summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/mathfixs/mathfixs.dtx
blob: 1f985e3707b78a36b262afb5783af6d2095c7ce4 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
% \iffalse
%
% mathfixs.dtx Copyright (C) 2018 Niklas Beisert
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
%
% The Current Maintainer of this work is Niklas Beisert.
%
% This work consists of the files mathfixs.dtx and mathfixs.ins
% and the derived files mathfixs.sty and mafxsamp.tex.
%
%<package|sample>\NeedsTeXFormat{LaTeX2e}[1996/12/01]
%<package>\ProvidesPackage{mathfixs}[2018/12/30 v1.01 various fixes for math mode]
%<sample>\ProvidesFile{mafxsamp.tex}[2018/12/30 v1.01 sample for mathfixs]
%<*driver>
%\ProvidesFile{mathfixs.drv}[2018/12/30 v1.01 mathfixs reference manual file]
\PassOptionsToClass{10pt,a4paper}{article}
\documentclass{ltxdoc}

\usepackage[margin=35mm]{geometry}
\usepackage{hyperref}
\usepackage{hyperxmp}
\usepackage[usenames]{color}

\hypersetup{colorlinks=true}
\hypersetup{pdfstartview=FitH}
\hypersetup{pdfpagemode=UseNone}
\hypersetup{pdfsource={}}
\hypersetup{pdflang={en-UK}}
\hypersetup{pdfcopyright={Copyright 2018 Niklas Beisert.
  This work may be distributed and/or modified under the
  conditions of the LaTeX Project Public License, either version 1.3
  of this license or (at your option) any later version.}}
\hypersetup{pdflicenseurl={http://www.latex-project.org/lppl.txt}}
\hypersetup{pdfcontactaddress={ETH Zurich, ITP, HIT K,
  Wolfgang-Pauli-Strasse 27}}
\hypersetup{pdfcontactpostcode={8093}}
\hypersetup{pdfcontactcity={Zurich}}
\hypersetup{pdfcontactcountry={Switzerland}}
\hypersetup{pdfcontactemail={nbeisert@itp.phys.ethz.ch}}
\hypersetup{pdfcontacturl={http://people.phys.ethz.ch/\xmptilde nbeisert/}}

\parskip1ex
\parindent0pt
\let\olditemize\itemize
\def\itemize{\olditemize\parskip0pt}

\begin{document}

\title{The \textsf{mathfixs} Package}
\hypersetup{pdftitle={The mathfixs Package}}
\author{Niklas Beisert\\[2ex]
  Institut f\"ur Theoretische Physik\\
  Eidgen\"ossische Technische Hochschule Z\"urich\\
  Wolfgang-Pauli-Strasse 27, 8093 Z\"urich, Switzerland\\[1ex]
  \href{mailto:nbeisert@itp.phys.ethz.ch}
  {\texttt{nbeisert@itp.phys.ethz.ch}}}
\hypersetup{pdfauthor={Niklas Beisert}}
\hypersetup{pdfsubject={Manual for the LaTeX2e Package mathfixs}}
\date{30 December 2018, \textsf{v1.01}}
\maketitle

\begin{abstract}\noindent
\textsf{mathfixs} is a \LaTeXe{} package
to fix some odd behaviour in math mode such as
spacing around fractions and roots,
math symbols within bold text
as well as
capital Greek letters.
It also adds some related macros.
\end{abstract}

\begingroup
\parskip0ex
\tableofcontents
\endgroup

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\makeatletter
\newcommand{\timingprint}[2][l]{%
  \ifhmode\par\fi%
  \ifvmode%
    \@bsphack%
    \dimen@\prevdepth%
    \nointerlineskip%
    \if r#1%
      \smash{\rlap{\hspace{\textwidth}\parbox[t]{1cm}%
        {\raggedright\renewcommand{\bfdefault}{b}#2}}}%
    \else%
      \smash{\llap{\parbox[t]{1cm}%
        {\raggedleft\renewcommand{\bfdefault}{b}#2}}}%
    \fi%
    \prevdepth\dimen@%
    \@esphack%
  \fi}
\newcommand{\printmark}[1]{\timingprint{\footnotesize#1}}
\newcommand{\printremark}[1]{%
  \timingprint[r]{\tiny\sffamily\hrule#1\hrule}}
\makeatother


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

Undoubtedly, \TeX{} and \LaTeX{} are excellent at
producing visually appealing mathematical expressions.
However, some commonly used macros produce output which
sometimes appears unbalanced under certain conditions.
Depending on the level of sophistication, such artefacts
are typically either ignored or fixed by some manual adjustments
wherever they appear.
This package addresses some of the issues
encountered commonly (by the author),
and provides fixes or additional macros to handle such situations.
At present the package is mainly concerned with:
%
\begin{itemize}
\item
spacing of fractions, roots and symbols
\item
alternative versions of fractions
\item
representation of (capital) Greek letters
\item
math symbols within bold text
\end{itemize}
%
Additional fixes and features may be added
to the package in later versions.
All of these features can be selected and customised
to some extent to accommodate for the desired style.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Usage}

