New Axes
Key New Axes of function Rearrange in Tablerefers to a text that dictates how the coordinate axes of the referenced table are rearranged.
An empty text means no rearrangement.
The sequence of axes is specified using as separator the comma symbol ",".
Selected axes may be merged (see details below) with the directional plus symbol "+" ("directional" here means a + b ≠ b + a).
A range of consecutive axes may be merged with the dash symbol "-" ("directional" here means a - b ≠ b - a).
For example, consider a table A with 7 axes denoted as A₁ A₂ A₃ A₄ A₅ A₆ A₇ that are assumed to be ordered in the indicated sequence.
These axes are represented by their respective indices 1 2 3 4 5 6 7
A text such as "3 , 2 , 4 + 6" means starting with the 3rd axis A₃, then adding the 2nd axis A₂, then adding the cross product A₄×A₆ (see details below) and finally appending all remaining axes in the initial order, i.e. A₁ A₅ A₇
Note that 4 + 6 ≠ 6 + 4 because 4 + 6 → A₄×A₆ while 6 + 4 → A₆×A₄
A text such as "3 , 2 , 4 - 6" means starting with the 3rd axis A₃, then adding the 2nd axis A₂, then adding the cross product A₄×A₅×A₆ and finally appending all remaining axes in the initial order, i.e. A₁ A₇
Note that 4 - 6 ≠ 6 - 4 because 4 - 6 refers to a cross product A₄×A₅×A₆ formed by all axes from A₄ to A₆, while 6 - 4 refers to a cross product A₆×A₅×A₄ formed by all axes from A₆ to A₄
If the axes carry titles, they can be also represented by their respective titles but with the title prefix # stripped away.
For example, if the table happens to have the titles #T1 #T2 #T3 #T4 #T5 #T6 #T7 then the index-based text such as "3 , 2 , 4 + 6" is equivalent to the title-based text "T3 , T2 , T4 + T6".
For simplicity, all examples below will use the index notation.
PURE AXIS REORDERING
Here are a few examples that involve the production of a new table B by reordering the axes of A without any merging operation.
Since no merging of axes is involved, B will have 7 axes denoted as B₁ B₂ B₃ B₄ B₅ B₆ B₇
"2 , 1" → The axis A₂ is chosen as the first axis of B. The axis A₁ is chosen as the second axis of B. The remaining axes A₃ A₄ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 7 axes:
(B₁ B₂ B₃ B₄ B₅ B₆ B₇) = (A₂ A₁ A₃ A₄ A₅ A₆ A₇)
Note the same transformation is afforded by the texts:
"2 , 1 , 3" , "2 , 1 , 3 , 4" , "2 , 1 , 3 , 4 , 5" etc
"2 , 3" → The axis A₂ is chosen as the first axis of B. The axis A₃ is chosen as the second axis of B. The remaining axes A₁ A₄ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 7 axes:
(B₁ B₂ B₃ B₄ B₅ B₆ B₇) = (A₂ A₃ A₁ A₄ A₅ A₆ A₇)
Note the same transformation is afforded by the texts
"2 , 3 , 1" , "2 , 3 , 1 , 4" , "2 , 3 , 1 , 4 , 5" etc
"4 , 2" → The axis A₄ is chosen as the first axis of B. The axis A₂ is chosen as the second axis of B. The remaining axes A₁ A₃ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 7 axes:
(B₁ B₂ B₃ B₄ B₅ B₆ B₇) = (A₄ A₂ A₁ A₃ A₅ A₆ A₇)
Note the same transformation is afforded by the texts
"4 , 2 , 1" , "4 , 2 , 1 , 3" , "4 , 2 , 1 , 3 , 5" etc
PURE AXIS MERGING
Here are a few examples that involve the production of a new table B by merging selected A axes without any reordering operation.
Merging of two axes X and Y is defined as the formation of a new axis Z such that Z = X × Y, the cross product of X and Y.
Due to merging, B will have fewer than 7 axes.
