + 7 * 2.0 = 35 9 : 2 * 4.0 + 3 * 1.0 + 5 * 1.0 + 6 * 2.0 + 7 * 1.0 = 35 10 : 2 * 3.0 + 3 * 2.0 + 5 * 2.0 + 6 * 1.0 + 7 * 1.0 = 35 11 : 2 * 3.0 + 3 * 1.0 + 5 * 0.0 + 6 * 2.0 + 7 * 2.0 = 35 12 : 2 * 3.0 + 3 * 0.0 + 5 * 2.0 + 6 * 2.0 + 7 * 1.0 = 35 13 : 2 * 2.0 + 3 * 2.0 + 5 * 1.0 + 6 * 1.0 + 7 * 2.0 = 35 14 : 2 * 2.0 + 3 * 0.0 + 5 * 1.0 + 6 * 2.0 + 7 * 2.0 = 35 15 : 2 * 1.0 + 3 * 1.0 + 5 * 2.0 + 6 * 1.0 + 7 * 2.0 = 35 16 : 2 * 0.0 + 3 * 2.0 + 5 * 2.0 + 6 * 2.0 + 7 * 1.0 = 35 diophantine_nd_positive_test diophantine_nd_positive returns the positive solutions of a Diophantine equation in N variables. 2 * x 1 + 3 * x 2 = 18 2 solutions found. 0 : 2 * 6.0 + 3 * 2.0 = 18 1 : 2 * 3.0 + 3 * 4.0 = 18 6 * x 1 + 3 * x 2 + 13 * x 3 = 16 0 solutions found. 12 * x 1 + 9 * x 2 + 7 * x 3 = 60 1 solutions found. 0 : 12 * 1.0 + 9 * 3.0 + 7 * 3.0 = 60 2 * x 1 + 3 * x 2 + 5 * x 3 + 6 * x 4 = 24 4 solutions found. 0 : 2 * 5.0 + 3 * 1.0 + 5 * 1.0 + 6 * 1.0 = 24 1 : 2 * 2.0 + 3 * 3.0 + 5 * 1.0 + 6 * 1.0 = 24 2 : 2 * 2.0 + 3 * 1.0 + 5 * 1.0 + 6 * 2.0 = 24 3 : 2 * 1.0 + 3 * 2.0 + 5 * 2.0 + 6 * 1.0 = 24 2 * x 1 + 3 * x 2 + 5 * x 3 + 6 * x 4 + 7 * x 5 = 35 10 solutions found. 0 : 2 * 7.0 + 3 * 1.0 + 5 * 1.0 + 6 * 1.0 + 7 * 1.0 = 35 1 : 2 * 4.0 + 3 * 3.0 + 5 * 1.0 + 6 * 1.0 + 7 * 1.0 = 35 2 : 2 * 4.0 + 3 * 1.0 + 5 * 1.0 + 6 * 2.0 + 7 * 1.0 = 35 3 : 2 * 3.0 + 3 * 2.0 + 5 * 2.0 + 6 * 1.0 + 7 * 1.0 = 35 4 : 2 * 2.0 + 3 * 2.0 + 5 * 1.0 + 6 * 1.0 + 7 * 2.0 = 35 5 : 2 * 2.0 + 3 * 1.0 + 5 * 3.0 + 6 * 1.0 + 7 * 1.0 = 35 6 : 2 * 1.0 + 3 * 5.0 + 5 * 1.0 + 6 * 1.0 + 7 * 1.0 = 35 7 : 2 * 1.0 + 3 * 3.0 + 5 * 1.0 + 6 * 2.0 + 7 * 1.0 = 35 8 : 2 * 1.0 + 3 * 1.0 + 5 * 2.0 + 6 * 1.0 + 7 * 2.0 = 35 9 : 2 * 1.0 + 3 * 1.0 + 5 * 1.0 + 6 * 3.0 + 7 * 1.0 = 35 diophantine_nd_test(): Normal end of execution. Tue Oct 19 11:32:47 2021