To use the package \textsf{mathfixs} add the command
\begin{center}
|\usepackage{mathfixs}|
\end{center}
to the preamble of your \LaTeX{} document.
Furthermore you must select the desired features explicitly
as described below, otherwise the package will have no effect.
This is to avoid having to agree on
all the provided features and to allow for forward compatibility:
the package should remain open for future extensions
which may modify the default behaviour in an unintended fashion.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Package Features}

\DescribeMacro{\ProvideMathFix}
Features and options can be selected by the commands:
\begin{center}
\begin{tabular}{rl}
&|\usepackage[|\textit{opts}|]{mathfixs}|
\\
or&|\PassOptionsToPackage{|\textit{opts}|}{mathfixs}|
\\
or&|\ProvideMathFix{|\textit{opts}|}|
\end{tabular}
\end{center}
%
|\PassOptionsToPackage| must be used before |\usepackage|;
|\ProvideMathFix| must be used afterwards.
Note that if |\ProvideMathFix| is invoked within a block,
its definitions are valid only locally within the block.
\textit{opts} is a comma-separated list of features or options.
The available features and options are described below.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Fractions}

The package offers some improvements for the spacing of fractions
as well as definitions to typeset small rational numbers.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{frac}.}
\DescribeMacro{frac}
%
In many situations, \LaTeX{} typesets fractions with an
insufficient amount of surrounding space.
For example, the space between two consecutive fractions
almost make them appear as a single one:
%
\begin{center}
|x\frac{a+b}{c+d}\frac{e}{f}.|
\quad$\longrightarrow$\quad
$\displaystyle x\frac{a+b}{c+d}\frac{e}{f}.$
\end{center}
%
Also the space towards other symbols and punctuation marks
arguably is too small.
To make expressions more legible, sequences of fractions
are often coded with various custom spaces
(`|\,|', `|\:|', `|\;|', `|\ |', `|~|', etc.)
inserted, e.g.
%
\begin{center}
|x\,\frac{a+b}{c+d}\;\frac{e}{f}\ .|
\quad$\longrightarrow$\quad
$\displaystyle x\,\frac{a+b}{c+d}\;\frac{e}{f}\ .$
\end{center}
%
This looks better, but requires a lot of intervention
and depends very much on personal conventions.

The underlying technical reason for the shortcoming in spacing
around fractions
is that the latter are defined
to have the math class of ordinary objects (|\mathord|)
which results in no surrounding space.
A simple resolution is to assign the math class
of inner objects (|\mathinner|) to fractions
as described in the \textsf{\TeX{}book}, e.g.
%
\begin{center}
|x\mathinner{\frac{a+b}{c+d}}\mathinner{\frac{e}{f}}.|
\end{center}
%
Inner objects behave almost like ordinary objects,
but some space is added between them and
other inner or ordinary objects, e.g.:
%
\[
x\mathinner{\frac{a+b}{c+d}}\mathinner{\frac{e}{f}}.
\]
%
Importantly, no space is added between inner objects
and the ends of the math expression or subexpression in parentheses.
Also, no space is generated
in the script styles (|\|[|script|]|scriptstyle|).

\DescribeMacro{\frac}
The feature |frac| redefines the macro |\frac|
such that all fractions have the inner math class
producing some surrounding space in selected situations, e.g.:
%
\begin{center}
|x\frac{a+b}{c+d}\frac{e}{f}.|
\quad$\longrightarrow$\quad
$\displaystyle x\mathinner{\frac{a+b}{c+d}}\mathinner{\frac{e}{f}}.$
\end{center}
%
This makes adding custom space around fractions
unnecessary in almost all situations,
and leads to a rather uniform appearance
without further adjustments.

\DescribeMacro{\genfrac}
\DescribeMacro{\dfrac}
\DescribeMacro{\tfrac}
The macro |\genfrac| of the package \textsf{amsmath}
is modified suitably when the latter is loaded.
This also affects the macros |\dfrac| and |\tfrac| for fractions
in styles |\displaystyle| and |\textstyle|, respectively.
For |\genfrac| fractions with delimiters,
the inner math class is not applied
because the default math class is appropriate.

Note that when the |frac| feature is used,
spaces around fractions can be eliminated by using:
%
\begin{center}
|\mathord{\frac{|\textit{num}|}{|\textit{denom}|}}|
\end{center}
%
or simply (a block enclosed by braces |{|\ldots|}|
is considered an object with ordinary math class):
%
\begin{center}
|{\frac{|\textit{num}|}{|\textit{denom}|}}|
\end{center}
%
Furthermore, note that unlike the original macro |\frac|,
the redefined macro must be enclosed in a block
when passed as an argument. For example, |x^\frac{1}{2}|
produces an error and must be written as |x^{\frac{1}{2}}|.

