# ReplaceAll and Reduce

Posted 9 years ago
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 I set this formula: Reduce [Mod [31 x 90] == 4, {x}] that function, result: x = 154 = 64 mod90 If I wanted to apply the formula by replacing the result "4" with a list of values "M" Reduce [Mod [31 x 90] == M, {x}] ReplaceAll {M -> {}} 4,35,66,59,0,31,24,55,86 what is the correct syntax?
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Posted 9 years ago
 TableForm[Reduce[Mod[N x , 90] == M, {x}, Integers]]would instead can Map M with this list: {4, 35, 66, 59, 0, 31,24, 55, 86}, and N with this one: {7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43} and solve MOD for all possible pairs {M, N}?tnk
Posted 9 years ago
 thanks very much, I was despairing that someone help me!
Posted 9 years ago
 Hi,some comments:1) the function you give Reduce [Mod [31 x 90] == 4, {x}] does not seem to work in my version of Mathematica (10.0.2 on OSX 10.10.2). I can make it work if I slightly modify it: Reduce[Mod[31 x , 90] == 4, {x}, Integers] which gives C[1] \[Element] Integers && x == 64 + 90 C[1] as expected. 2) If I replace the 4 by M without specifying a list Reduce[Mod[31 x , 90] == M, {x}, Integers] I get a comprehensive list of results: C[1] \[Element] Integers && ((M == 0 && x == 90 C[1]) || (M == 1 && x == 61 + 90 C[1]) || (M == 2 && x == 32 + 90 C[1]) || (M == 3 && x == 3 + 90 C[1]) || (M == 4 && x == 64 + 90 C[1]) || (M == 5 && x == 35 + 90 C[1]) || (M == 6 && x == 6 + 90 C[1]) || (M == 7 && x == 67 + 90 C[1]) || (M == 8 && x == 38 + 90 C[1]) || (M == 9 && x == 9 + 90 C[1]) || (M == 10 && x == 70 + 90 C[1]) || (M == 11 && x == 41 + 90 C[1]) || (M == 12 && x == 12 + 90 C[1]) || (M == 13 && x == 73 + 90 C[1]) || (M == 14 && x == 44 + 90 C[1]) || (M == 15 && x == 15 + 90 C[1]) || (M == 16 && x == 76 + 90 C[1]) || (M == 17 && x == 47 + 90 C[1]) || (M == 18 && x == 18 + 90 C[1]) || (M == 19 && x == 79 + 90 C[1]) || (M == 20 && x == 50 + 90 C[1]) || (M == 21 && x == 21 + 90 C[1]) || (M == 22 && x == 82 + 90 C[1]) || (M == 23 && x == 53 + 90 C[1]) || (M == 24 && x == 24 + 90 C[1]) || (M == 25 && x == 85 + 90 C[1]) || (M == 26 && x == 56 + 90 C[1]) || (M == 27 && x == 27 + 90 C[1]) || (M == 28 && x == 88 + 90 C[1]) || (M == 29 && x == 59 + 90 C[1]) || (M == 30 && x == 30 + 90 C[1]) || (M == 31 && x == 1 + 90 C[1]) || (M == 32 && x == 62 + 90 C[1]) || (M == 33 && x == 33 + 90 C[1]) || (M == 34 && x == 4 + 90 C[1]) || (M == 35 && x == 65 + 90 C[1]) || (M == 36 && x == 36 + 90 C[1]) || (M == 37 && x == 7 + 90 C[1]) || (M == 38 && x == 68 + 90 C[1]) || (M == 39 && x == 39 + 90 C[1]) || (M == 40 && x == 10 + 90 C[1]) || (M == 41 && x == 71 + 90 C[1]) || (M == 42 && x == 42 + 90 C[1]) || (M == 43 && x == 13 + 90 C[1]) || (M == 44 && x == 74 + 90 C[1]) || (M == 45 && x == 45 + 90 C[1]) || (M == 46 && x == 16 + 90 C[1]) || (M == 47 && x == 77 + 90 C[1]) || (M == 48 && x == 48 + 90 C[1]) || (M == 49 && x == 19 + 90 C[1]) || (M == 50 && x == 80 + 90 C[1]) || (M == 51 && x == 51 + 90 C[1]) || (M == 52 && x == 22 + 90 C[1]) || (M == 53 && x == 83 + 90 C[1]) || (M == 54 && x == 54 + 90 C[1]) || (M == 55 && x == 25 + 90 C[1]) || (M == 56 && x == 86 + 90 C[1]) || (M == 57 && x == 57 + 90 C[1]) || (M == 58 && x == 28 + 90 C[1]) || (M == 59 && x == 89 + 90 C[1]) || (M == 60 && x == 60 + 90 C[1]) || (M == 61 && x == 31 + 90 C[1]) || (M == 62 && x == 2 + 90 C[1]) || (M == 63 && x == 63 + 90 C[1]) || (M == 64 && x == 34 + 90 C[1]) || (M == 65 && x == 5 + 90 C[1]) || (M == 66 && x == 66 + 90 C[1]) || (M == 67 && x == 37 + 90 C[1]) || (M == 68 && x == 8 + 90 C[1]) || (M == 69 && x == 69 + 90 C[1]) || (M == 70 && x == 40 + 90 C[1]) || (M == 71 && x == 11 + 90 C[1]) || (M == 72 && x == 72 + 90 C[1]) || (M == 73 && x == 43 + 90 C[1]) || (M == 74 && x == 14 + 90 C[1]) || (M == 75 && x == 75 + 90 C[1]) || (M == 76 && x == 46 + 90 C[1]) || (M == 77 && x == 17 + 90 C[1]) || (M == 78 && x == 78 + 90 C[1]) || (M == 79 && x == 49 + 90 C[1]) || (M == 80 && x == 20 + 90 C[1]) || (M == 81 && x == 81 + 90 C[1]) || (M == 82 && x == 52 + 90 C[1]) || (M == 83 && x == 23 + 90 C[1]) || (M == 84 && x == 84 + 90 C[1]) || (M == 85 && x == 55 + 90 C[1]) || (M == 86 && x == 26 + 90 C[1]) || (M == 87 && x == 87 + 90 C[1]) || (M == 88 && x == 58 + 90 C[1]) || (M == 89 && x == 29 + 90 C[1])) Sorry for the awkward typesetting.3) If I want substitute M by the values of your list I think that this syntax will do: Reduce[Mod[31 x , 90] == #, {x}, Integers] & /@ {4, 35, 66, 59, 0, 31,24, 55, 86} It gives {C[1] \[Element] Integers && x == 64 + 90 C[1], C[1] \[Element] Integers && x == 65 + 90 C[1], C[1] \[Element] Integers && x == 66 + 90 C[1], C[1] \[Element] Integers && x == 89 + 90 C[1], C[1] \[Element] Integers && x == 90 C[1], C[1] \[Element] Integers && x == 1 + 90 C[1], C[1] \[Element] Integers && x == 24 + 90 C[1], C[1] \[Element] Integers && x == 25 + 90 C[1], C[1] \[Element] Integers && x == 26 + 90 C[1]} Cheers,M.