On 17/01/2017 12:00 a.m., Frank Mittelbach wrote:
> Am 16.01.2017 um 11:41 schrieb David Carlisle:
>> Any apparent correspondence between inner and outer math and
>> displaystyle and textstyle is more or less accidental.
> \ifinner is described in the TeXbook simply as
> True if \TeX\ is in internal vertical mode, or restricted
> horizontal mode, or (nondisplay) math mode (see Chapter~13).
> which is unfortunately an over-simplification as the "style" can be
> explicitly set via \displaystyle and \textstyle and that is not
> reflected by the \ifinner test.
> Most math environment do exactly this, ie typesetting the formulas using
> $...$ = \ifinner=true but changing the style to \displaystyle when
> needed (with still \ifinner=true) which makes \ifinner pretty useless
> inside math
> As Joseph said, that is really only reflected when you look at \mathchoice
Thank you to all respondents who have made it clear that

"Math modes can be tested for: \ifmmode is true in display and 
non-display math mode, and \ifinner is true in non-display mode, but not 
in display mode"

(Eijkhout, "TeX by Topic", Section 23.1) is by no means generally true. 
(Although I suspect that in the *particular* circumstances that I was 
using the \ifinner test it does the job.)


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