\DescribeMacro{fracclass}
\DescribeMacro{fracdelimclass}
The option |fracclass=|\textit{class}
can be used to customise the math class of fractions
to any desired command \textit{class} accepting
the expression for the fraction as its single parameter.
Likewise, the option |fracdelimclass=|\textit{class}
customises the math class of fractions with delimiters
generated by |\genfrac| such as |\|[|d|$\vert$|t|]|binom|.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{rfrac}.}
\DescribeMacro{rfrac}
%
Rational numbers as coefficients to
some simple terms often stick out visually
from displayed math expressions, e.g.:
%
\[
\frac{1}{2}x^2 + \frac{1}{6} y^3 + \frac{1}{4} x^2 y^2
\]
%
Arguably, typesetting such fractions in text style
has a more uniform appearance:
%
\[
{\textstyle\frac{1}{2}}x^2
+ {\textstyle\frac{1}{6}} y^3
+ {\textstyle\frac{1}{4}} x^2 y^2
\]
%

\DescribeMacro{\rfrac}
The feature |rfrac| defines the macro |\rfrac|
to typeset a fraction in text style or smaller.
It is similar to |\tfrac| of the package \textsf{amsmath},
but it will not choose text style when in the script styles
and it will not produce surrounding space
when the feature |frac| is used.
The optional argument |rfrac={\|\textit{cmd}|}| specifies
an alternative command name |\|\textit{cmd} for |\rfrac|.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{vfrac}.}
\DescribeMacro{vfrac}
\DescribeMacro{\vfrac}
%
Common or vulgar fractions such as $^1\!/\!_2$
can be typeset in a simple fashion
as a superscript numerator followed by a slash
and a subscript denominator.
The spacing around the slash should be reduced
to join the expression.
The package provides this representation
as the feature |vfrac| defining the macro |\vfrac|.
It is similar to |\nicefrac| of the package \textsf{nicefrac}
or the more advanced implementation |\sfrac| of the package \textsf{xfrac}.
As vulgar fractions are often (mainly) used within plain text,
the macro |\vfrac| also works in text mode.
The optional argument |vfrac={\|\textit{cmd}|}| specifies
an alternative command name |\|\textit{cmd} for |\vfrac|.

\DescribeMacro{vfracclass}
\DescribeMacro{vfracskippre}
\DescribeMacro{vfracskippost}
The option |vfracclass=|\textit{class}
can be used to customise the math class of the vulgar fraction.
The options |vfracskippre=|\textit{muskip}
and |vfracskippost=|\textit{muskip}
defines the (negative) skip around the slash
(must be given in math units |mu|).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Roots}

The \TeX{} implementations of radicals, mostly those with exponents,
have some uneven spacing, e.g.:
%
\[
y\sqrt{x}z,\qquad
y\sqrt[]{x}z,\qquad
y\sqrt[i]{x}z,\qquad
y\sqrt[n]{x}z,\qquad
y\sqrt[3]{x}z,\qquad
y\sqrt[123]{x}z
\]
%
They work best if no exponent is specified
or if the exponent is a single numerical digit.
The spacing is slightly different if the exponent is $n$ or $i$.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{root}.}
\DescribeMacro{root}
\DescribeMacro{\sqrt}
\DescribeMacro{\root}
%
The package provides an alternative mechanism for the
placement of the exponent next to the radical.
It first measures the extents of the exponent
and the radical sign and then places them accordingly.
It also adds some space at the end of the radicand.
The refined definition produces the following representation
without further spacing adjustments
%
\[
y\sqrt{x\mskip2mu}z,\qquad
y\sqrt{x\mskip2mu}z,\qquad
y\mskip5mu
  \sqrt[{\makebox[0pt][r]{$\scriptscriptstyle i$}}]{x\mskip2mu}z,\qquad
y\mskip5mu
  \sqrt[{\makebox[0pt][r]{$\scriptscriptstyle n$}}]{x\mskip2mu}z,\qquad
y\mskip5mu
  \sqrt[{\makebox[0pt][r]{$\scriptscriptstyle 3$}}]{x\mskip2mu}z,\qquad
y\mskip-5mu
  \sqrt[123]{x\mskip2mu}z
\]
%

\DescribeMacro{rootclass}
\DescribeMacro{rootskipend}
\DescribeMacro{rootskippre}
\DescribeMacro{rootskippost}
The option |rootclass=|\textit{class}
can be used to customise the math class of the vulgar fraction.
The option |rootskipend=|\textit{muskip}
defines the additional skip at the end of the radicand
within the radical (must be given in math units |mu|).
The options |rootskippre=|\textit{muskip}
and |rootskippost=|\textit{muskip}
define additional skip around the radical.

\DescribeMacro{rootclose}
The option |rootclose| adds a closing mark
to the end of the top bar of radicals:
%
\[
\setbox0\hbox{$\sqrt{a\mskip2mu}$}\copy0\lower\fontdimen8\textfont3
\hbox{\vrule width\fontdimen8\textfont3 height \ht0 depth -0.8\ht0}
\]
%
The optional argument |rootclose=|\textit{height}
specifies the starting height with a default value of $0.8$.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Space Representing Multiplication Signs}

Mathematical expressions regularly omit explicit multiplication signs
between factors, e.g. $x^2yz$. All is well unless
some of the factors are compound expressions such as
$\Delta x$ or differentials $dx$ (or $\mathrm{d}x$)
where additional space is typically inserted by
commands like `|\,|'.

