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I have the two lists:

s1 ={0.,0.00333333,0.00666667,0.01,0.0133333,0.0166667,0.02,0.0233333,0.0266667,0.03,0.0333333,0.0366667,0.04,0.0433333,0.0466667,0.05,0.0533333,0.0566667,0.06,0.0633333,0.0666667,0.07,0.0733333,0.0766667,0.08,0.0833333,0.0866667,0.09,0.0933333,0.0966667,0.1,0.103333,0.106667,0.11,0.113333,0.116667,0.12,0.123333,0.126667,0.13,0.133333,0.136667,0.14,0.143333,0.146667,0.15,0.153333,0.156667,0.16,0.163333,0.166667,0.17,0.173333,0.176667,0.18,0.183333,0.186667,0.19,0.193333,0.196667,0.2,0.203333,0.206667,0.21,0.213333,0.216667,0.22,0.223333,0.226667,0.23,0.233333,0.236667,0.24,0.243333,0.246667,0.25,0.253333,0.256667,0.26,0.263333,0.266667,0.27,0.273333,0.276667,0.28,0.283333,0.286667,0.29,0.293333,0.296667,0.3,0.303333,0.306667,0.31,0.313333,0.316667,0.32,0.323333,0.326667,0.33,0.333333,0.336667,0.34,0.343333,0.346667,0.35,0.353333,0.356667,0.36,0.363333,0.366667,0.37,0.373333,0.376667,0.38,0.383333,0.386667,0.39,0.393333,0.396667,0.4,0.403333,0.406667,0.41,0.413333,0.416667,0.42,0.423333,0.426667,0.43,0.433333,0.436667,0.44,0.443333,0.446667,0.45,0.453333,0.456667,0.46,0.463333,0.466667,0.47,0.473333,0.476667,0.48,0.483333,0.486667,0.49,0.493333,0.496667,0.5,0.503333,0.506667,0.51,0.513333,0.516667,0.52,0.523333,0.526667,0.53,0.533333,0.536667,0.54,0.543333,0.546667,0.55,0.553333,0.556667,0.56,0.563333,0.566667,0.57,0.573333,0.576667,0.58,0.583333,0.586667,0.59,0.593333,0.596667,0.6,0.603333,0.606667,0.61,0.613333,0.616667,0.62,0.623333,0.626667,0.63,0.633333,0.636667,0.64,0.643333,0.646667,0.65,0.653333,0.656667,0.66,0.663333};

and 

s2={0.,0.00222222,0.00444444,0.00666667,0.00888889,0.0111111,0.0133333,0.0155556,0.0177778,0.02,0.0222222,0.0244444,0.0266667,0.0288889,0.0311111,0.0333333,0.0355556,0.0377778,0.04,0.0422222,0.0444444,0.0466667,0.0488889,0.0511111,0.0533333,0.0555556,0.0577778,0.06,0.0622222,0.0644444,0.0666667,0.0688889,0.0711111,0.0733333,0.0755556,0.0777778,0.08,0.0822222,0.0844444,0.0866667,0.0888889,0.0911111,0.0933333,0.0955556,0.0977778,0.1,0.102222,0.104444,0.106667,0.108889,0.111111,0.113333,0.115556,0.117778,0.12,0.122222,0.124444,0.126667,0.128889,0.131111,0.133333,0.135556,0.137778,0.14,0.142222,0.144444,0.146667,0.148889,0.151111,0.153333,0.155556,0.157778,0.16,0.162222,0.164444,0.166667,0.168889,0.171111,0.173333,0.175556,0.177778,0.18,0.182222,0.184444,0.186667,0.188889,0.191111,0.193333,0.195556,0.197778,0.2,0.202222,0.204444,0.206667,0.208889,0.211111,0.213333,0.215556,0.217778,0.22,0.222222,0.224444,0.226667,0.228889,0.231111,0.233333,0.235556,0.237778,0.24,0.242222,0.244444,0.246667,0.248889,0.251111,0.253333,0.255556,0.257778,0.26,0.262222,0.264444,0.266667,0.268889,0.271111,0.273333,0.275556,0.277778,0.28,0.282222,0.284444,0.286667,0.288889,0.291111,0.293333,0.295556,0.297778,0.3,0.302222,0.304444,0.306667,0.308889,0.311111,0.313333,0.315556,0.317778,0.32,0.322222,0.324444,0.326667,0.328889,0.331111,0.333333,0.335556,0.337778,0.34,0.342222,0.344444,0.346667,0.348889,0.351111,0.353333,0.355556,0.357778,0.36,0.362222,0.364444,0.366667,0.368889,0.371111,0.373333,0.375556,0.377778,0.38,0.382222,0.384444,0.386667,0.388889,0.391111,0.393333,0.395556,0.397778,0.4,0.402222,0.404444,0.406667,0.408889,0.411111,0.413333,0.415556,0.417778,0.42,0.422222,0.424444,0.426667,0.428889,0.431111,0.433333,0.435556,0.437778,0.44,0.442222};

I want to find the intersection of the two lists and the position of the elements of intersection in each list, something like this:

{{p1 (element of intersection), g1 (position of p1 in s1), h1 (position of p1 in s2), {.....}, {......}......} Thanks for help.

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  • $\begingroup$ Can s1 and s2 have repeated entries? $\endgroup$ Commented Mar 22, 2018 at 1:53
  • $\begingroup$ @J.M. NO. Elements are distinct. $\endgroup$ Commented Mar 22, 2018 at 2:01

4 Answers 4

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{#, Position[s1, #][[1, 1]], Position[s2, #][[1, 1]]} & /@ Intersection[s1, s2]

This finds the set of elements in the Intersection, and then makes a list with 1) each such element, 2) that element's location in list s1, and 3) that element's location in s2.

