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Using jq, how to subtract 2 arrays with different keys and values from two JSON files?

This sounds like a basic question but I have been searching for a better solution for some time already...

I have the following files:

file0.json:

{ 
   "d": {
   "aaData": [ 
              {"a":1}, 
              {"a":2},
              {"a":3},
              {"a":4}
             ]
        }
}

and

file1.json:

[ 
    {"b":1},
    {"b":2},
    {"b":7}
]

and I want a subtraction between then with the expected result:

{
  "key": 3
}
{
  "key": 4
}

I thought of the following command would do the job:

bash$ jq -s '[.d.aaData[].a] - [.[].b] | { key: .}' file0.json file1.json

but it gives me the following error:

Cannot index array with string "b"

What makes sense, since [.[1].b] would't create an array, but something like [1][2][7]

the only way I managed to get the expected result was coding in my bash script the dirty solution:

bash$ a=$(jq '[.d.aaData[].a] | {key1: .}' file0.json)
bash$ b=$(jq '[.[].b] | {key2: . }' file1.json)
bash$ c=$(echo -n $a,$b)
bash$ echo $c
{ "key1": [ 1, 2, 3, 4 ] },{ "key2": [ 1, 2, 7 ] }
bash$ d=${c//"},{"/","}
bash$ echo $d
{ "key1": [ 1, 2, 3, 4 ] , "key2": [ 1, 2, 7 ] }
bash$ echo -n $d | jq '.key1 - .key2 | { key: .[] }'
{
  "key": 3
}
{
  "key": 4
}

I'm quite sure there is a better way to do it with jq.... just can't find how...

Select only the values in a that are different from all values in b .

jq -n --argfile a file0.json --argfile b file1.json '
  $a.d.aaData[].a as $a 
  | select([$b[].b]
  | all(. != $a))
  | {key: $a}'

Here is a solution which uses the jq - array difference operator:

    [ $file0.d.aaData[] | {key:.a} ]
  - [ $file1[]          | {key:.b} ]
| .[]    

Assuming filter.json contains this filter then

jq -M -n --argfile file0 file0.json --argfile file1 file1.json -f filter.json

produces

{
  "key": 3
}
{
  "key": 4
}

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