A simple method to declare (or define) compound expressions
with a suitable amount of surrounding space
is to encapsulate them in a |\mathinner| block, e.g.
%
\begin{center}
|12c\mathinner{\Delta x}\mathinner{\Delta y}z|
\quad$\longrightarrow$\quad
$12c\mathinner{\Delta x}\mathinner{\Delta y}$
\\
|\int x\mathinner{dx}|
\quad$\longrightarrow$\quad
$\displaystyle\int x\mathinner{dx}$
\end{center}
%
Importantly, |\mathinner| will not add any space
at the ends of an expression
(or a subexpression in parentheses).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{multskip}.}
\DescribeMacro{multskip}
\DescribeMacro{\.}
%
Furthermore, the package provides the feature |multskip|
to encode a space representing an omitted multiplication sign
by the short command `|\.|', e.g.:
%
\begin{center}
|12c\.\Delta x\.\Delta y\.z|
\qquad or\qquad
|\int x\.dx|
\end{center}
%
The macro `|\.|' produces some amount of space in math mode
(while retaining its original definition as an accent in text mode)
and by default it is equivalent to `|\,|'.
However, the macro `|\.|' is intended to describe this space unambiguously
as a multiplication sign.
In particular, the amount of space can be configured by
the option |multskip=|\textit{muskip} (given in math units |mu|),
or the command could be customised further
to a visually different representation.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Greek Letters}

\TeX{} defines Greek letters in math mode somewhat differently
from Latin letters. The following two features redefine
to the standard \TeX{} Greek letters.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{greekcaps}.}
\DescribeMacro{greekcaps}
%
Capital Greek letters are declared as operators instead of plain letters,
and therefore they are typeset in an upright shape.
To typeset them in italic shape
(as all the other letters representing variables)
one can use |\mathnormal|,
but this may be tedious if most capital Greek letters in a document
actually represent variables.

The feature |greekcaps| redefines the 11 capital Greek letters
|\Gamma|, |\Delta|, |\Theta|, |\Lambda|, |\Xi|, |\Pi|,
|\Sigma|, |\Upsilon|, |\Phi|, |\Psi| and |\Omega|
provided by \TeX{} to have a default italic shape.
Upright capital Greek letters remain accessible
by switching to the upright shape using |\mathrm|
or by declaring them as part of an operator,
e.g. |\operatorname| or |\DeclareMathOperator|
(package \textsf{amsmath}).

The optional argument |greekcaps=|\textit{pre} will
instead define the macros |\|\textit{pre}|Gamma|, etc.,
and keep the original definitions.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{greeklower}.}
\DescribeMacro{greeklower}
%
Lowercase Greek letters are fixed to the default math italic
font because (unfortunately) no upright counterparts exist
in the Compute Modern family of fonts.

The feature |greeklower| redefines the 23 lowercase Greek letters
|\alpha|, \ldots, |\omega|
as well as their 6 variants
|\varepsilon|, |\vartheta|, |\varpi|, |\varphi|, |\varrho| and |\varsigma|
defined by \TeX{}
to be elements of the regular math alphabet.
This allows them to be typeset in different font series
such as |\mathbold| described below.
However, when trying to cast them in upright shape
they will be typeset as altogether different symbols,
e.g. |\mathrm{\alpha}| becomes the ligature `ff'
which occupies the same slot in the \TeX{} font encodings OML vs.\ OT1.
Hence, some caution is needed when this feature is used.

The optional argument |greeklower=|\textit{pre} will
instead define the macros |\|\textit{pre}|alpha|, etc.,
and keep the original definitions.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Bold Fonts}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{autobold}.}
\DescribeMacro{autobold}
%
Sectioning commands such as |\chapter|, |\section|, |\paragraph|,
etc., but also |\maketitle| often change the font series to bold.
However, any math symbols contained in the titles
are typeset in the regular, non-bold series by default leading to
a non-uniform appearance or calling for further manual adjustments
using |\boldmath|.
One might argue that it is bad practice to have math symbols in titles
in the first place,
but this point of view perhaps does not apply universally.

\DescribeMacro{\bfseries}
\DescribeMacro{\mdseries}
The feature |autobold| overwrites the \LaTeX{} font commands
|\bfseries|, |\mdseries| as well as |\normalfont|
to automatically switch the math fonts to their bold version.
Derived commands such as |\section|, etc., will also
switch the math fonts to the bold series.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{Feature \texttt{mathbold}.}
\DescribeMacro{mathbold}
\DescribeMacro{\mathbold}
%
The feature |mathbold| defines a bold italic math font |\mathbold|.
To typeset bold italic letters simply use |\mathbold{abc}|.
To make this work for lowercase Greek letters as well,
the feature |greeklower| must be activated.
The optional argument |mathbold={\|\textit{cmd}|}| specifies
an alternative command name |\|\textit{cmd} for |\mathbold|, e.g.
|mathbold={\mathbit}|.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Information}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Copyright}

Copyright \copyright{} 2018 Niklas Beisert

This work may be distributed and/or modified under the
conditions of the \LaTeX{} Project Public License, either version 1.3
of this license or (at your option) any later version.
The latest version of this license is in
  \url{http://www.latex-project.org/lppl.txt}
and version 1.3 or later is part of all distributions of \LaTeX{}
version 2005/12/01 or later.