If there are repeated entries of an intersection element, use this:

{#, Position[s1, #], Position[s2, #]} & /@ Intersection[s1, s2]
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  • $\begingroup$ Perfect. Many thanks $\endgroup$ Commented Mar 22, 2018 at 1:56
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Using a modification of @Szabolcs's positionDuplicates in this Q/A

ClearAll[intersectionAndPositions] intersectionAndPositions = Module[{l = Length@#, s = Join[##], g}, g = Mod[Select[GatherBy[Range[Length@s], s[[#]] &], Length@# >= 2 &], l, 1]; {s[[#[[1]]]], #} & /@ g] &; intersectionAndPositions [s1, s2] // Grid[#, Dividers -> All] & // TeXForm

$$\begin{array}{|c|c|} \hline 0. & \{1,1\} \\ \hline 0.00666667 & \{3,4\} \\ \hline 0.0133333 & \{5,7\} \\ \hline 0.02 & \{7,10\} \\ \hline 0.0266667 & \{9,13\} \\ \hline 0.0333333 & \{11,16\} \\ \hline 0.04 & \{13,19\} \\ \hline 0.0466667 & \{15,22\} \\ \hline 0.0533333 & \{17,25\} \\ \hline 0.06 & \{19,28\} \\ \hline 0.0666667 & \{21,31\} \\ \hline 0.0733333 & \{23,34\} \\ \hline 0.08 & \{25,37\} \\ \hline 0.0866667 & \{27,40\} \\ \hline 0.0933333 & \{29,43\} \\ \hline 0.1 & \{31,46\} \\ \hline 0.106667 & \{33,49\} \\ \hline 0.113333 & \{35,52\} \\ \hline 0.12 & \{37,55\} \\ \hline 0.126667 & \{39,58\} \\ \hline 0.133333 & \{41,61\} \\ \hline 0.14 & \{43,64\} \\ \hline 0.146667 & \{45,67\} \\ \hline 0.153333 & \{47,70\} \\ \hline 0.16 & \{49,73\} \\ \hline 0.166667 & \{51,76\} \\ \hline 0.173333 & \{53,79\} \\ \hline 0.18 & \{55,82\} \\ \hline 0.186667 & \{57,85\} \\ \hline 0.193333 & \{59,88\} \\ \hline 0.2 & \{61,91\} \\ \hline 0.206667 & \{63,94\} \\ \hline 0.213333 & \{65,97\} \\ \hline 0.22 & \{67,100\} \\ \hline 0.226667 & \{69,103\} \\ \hline 0.233333 & \{71,106\} \\ \hline 0.24 & \{73,109\} \\ \hline 0.246667 & \{75,112\} \\ \hline 0.253333 & \{77,115\} \\ \hline 0.26 & \{79,118\} \\ \hline 0.266667 & \{81,121\} \\ \hline 0.273333 & \{83,124\} \\ \hline 0.28 & \{85,127\} \\ \hline 0.286667 & \{87,130\} \\ \hline 0.293333 & \{89,133\} \\ \hline 0.3 & \{91,136\} \\ \hline 0.306667 & \{93,139\} \\ \hline 0.313333 & \{95,142\} \\ \hline 0.32 & \{97,145\} \\ \hline 0.326667 & \{99,148\} \\ \hline 0.333333 & \{101,151\} \\ \hline 0.34 & \{103,154\} \\ \hline 0.346667 & \{105,157\} \\ \hline 0.353333 & \{107,160\} \\ \hline 0.36 & \{109,163\} \\ \hline 0.366667 & \{111,166\} \\ \hline 0.373333 & \{113,169\} \\ \hline 0.38 & \{115,172\} \\ \hline 0.386667 & \{117,175\} \\ \hline 0.393333 & \{119,178\} \\ \hline 0.4 & \{121,181\} \\ \hline 0.406667 & \{123,184\} \\ \hline 0.413333 & \{125,187\} \\ \hline 0.42 & \{127,190\} \\ \hline 0.426667 & \{129,193\} \\ \hline 0.433333 & \{131,196\} \\ \hline 0.44 & \{133,199\} \\ \hline \end{array}$$

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  • $\begingroup$ Excellent (+1) but this code gives ambiguous output when a list contains repeated entries in the intersection. (Admittedly, the OP precludes such cases.) $\endgroup$ Commented Mar 22, 2018 at 2:14
  • $\begingroup$ @kglr Thanks for your input. $\endgroup$ Commented Mar 22, 2018 at 2:19
  • $\begingroup$ @DavidG.Stork, thank you for the vote. For the repeated entries case, you can SplitBy the index set before applying Mod. $\endgroup$ Commented Mar 22, 2018 at 2:26
  • $\begingroup$ @qahtah, my pleasure. $\endgroup$ Commented Mar 22, 2018 at 2:27
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Merge[Apply @ Join] @ KeyIntersection[PositionIndex /@ {s1, s2}]; Dataset[%, MaxItems -> 6]

enter image description here

Convert to list (if wanted)

KeyValueMap[List][%%][[1 ;; 6]]

{{0., {1, 1}}, {0.00666667, {3, 4}}, {0.0133333, {5, 7}}, {0.02, {7, 10}}, {0.0266667, {9, 13}}, {0.0333333, {11, 16}}}

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FWIW:

dm = DistanceMatrix[s1, s2]; pos = Position[dm, 0.]; Grid[{s1[[#[[1]]]], #} & /@ pos, Frame -> All]

enter image description here

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