Discussion:
[bug #59031] the \[Im] and \[Re] escapes are wrong
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G. Branden Robinson
2020-08-28 11:01:26 UTC
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URL:
<https://savannah.gnu.org/bugs/?59031>

Summary: the \[Im] and \[Re] escapes are wrong
Project: GNU troff
Submitted by: gbranden
Submitted on: Fri 28 Aug 2020 11:01:24 AM UTC
Category: Core
Severity: 3 - Normal
Item Group: Incorrect behaviour
Status: Need Info
Privacy: Public
Assigned to: gbranden
Open/Closed: Open
Discussion Lock: Any
Planned Release: None

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Details:

Blackletter/fraktur fonts are NOT generally used for the names of standard
number sets (naturals, integers, rationals, reals, complex numbers). Instead,
double-struck letters are typically used for this purpose. And in turn,
double-struck and blackletter faces are not the same.

See <https://mathworld.wolfram.com/Doublestruck.html>.

Given that:

I submit that at least one of the following is true.

1. The descriptions of these glyph names in groff_char(7) is wrong.


\[Im] \e[Im] Ifraktur u2111 Gothic I, imaginary
\[Re] \e[Re] Rfraktur u211C Gothic R, real


2. Their association with the Ifraktur and Rfraktur names in the Adobe Glyph
List (AGL) is incorrect.

3. The glyph names themselves are wrong to imply idiomatic usage as indicators
for the sets of real and imaginary numbers. (The complex field ā„‚ is more
commonly referred to than the set of imaginaries, which, being a 1-space
anyway, can be represented by simply by iā„ (where i is the imaginary
unit).

Unfortunately, this problem goes all the way back to the beginning.


^351da0dc doc/chars.tr (James Clark 1991-06-02 04:20:34 -0500 564)
.C2 Im Ifraktur "Fraktur I, imaginary"
^351da0dc doc/chars.tr (James Clark 1991-06-02 04:20:34 -0500 565)
.C2 Re Rfraktur "Fraktur R, real"


A variety of solutions suggest themselves.

A. Retire (delete, unsupport) the glyph names and let the user use
Unicode-form special character escapes if they need these symbols. As they
already do if they want the correct glyph for the reals.

B. Retain the mnemonics of the glyph name, remapping \[Im] and \[Re] to
U+1D540 and U+221D, respectively. Note that the former is outside the Basic
Multilingual Plane. This means dropping the AGL associations and the "Gothic"
part of the glyph descriptions.

C. Retain the mappings but rename them to be less misleading. We could go
ahead and use long glyph names for this purpose. I share the general
consensus expressed on the groff list in recent years that the groff glyph
list should be frozen, but this is an outright error and should be corrected.

D. Continue to be wrong and further cede the field of mathematical typography
to TeX.

Solutions A, B, and C would merit NEWS items. Solution D requires only an
admission of error in the groff_char(7) man page. And perhaps a suggestion
for .char remappings that one can add to one's documents.

groff mavens--what say you?




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Ingo Schwarze
2020-08-28 11:20:51 UTC
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Follow-up Comment #1, bug #59031 (project groff):

This report appears to be invalid.

\(Re and \(Im represent the functions "real part" and "imaginary part". Both
functions are surjective, but not injective funtions taking a complex argument
and delivering a real result. \(Re is also idempotent, but \(Im is not.

I don't think there is anything wrong with the current situation.

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G. Branden Robinson
2020-08-28 11:37:45 UTC
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Follow-up Comment #2, bug #59031 (project groff):

I was wondering if anyone was going to raise that red herring.

I know what Re() and Im() are.

No mention of functions is made anywhere. And I've never seen Fraktur R and I
used as symbols for those functions. Now, admittedly, I have only a lowly
engineering mathematics education and not a real one, but I work with several
and would be happy to bring this issue to them.