This work has the LPPL maintenance status `maintained'.

The Current Maintainer of this work is Niklas Beisert.

This work consists of the files |README.txt|, |mathfixs.ins| and |mathfixs.dtx|
as well as the derived files |mathfixs.sty|, |mafxsamp.tex| and |mathfixs.pdf|.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Files and Installation}

The package consists of the files:
%
\begin{center}
\begin{tabular}{ll}
    |README.txt|   & readme file \\
    |mathfixs.ins| & installation file \\
    |mathfixs.dtx| & source file \\
    |mathfixs.sty| & package file \\
    |mafxsamp.tex| & sample file \\
    |mathfixs.pdf| & manual
\end{tabular}
\end{center}
%
The distribution consists of the files
|README.txt|, |mathfixs.ins| and |mathfixs.dtx|.
%
\begin{itemize}
\item
Run (pdf)\LaTeX{} on |mathfixs.dtx|
to compile the manual |mathfixs.pdf| (this file).
\item
Run \LaTeX{} on |mathfixs.ins| to create the package |mathfixs.sty|
and the sample |mafxsamp.tex|.
Copy the file |mathfixs.sty| to an appropriate directory of your \LaTeX{}
distribution, e.g.\ \textit{texmf-root}|/tex/latex/mathfixs|.
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Related CTAN Packages}

The package is related to other packages available at CTAN:
\begin{itemize}
\item
This package uses the package
\href{http://ctan.org/pkg/keyval}{\textsf{keyval}}
from the \href{http://ctan.org/pkg/latex-graphics}{\textsf{graphics}} bundle
to process the options for the package, environments and macros.
Compatibility with the \textsf{keyval} package
has been tested with v1.15 (2014/10/28).
\item
This package was designed to be compatible with
the package \href{http://ctan.org/pkg/amsmath}{\textsf{amsmath}}.
To prevent \textsf{amsmath} from overwriting some features,
it should be loaded before the present package.
Compatibility with the \textsf{amsmath} package
has been tested with v2.17a (2017/09/02).
\item
This package reproduces the functionality of the
package \href{http://ctan.org/pkg/fixmath}{\textsf{fixmath}} v0.9 (2000/04/11)
from the bundle \href{http://ctan.org/pkg/was}{\textsf{was}}.
\item
Functionality to typeset common fractions is also provided by
the packages \href{http://ctan.org/pkg/nicefrac}{\textsf{nicefrac}}
from the bundle \href{http://ctan.org/pkg/units}{\textsf{units}}
and \href{http://ctan.org/pkg/xfrac}{\textsf{xfrac}}
offering a more advanced implementation.
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Feature Suggestions}
%
%The following is a list of features which may be useful for future
%versions of this package:
%%
%\begin{itemize}
%\item
% redefine macros |\Re|, |\Im|, |\mod|
% complete macros for trigonometric functions?
%\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Revision History}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{v1.01:} 2018/12/30

\begin{itemize}
\item
fix for |\vfrac| in aligned math
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\paragraph{v1.0:} 2018/01/17

\begin{itemize}
\item
first version published on CTAN
\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendix

\settowidth\MacroIndent{\rmfamily\scriptsize 000\ }

 \DocInput{mathfixs.dtx}

\end{document}
%</driver>
% \fi
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Sample File}
%\iffalse
%<*sample>
%\fi
%
% In this section we provide an example of how to use
% some of the \textsf{mathfixs} features.
% We also test the behaviour in some special cases.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Preamble.}
%
% Standard document class:
%    \begin{macrocode}
\documentclass[12pt]{article}
%    \end{macrocode}

% Use package \textsf{geometry} to adjust the page layout,
% adjust the paragraph shape:
%    \begin{macrocode}
\usepackage{geometry}
\geometry{layout=a4paper}
\geometry{paper=a4paper}
\geometry{margin=3cm}
\parindent0pt
%    \end{macrocode}

% Include \textsf{amsmath} and the \textsf{mathfixs} package:
%    \begin{macrocode}
\RequirePackage{amsmath}
\RequirePackage[autobold]{mathfixs}
%    \end{macrocode}

% Declare features to be implemented globally:
%    \begin{macrocode}
\ProvideMathFix{greekcaps,mathbold}
\ProvideMathFix{frac,rfrac,vfrac}
\ProvideMathFix{multskip}
%    \end{macrocode}

% Start document body:
%    \begin{macrocode}
\begin{document}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Fractions.}
%    \begin{macrocode}
\paragraph{Fractions.}
%    \end{macrocode}

