Mathematica Asked on August 5, 2021
I have a tuple mytup
.
Assume two arbitrary elements from the tuples are {a1, a2, a3, a4, a5, a6, a7, a8, a9}
and {b1, b2, b3, b4, b5, b6, b7, b8, b9}
.
Now I want to delete the element that satisies the condition:
a1 = b1
a2 = -b2
a3 = b3
a4 = b4
a5 = -b5
a6 = b6
a7 = b7
a8 = -b8
a9 = -b9
and the deleted element should have a8 = -1
and a9 = 1
.
I tried using Gather
and First
to select the first element from each group but this does not work as the element with a8 = -1
and a9 = 1
is not always placed first in the group.
Is there a good way to do this?
UPDATE: from my tuple below, all elements have a8 = 1
and a9 = -1
or a8 = -1
and a9 = 1
. However, the bigger data may include pairs with a8
, and a9
are not plus or minus 1 and no element from this pair is deleted.
For example, both {0, -1, -1, 1, 0, -1, d, 2, 3}, {0, 1, -1, 1, 0, -1, d, -2, -3}
are kept.
mytup = {{0, -1, -1, 1, 0, -1, d, 0, 1}, {0, -1, -1, 1, 0, -1, d, 1,
0}, {0, -1, -1, 1, 0, -1, d, 1, -1}, {0, -1, -1, 1, 0, -1, d, -1,
1}, {0, -1, -1, 1, 0, 0, d, 0, 1}, {0, -1, -1, 1, 0, 0, d, 1,
0}, {0, -1, -1, 1, 0, 0, d, -1, 1}, {0, -1, 0, 1, 0, -1, d, 0,
1}, {0, -1, 0, 1, 0, -1, d, 1, 0}, {0, 0, -1, 1, -1, -1, d, 0,
1}, {0, 0, -1, 1, -1, -1, d, -1, 1}, {0, 0, -1, 1, -1, 0, d, 0,
1}, {0, 0, -1, 1, -1, 0, d, -1, 1}, {0, 0, -1, 1, 0, -1, d, 0,
1}, {0, 0, -1, 1, 0, -1, d, 1, 0}, {0, 0, -1, 1, 0, -1, d,
1, -1}, {0, 0, -1, 1, 0, -1, d, -1, 1}, {0, 0, -1, 1, 0, 0, d, 0,
1}, {0, 0, -1, 1, 0, 0, d, 1, 0}, {0, 0, -1, 1, 0, 0, d,
1, -1}, {0, 0, -1, 1, 0, 0, d, -1, 1}, {0, 0, -1, 1, 1, -1, d, 0,
1}, {0, 0, -1, 1, 1, -1, d, 1, 0}, {0, 0, -1, 1, 1, -1, d,
1, -1}, {0, 0, -1, 1, 1, 0, d, 0, 1}, {0, 0, -1, 1, 1, 0, d, 1,
0}, {0, 0, -1, 1, 1, 0, d, 1, -1}, {0, 1, -1, 1, 0, -1, d,
1, -1}, {0, 1, -1, 1, 0, -1, d, -1, 1}, {0, 1, -1, 1, 0, 0, d, 1,
0}, {0, 1, -1, 1, 0, 0, d, 1, -1}, {0, 1, 0, 1, 0, -1, d, 0,
1}, {0, 1, 0, 1, 0, -1, d, 1, 0}, {1, -1, -1, 1, 0, -1, d, 0,
1}, {1, -1, -1, 1, 0, -1, d, 1, 0}, {1, -1, -1, 1, 0, 0, d, 0,
1}, {1, -1, -1, 1, 0, 0, d, 1, 0}, {1, -1, -1, 1, 0, 0, d, -1,
1}, {1, -1, 0, 1, 0, -1, d, 1, -1}, {1, -1, 0, 1, 0, -1, d, -1,
1}, {1, 0, -1, 1, 0, 0, d, 0, 1}, {1, 0, -1, 1, 0, 0, d, 1,
0}, {1, 0, -1, 1, 0, 0, d, 1, -1}, {1, 0, -1, 1, 0, 0, d, -1,
1}, {1, 0, -1, 1, 1, -1, d, 0, 1}, {1, 0, -1, 1, 1, -1, d, 1,
0}, {1, 0, -1, 1, 1, 0, d, 0, 1}, {1, 0, -1, 1, 1, 0, d, 1,
0}, {1, 0, -1, 1, 1, 0, d, 1, -1}, {1, 0, -1, 1, 1, 0, d, -1,
1}, {1, 0, 0, 1, 1, -1, d, 1, 0}, {1, 0, 0, 1, 1, -1, d, 1, -1}};
gathered =
Gather[mytup, ((#1[[1]] == #2[[1]]) && (#1[[2]] == -#2[[2]]) &&
(#1[[3 ;; 4]] == #2[[3 ;;
4]]) && (#1[[5]] == -#2[[5]]) && (#1[[6]] == #2[[6]]) &&
(#1[[7]] == #2[[7]]) && (#1[[8]] == -#2[[8]]) && (#1[[9]] ==
-#2[[9]])) &];
result = Map[First]@gathered
I think one way to do this is:
Select[mytup,
!(#[[8]] == -1
&& #[[9]] == 1
&& MemberQ[mytup, # * {1, -1, 1, 1, -1, 1, 1, -1, -1}])
&]
This keeps exactly the ones that fail the criterion, i.e. deletes the ones that do satisfy having their 8th part be -1
, their 9th part be 1
, and such that the list contains some member equal to {1, -1, 1, 1, -1, 1, 1, -1, -1}
times the considered element.
Let me know if this works for you!
Correct answer by thorimur on August 5, 2021
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