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These terms are defined in the OpenType Math Tables as follows :

  1. StretchStackTopShiftUp Standard shift up applied to the top element of the stretch stack.
  2. StretchStackBottomShiftDown Standard shift down applied to the bottom element of the stretch stack.
  3. StretchStackGapAboveMin Minimum gap between the ink of the stretched element, and the (ink) bottom of the element above.
  4. StretchStackGapBelowMin Minimum gap between the ink of the stretched element, and the (ink) top of the element below.

Please note that this paper does not have a figure for these constants.

I also would like to know what is a "stretch stack".

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Are you the same person as tex.stackexchange.com/users/5122/belloc? In that case, you should register, so that your user accounts can be merged. – Caramdir May 31 '11 at 23:29
@Caramdir If there is no problem, I'd like to continue to use this forum unregistered, although I don't know exactly what the difference entails. – bellochio Jun 1 '11 at 10:55
As long as you are unregistered the system tends to create a new user for you from time to time. This means that you lose control over your questions (e.g. you cannot edit them or add comments) and lose your reputation points (and with them various privileges). – Caramdir Jun 1 '11 at 16:09
How do I merge the two accounts ? – bellochio Jun 1 '11 at 17:07
Ask a mod (e.g. via the flag link, in the chat or on meta) – Caramdir Jun 1 '11 at 18:03

Stretch stacks are items that are vertically stacked and stretch to match the width of their base element. Because they are similar to left/right delimiters, LuaTeX calls them “under delimiters” and “over delimiters.” A popular example is underbraces: they are constructed by the macro package in traditional TeX, but by the engine in LuaTeX (with a suitable definition of \underbrace, of course). See section 5.10 of the LuaTeX manual.

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Would it be possible for you to give me an idea what those entities (StackTopShiftUp, ...) are in your definition. The LuaTex Manual defines \Umathoverdelimiterbgap as the vertical baseline clearance for limits below operators, which doesn't seem to be the same as the OpenType definition given above. – bellochio Jun 1 '11 at 11:03
LuaTeX uses \Umathunderdelimitervgap = StretchStackGapAboveMin and \Umathunderdelimiterbgap = StretchStackBottomShiftDown (see mlist.w, lines 370–388). Since I don't have the source code of MS Word, I don't know whether that matches the intended meaning. – Philipp Jun 1 '11 at 19:30

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