% Fraction spacing:
%    \begin{macrocode}
\[
x\frac{a+b}{c+d}\frac{e}{f}.
\]
%    \end{macrocode}

% Vulgar fractions:
%    \begin{macrocode}
Recipe for $\approx 3$ pancakes (scale accordingly):
Whisk together one large egg, $\vfrac{1}{8} \ell$ milk,
$50\mathinner{\mathrm{g}}$ flour
(mix \vfrac{2}{3} wholemeal flour and \vfrac{1}{3} white flour); fry in pan.
Feel free to use more flour than indicated.
%    \end{macrocode}

% Rational numbers:
%    \begin{macrocode}
\[
\rfrac{1}{2}x^2 + \rfrac{1}{6} y^3 + \rfrac{1}{4} x^2 y^2
\]
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Radicals.}
%    \begin{macrocode}
\paragraph{Radicals.}
%    \end{macrocode}

% Original radicals spacing:
%    \begin{macrocode}
\[
y\sqrt{x}z,\qquad
y\sqrt[]{x}z,\qquad
y\sqrt[i]{x}z,\qquad
y\sqrt[n]{x}z,\qquad
y\sqrt[3]{x}z,\qquad
y\sqrt[123]{x}z
\]
%    \end{macrocode}

% Radicals spacing
% (feature introduced in document body):
%    \begin{macrocode}
\ProvideMathFix{root}
\[
y\sqrt{x}z,\qquad
y\sqrt[]{x}z,\qquad
y\sqrt[i]{x}z,\qquad
y\sqrt[n]{x}z,\qquad
y\sqrt[3]{x}z,\qquad
y\sqrt[123]{x}z
\]
%    \end{macrocode}

% Radicals with closing mark
% (using a locally defined option):
%    \begin{macrocode}
\[
\ProvideMathFix{rootclose}
y\sqrt{x}z,\qquad
y\sqrt[]{x}z,\qquad
y\sqrt[i]{x}z,\qquad
y\sqrt[n]{x}z,\qquad
y\sqrt[3]{x}z,\qquad
y\sqrt[123]{x}z
\]
%    \end{macrocode}

% Radicals with class |\mathinner|:
%    \begin{macrocode}
\[
\ProvideMathFix{rootclass={\mathinner}}
y\sqrt{x}z,\qquad
y\sqrt[]{x}z,\qquad
y\sqrt[i]{x}z,\qquad
y\sqrt[n]{x}z,\qquad
y\sqrt[3]{x}z,\qquad
y\sqrt[123]{x}z
\]
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Spaces Representing Multiplication.}
%    \begin{macrocode}
\paragraph{Spaces Representing Multiplication.}
%    \end{macrocode}

% Explicit spacing:
%    \begin{macrocode}
\newcommand{\der}{\mathrm{d}}
\[
\int x\.\der x
\]
%    \end{macrocode}

% Implicit spacing:
%    \begin{macrocode}
\newcommand{\diff}[1]{\mathinner{\der#1}}
\[
\int x\diff{x}
\]
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Greek Letters.}
%    \begin{macrocode}
\paragraph{Greek Letters.}
%    \end{macrocode}

% Capital letters:
%    \begin{macrocode}
\[
\Gamma \qquad
\mathrm{\Gamma} \qquad
c\operatorname{\Gamma}(x)
\]
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Bold Text with Math Symbols.}
%    \begin{macrocode}
\paragraph{Bold Text with Math Symbols: $abc123\alpha\Gamma$.}
%    \end{macrocode}

% Capital letters:
%    \begin{macrocode}
\[
aG\alpha\Gamma
\qquad\mathbold{aG\alpha\Gamma}
\qquad\ProvideMathFix{greeklower}\mathbold{aG\alpha\Gamma}
\]
%    \end{macrocode}

% End of document body:
%    \begin{macrocode}
\end{document}
%    \end{macrocode}
%\iffalse
%</sample>
%\fi
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Implementation}
%\iffalse
%<*package>
%\fi
%
% In this section we describe the package |mathfixs.sty|.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Required Packages.}
%
% The package loads the package
% \textsf{keyval}
% if not yet present.
% \textsf{keyval} is used for extended options processing:
%    \begin{macrocode}
\RequirePackage{keyval}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Automatically Bold Maths.}
%
% \macro{\bfseries}
% \macro{\mdseries}
% \macro{\normalfont}
% Define replacements for |\bfseries|, |\mdseries| and |\normalfont|
% by appending |\boldmath| or |\unboldmath|
% (if not already in math mode where font selection works differently).
% The chain of |\expandafter| directives fills in the original definition:
%    \begin{macrocode}
\expandafter\def\expandafter\mafx@bfseries\expandafter
  {\bfseries\ifmmode\else\boldmath\fi}
\expandafter\def\expandafter\mafx@mdseries\expandafter
  {\mdseries\ifmmode\else\unboldmath\fi}
\expandafter\def\expandafter\mafx@normalfont\expandafter
  {\normalfont\ifmmode\else\unboldmath\fi}
%    \end{macrocode}

