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I am trying to create a function that generates a tensor according to a list, each of whose elements specifies the range of the corresponding dimension of the tensor and whose length specifies the total dimension of the tensor. I tried two versions using mainly "Table" and "Splice" functions.

Version 1:

ClearAll[i]
imax = {2, 3, 4};
Table[i[n], {n, Length[imax]}]
Table[{i[n], imax[[n]]}, {n, Length[imax]}]
Table[%%, Splice[%, Table]]

which produces

{i[1], i[2], i[3]}
{{i[1], 2}, {i[2], 3}, {i[3], 4}}
Table[%%, Splice[%, Table]]

where "Splice" fails to work.

Version 2:

ClearAll[i]
imax = {2, 3, 4};
Table[i[n], {n, Length[imax]}]
Table[{i[n], imax[[n]]}, {n, Length[imax]}]
Table[%%, Splice[{{i[1], 2}, {i[2], 3}, {i[3], 4}}, Table]]

which produces

{i[1], i[2], i[3]}
{{i[1], 2}, {i[2], 3}, {i[3], 4}}
{{{{1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}}, {{1, 2, 1}, {1, 2, 
    2}, {1, 2, 3}, {1, 2, 4}}, {{1, 3, 1}, {1, 3, 2}, {1, 3, 3}, {1, 
    3, 4}}}, {{{2, 1, 1}, {2, 1, 2}, {2, 1, 3}, {2, 1, 4}}, {{2, 2, 
    1}, {2, 2, 2}, {2, 2, 3}, {2, 2, 4}}, {{2, 3, 1}, {2, 3, 2}, {2, 
    3, 3}, {2, 3, 4}}}}

where "Splice" works as expected.

Questions:

  1. Why "Splice" does not work in the first version?
  2. How can I embed "Splice" properly into "Table", so that I could make a function such as
TensorByList[list_]:=Module[{tensor},...;tensor]

which creates a tensor without a need to setup the iterators, which was the case with "Table" when I want to create a high dimension tensor:

Table[{i1,i2,...},{i1,i1max},{i2,i2max},...]
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    $\begingroup$ Welcome to the Mathematica Stack Exchange. I will admit that I cannot understand your question; but try: Array[List, {2, 3, 4}]. A good question should (1) present the task that needs to be accomplished, (2) input data available in copy-paste-able form, and (3) desired output. Optionally, you can provide other details. As presented, your question is asking the participants primarily to do a code review. $\endgroup$
    – Syed
    Sep 2, 2022 at 7:16
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    $\begingroup$ According to document of Splice: "Splice is resolved as part of the standard evaluation process. It is not resolved in expressions that are held or inactive. " Table is a function with HoldAll attribute (it does analyze its argument to some degree, though), so the behavior of version 1 is actually expected, and the standard way to fix the code is to use Evaluate: Table[%%, Evaluate@Splice[%, Table]]. So, the real problem is not "Why "Splice" does not work in the first version?", but "Why "Splice" works in the second version?", which I'm not sure how to answer. $\endgroup$
    – xzczd
    Sep 2, 2022 at 7:30
  • $\begingroup$ @Syed Indeed, the code sample given by OP isn't minimal, but (s)he isn't asking for code review. This is definitely an on-topic problem about the core language. (Particularly related to evaluation order and the surprisng evaluation mechanism of Table and Splice. $\endgroup$
    – xzczd
    Sep 2, 2022 at 7:34
  • $\begingroup$ Related: mathematica.stackexchange.com/a/270864/1871 $\endgroup$
    – xzczd
    Sep 2, 2022 at 7:36
  • $\begingroup$ @xzczd, I stand corrected then. Thanks for the feedback. $\endgroup$
    – Syed
    Sep 2, 2022 at 7:41

1 Answer 1

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It is easier to use "Array" instead of "Table" and "Splice" because "Array" takes a list of dimensions:

i = 1;
tensor = Array[a[i++] &, imax];
tensor // MatrixForm

enter image description here

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  • $\begingroup$ +1 Interesting use of increment here! Can you give any hint as to your intuition when writing this? $\endgroup$ Sep 2, 2022 at 19:07
  • $\begingroup$ a[i++] simply numerates the different tensor elements. $\endgroup$ Sep 2, 2022 at 19:51

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