Spacing between columns in the amsmath's cases environment

Question

As most of you may already know, the amsmath package provides a cases environment. As the example in the user guide indicates, the typical usage of the environment is to construct a formula with different values in different conditions. Its implementation says an em quad is inserted between the columns:
renewenvironment{cases}{%
  matrix@checkcasesenv@cases
}{%
  endarrayright.%
}
defenv@cases{%
  let@ifnextcharnew@ifnextchar
  leftlbrace
  defarraystretch{1.2}%
  array{@{}l@{quad}l@{}}%
}

On the other hand, Mathematics into Type says in Section 3.1.6b that two-em quad is used

Between a symbolic statement and a condition on the statement.

and the example is

[
  x^n - y^n - z^n = A qquad (n = 0, 1, dotsc, p).
]

I think this is the case which the cases environment should fall under, but quad instead of qquad is used as noted above. This is confusing me.
Which spacing is better from the AMS viewpoint? Are there other references mentioning these situations?

barbara beeton · Answer

the cases environment was originally defined with the commands
cases ... endcases in amstex, and later converted to latex syntax
in amsmath.  so for the answer, one has to look at the history.

i didn't find any explicit commentary on the choice of one quad vs. two,
but there are other resources available.

a senior copyeditor, who trained under ellen swanson (author of math into type)
said that if the condition starts with a word -- which the conditions on cases
often do -- then a double quad is too much.  a single quad is sufficient in that
situation.

so i checked the published documentation in joy of tex.  in the first edition,
the example for cases has a double quad:

however, in the second edition, this has been reduced to a single quad:

(that does look much better.)

this is the equivalent of how cases is defined in amsmath.

other examples of math with a condition -- with "raw" math, no words -- do
use the double quad as shown in section 3.1.6b of math into type.

Spacing between columns in the amsmath's cases environment

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