% \macro{autobold}
% Implement the |autobold| fix:
%    \begin{macrocode}
\define@key{mafx@}{autobold}[]{%
  \let\bfseries=\mafx@bfseries
  \let\mdseries=\mafx@mdseries
  \let\normalfont=\mafx@normalfont
}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Bold Italic Math.}
%
% \macro{mathbold}
% \macro{\mathbold}
% Define a new math alphabet |\mathbold|
% as the bold series and italic shape
% of the standard computer modern math font
% (see package \textsf{fixmath}):
%
%    \begin{macrocode}
\DeclareMathAlphabet{\mafx@mathbold}{OML}{cmm}{b}{it}
%    \end{macrocode}

% \macro{autobold}
% Implement |\mathbold| (or alterantive macro name):
%    \begin{macrocode}
\define@key{mafx@}{mathbold}[\mathbold]{\let#1=\mafx@mathbold}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Spacing Adjustment for Fractions.}
%
% Save primitive definition of |\over| into |\@@over|
% (compatible with \textsf{amsmath}):
%
%    \begin{macrocode}
\ifdefined\@@over\else\let\@@over=\over\fi
%    \end{macrocode}

% Define math class selectors for fractions (without/with delimiters):
%    \begin{macrocode}
\def\mafx@frac@class{\mathinner}
\def\mafx@frac@delimclass{\mathopen{}\mathclose}
%    \end{macrocode}

% \macro{\frac}
% Define replacement for |\frac| which uses a configurable
% math class selector:
%    \begin{macrocode}
\DeclareRobustCommand{\mafx@frac}[2]{%
    \mafx@frac@class{\begingroup#1\endgroup\@@over#2}}
%    \end{macrocode}

% \macro{\genfrac}
% Define replacement for |\@genfrac| (called by |\genfrac|)
% which uses the appropriate math class selector.
% If the package \textsf{amsmath} is not loaded, this definition will
% have no impact:
%    \begin{macrocode}
\def\mafx@@genfrac#1#2#3#4#5{\begingroup%
  \ifx#2\@@overwithdelims\let\mafx@frac@class\mafx@frac@delimclass\fi%
  \ifx#2\@@abovewithdelims\let\mafx@frac@class\mafx@frac@delimclass\fi%
  \ifx#2\@@atopwithdelims\let\mafx@frac@class\mafx@frac@delimclass\fi%
  \mafx@frac@class{#1{\begingroup#4\endgroup#2#3\relax#5}}%
  \endgroup}
%    \end{macrocode}

% \macro{frac}
% Implement the replacement for |\frac| and |\genfrac|:
%    \begin{macrocode}
\define@key{mafx@}{frac}[]{%
  \let\frac=\mafx@frac
  \let\@genfrac=\mafx@@genfrac
}
%    \end{macrocode}

% \macro{fracclass}
% \macro{fracdelimclass}
% Configure the math classes for fractions (without/with delimiters):
%    \begin{macrocode}
\define@key{mafx@}{fracclass}{\def\mafx@frac@class{#1}}
\define@key{mafx@}{fracdelimclass}{\def\mafx@frac@delimclass{#1}}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Small Fractions.}
%
% \macro{\rfrac}
% Define a fraction in text style or smaller
% using the ordinary math class (no surrounding space), e.g.: $\frac{1}{2}$:
%    \begin{macrocode}
\DeclareRobustCommand{\mafx@rfrac}[2]{{\mathchoice%
  {\textstyle{\begingroup#1\endgroup\@@over#2}}%
  {\begingroup#1\endgroup\@@over#2}%
  {\begingroup#1\endgroup\@@over#2}%
  {\begingroup#1\endgroup\@@over#2}}}
%    \end{macrocode}

% \macro{rfrac}
% Implement |\rfrac| (or alternative macro name):
%    \begin{macrocode}
\define@key{mafx@}{rfrac}[\rfrac]{\let#1=\mafx@rfrac}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Vulgar Fractions.}
%
% Define the math class and spacing parameters as (negative) spaces
% around the dividing slash:
%    \begin{macrocode}
\def\mafx@vfrac@class{\mathinner}
\def\mafx@vfrac@preskip{\thinmuskip}
\def\mafx@vfrac@postskip{0.6667\thinmuskip}
%    \end{macrocode}
%
% \macro{\vfrac}
% Define a vulgar representation of a rational number, e.g.: $^1\!/\!_2$.
% Automatically switch to math mode if in text mode:
%    \begin{macrocode}
\DeclareRobustCommand{\mafx@vfrac}[2]{\ifmmode%
  \mafx@vfrac@class{\textstyle%
    ^{#1}\mkern-\mafx@vfrac@preskip/\mkern-\mafx@vfrac@postskip_{#2}}%
  \else$\mafx@vfrac{#1}{#2}$\fi}
%    \end{macrocode}

% \macro{vfrac}
% Implement |\vfrac| (or alternative macro name):
%    \begin{macrocode}
\define@key{mafx@}{vfrac}[\vfrac]{\let#1=\mafx@vfrac}
%    \end{macrocode}