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G. Branden Robinson
2020-08-28 11:39:04 UTC
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Follow-up Comment #3, bug #59031 (project groff):

Okay, this is actually a disputed issue:

https://math.stackexchange.com/questions/234223/whats-more-common-re-im-or-fraktur-r-fraktur-i-for-real-imaginary-part

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G. Branden Robinson
2020-08-28 17:31:09 UTC
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Update of bug #59031 (project groff):

Item Group: Incorrect behaviour => Documentation
Status: Need Info => In Progress


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Ingo Schwarze
2020-08-29 00:48:25 UTC
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Update of bug #59031 (project groff):

Item Group: Documentation => Incorrect behaviour
Status: In Progress => Need Info

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Follow-up Comment #4:

You were explicitly talking about *sets*, so i made it clear that these
symbols do not represent sets but functions. The reason that the word
"function" is not in groff_char(7) is probably just that there is not enough
space. Mentioning the "Gothic" is more important, because with "Gothic" the
"function" is clear. With "function" or "part" but without "Gothic", it would
not be clear which glyph these produce because as you say, there are different
possibilities to represent these functions (but *if* the Gothics are used in
the context of complex numbers, their meaning is clear).

All three of your points are wrong.
1. The descriptions are correct and clear.
2. Representing these function with Gothic is a valid choice.
3. The glyph names are not wrong. The Gothic R and I symbols are commonly
read aloud as "Re" and "Im". These symbols do not indicate sets and the
symbols do not imply that. Your parenthetic remark makes no sense to me, but
most definitely C is not the same as iR in any sense.

All your solutions are wrong, too.
A. Breaks compatibility and removes useful functionality for no reason
whatsoever.
B. is just outrageously wrong. \(Re, i.e. the Re() function, is never
represented with a double-struck R, and the field of real numbers is never
called "Re"; when read, it is "er". Besides, U+221D is "PROPORTIONAL TO".
\(Im is never represented with a double-struck I. Even iR is usually not
represented with a double-struck I because it does not form a ring (is not
closed under multiplication). Double-struck letters are commonly used for
sets having a structure (like a field, ring, whatever), not for bare sets.
C. also breaks compatibility and functionality for no reason. There is no
error.
D. is the correct solution, except that nothing is wrong.

If you want to represent Re() and Im() as Re() and Im() in your printed
formula, which, as you say, is indeed one valid choice, you can simply put the
strings "Re(" etc. into your roff(7) source and don't need any escapes. But
if you want the Gothics, the escapes are needed to keep the source readable.

So please, just drop this already.

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G. Branden Robinson
2020-08-29 13:27:21 UTC
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Follow-up Comment #5, bug #59031 (project groff):

Hi Ingo,

Before I address your discursive points, I have to ask: why did you change
this ticket's "Item Group" back from "Documentation" to "Incorrect behaviour"?
I changed it to "Documentation" after consulting the URL in comment #3,
<https://math.stackexchange.com/questions/234223/whats-more-common-re-im-or-fraktur-r-fraktur-i-for-real-imaginary-part>.

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Ingo Schwarze
2020-08-29 19:40:35 UTC
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Update of bug #59031 (project groff):

Item Group: Incorrect behaviour => Documentation
Status: Need Info => In Progress

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Follow-up Comment #6:

Sorry, setting back the item group and the status was unintentional, i did not
even notice it. I'm not 100% sure why that happened. I think i still had an
earlier version of the ticket open in my browser when i wrote comment #4, and
maybe submitting the comment in that situation implied also setting the other
fields as they happened to be in my browser, where they maybe still contained
outdated values? On the other hand, i could already see your comments #2 and
#3, which is kind of strange...

I'm not opposed to explaining in more detail in the documentation what \(Re
and \(Im are if you find the space needed to do that and if you consider that
helpful - the discussion in this ticket may indicate that there is indeed some
potential for misunderstandings and confusion.

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G. Branden Robinson
2020-08-29 23:02:26 UTC
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Update of bug #59031 (project groff):

Summary: the \[Im] and \[Re] escapes are wrong => the \[Im]
and \[Re] escapes are inadequately described


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G. Branden Robinson
2020-09-01 18:24:20 UTC
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Update of bug #59031 (project groff):

Status: In Progress => Fixed
Open/Closed: Open => Closed
Planned Release: None => 1.22.5

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Follow-up Comment #7:

Fixed in 84639dd9012ae3efce2c38d9154e0df35df4d260.

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