"1 + 2" → The axes A₁ and A₂ are merged and compose the first axis of B. The remaining axes A₃ A₄ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 6 axes:
(B₁ B₂ B₃ B₄ B₅ B₆) = (A₁×A₂ A₃ A₄ A₅ A₆ A₇)
Note the same transformation is afforded by the texts:
"1 + 2 , 3" , "1 + 2 , 3 , 4" , "1 + 2 , 3 , 4 , 5" etc
Since the merged axes A₁ and A₂ are consecutive, the dash symbol "-" may be also used:
"1 - 2 , 3" , "1 - 2 , 3 , 4" , "1 - 2 , 3 , 4 , 5" etc
"1 , 2 + 3" → The axis A₁ is chosen as the first axis of B. The axes A₂ and A₃ are merged and compose the second axis of B. The remaining axes A₄ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 6 axes:
(B₁ B₂ B₃ B₄ B₅ B₆) = (A₁ A₂×A₃ A₄ A₅ A₆ A₇)
Note the same transformation is afforded by the texts
"1 , 2 + 3 , 4" , "1 , 2 + 3 , 4 , 5" , "1 , 2 + 3 , 4 , 5 , 6" etc
Since the merged axes A₂ and A₃ are consecutive, the dash symbol "-" may be also used:
"1 , 2 - 3 , 4" , "1 , 2 - 3 , 4 , 5" , "1 , 2 - 3 , 4 , 5 , 6" etc
"1 + 2 + 3" → The axes A₁ A₂ and A₃ are merged and compose the first axis of B. The remaining axes A₄ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 5 axes:
(B₁ B₂ B₃ B₄ B₅) = (A₁×A₂×A₃ A₄ A₅ A₆ A₇)
Note the same transformation is afforded by the texts:
"1 + 2 + 3 , 4" , "1 + 2 + 3 , 4 , 5" , "1 + 2 + 3 , 4 , 5 , 6" etc
Since the merged axes A₁ A₂ and A₃ are consecutive, the dash symbol "-" may be also used:
"1 - 3 , 4" , "1 - 3 , 4 , 5" , "1 - 3 , 4 , 5 , 6" etc
AXIS REORDERING AND MERGING
Here are a few examples that involve the production of a new table B by reordering and merging the axes of A.
Due to merging, B will have fewer than 7 axes.
"2 + 1" → The axes A₂ and A₁ are merged in the indicated order and compose the first axis of B. The remaining axes A₃ A₄ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 6 axes:
(B₁ B₂ B₃ B₄ B₅ B₆) = (A₂×A₁ A₃ A₄ A₅ A₆ A₇)
Note the same transformation is afforded by the texts
"2 + 1 , 3" , "2 + 1 , 3 , 4" , "2 + 1 , 3 , 4 , 5" etc
Since the merged axes A₂ and A₁ are consecutive, the dash symbol "-" may be also used:
"2 - 1 , 3" , "2 - 1 , 3 , 4" , "2 - 1 , 3 , 4 , 5" etc
"2 + 3" → The axes A₂ and A₃ are merged and compose the first axis of B. The remaining axes A₁ A₄ A₅ A₆ A₇ are appended keeping their order.
The result is a table B with the following 6 axes:
(B₁ B₂ B₃ B₄ B₅ B₆) = (A₂×A₃ A₁ A₄ A₅ A₆ A₇)
Note the same transformation is afforded by the texts
"2 + 3 , 1" , "2 + 3 , 1 , 4" , "2 + 3 , 1 , 4 , 5" etc
Since the merged axes A₂ and A₃ are consecutive, the dash symbol "-" may be also used:
"2 - 3 , 1" , "2 - 3 , 1 , 4" , "2 - 3 , 1 , 4 , 5" etc
Note this key is prefixed by -, which indicates it is not regarded as part of the object's data.
It appears only in the wizard to help the user with the data entry task.
It is never shown in the object's contents or in the pasted spreadsheet range.
It is also never part of the exported object's data.
IMPORTANT:
In the case where the object is part of another parent object, the value shown here can be ignored as it may not be at synch with the object's contained data.