% \macro{vfracclass}
% \macro{vfracskippre}
% \macro{vfracskippost}
% Define configurable skip parameters for |\vfrac|:
%    \begin{macrocode}
\define@key{mafx@}{vfracclass}{\def\mafx@vfrac@class{#1}}
\define@key{mafx@}{vfracskippre}{\def\mafx@vfrac@preskip{#1}}
\define@key{mafx@}{vfracskippost}{\def\mafx@vfrac@postskip{#1}}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Spacing Adjustment for Roots.}
%
% Define some parameters for the improved root macros.
% |\mafx@root@close| stores the relative height
% where the closing bar for the radical starts;
% empty disables the closing bar.
% |\mafx@root@class| stores the math class for a root.
% |\mafx@root@endskip| stores space to be added after the radicant
% but within the radical in math units.
% |\mafx@root@preskip| and |\mafx@root@postskip| store space to be added
% before or after the radical sign:
%    \begin{macrocode}
\let\mafx@root@close=\@empty
\def\mafx@root@class{}
\def\mafx@root@endskip{0.6667\thinmuskip}
\def\mafx@root@preskip{0mu}
\def\mafx@root@postskip{0.3333\thinmuskip}
%    \end{macrocode}

% \macro{\sqrt}
% Replacement for |\sqrt| which passes an
% empty first argument instead of calling |\sqrtsign|:
%    \begin{macrocode}
\DeclareRobustCommand\mafx@sqrt{\@ifnextchar[\@sqrt{\@sqrt[]}}
\def\mafx@@sqrt[#1]{\root#1\of}
%    \end{macrocode}

% \macro{\root}
% Replacement for |\root| \ldots|\of|
% which stores the |\leftroot| and |\uproot| parameters
% specified in the exponent (see package \textsf{amsmath}).
% It does so by first storing them in global parameters
% and then converting them to local ones to avoid
% interference with nested radicals.
% As usual, the macro then passes on to |\r@@t|
% with |\mathpalette|:
%    \begin{macrocode}
\def\mafx@root#1\of{
  \setbox\rootbox\hbox{$\m@th\scriptscriptstyle{%
    \gdef\mafx@gleftroot{0}\gdef\mafx@guproot{0}%
    \def\leftroot##1{\gdef\mafx@gleftroot{##1}}%
    \def\uproot##1{\gdef\mafx@guproot{##1}}%
    #1}$}%
  \let\mafx@leftroot=\mafx@gleftroot%
  \let\mafx@uproot=\mafx@guproot%
  \mathpalette\r@@t}
%    \end{macrocode}

% The replacement for |\r@@t| typesets the radical by
% placing the exponent in an elevated box.
% First, select desirect math class:
%    \begin{macrocode}
\def\mafx@r@@t#1#2{\mafx@root@class{%
%    \end{macrocode}
% Determine the font selector for the current style:
%    \begin{macrocode}
  \ifx#1\scriptstyle\let\mafx@tmp@fontsel=\scriptfont\else%
  \ifx#1\scriptscriptstyle\let\mafx@tmp@fontsel=\scriptscriptfont\else%
  \let\mafx@tmp@fontsel=\textfont\fi\fi%
%    \end{macrocode}
% Generate a radical with empty radicand in cramped style
% (see package \textsf{mathtools})
% at the desired height and depth and store in a box
% for subsequent measurements:
%    \begin{macrocode}
  \sbox\z@{$\m@th#1\nulldelimiterspace=\z@\radical\z@{#2}$}%
  \setlength\dimen@{\ht\z@}%
  \ifx#1\displaystyle
    \addtolength\dimen@{-\fontdimen8\textfont3}%
    \addtolength\dimen@{-0.25\fontdimen5\textfont2}%
  \else
    \addtolength\dimen@{-1.25\fontdimen8\mafx@tmp@fontsel3}%
  \fi
  \setbox\z@=\hbox{$\m@th#1\sqrtsign{%
    \vrule width0pt height\dimen@ depth\dp\z@}$}%
%    \end{macrocode}
% Shift to start of exponent box such that end
% will reside at 60\% of radical sign.
% Do not shift if exponent box is sufficiently wide:
%    \begin{macrocode}
  \setlength\dimen@{-\wd\rootbox}%
  \addtolength\dimen@{0.6\wd\z@}%
  \ifdim\dimen@>0pt\else\setlength\dimen@{0pt}\fi%
  \kern\dimen@%
%    \end{macrocode}
% Compute elevation of exponent box as 60\% of radical sign.
% Add length specified by |\uproot|:
%    \begin{macrocode}
  \setlength\dimen@{0.6\ht\z@}\addtolength\dimen@{-0.6\dp\z@}%
  \setbox\@ne\hbox{$\m@th#1\mskip\mafx@uproot mu$}%
  \addtolength\dimen@{\wd\@ne}%
%    \end{macrocode}
% Place exponent box and return to intended start of radical sign:
%    \begin{macrocode}
  \mkern-\mafx@leftroot mu%
  \raise\dimen@\copy\rootbox%
  \mkern\mafx@leftroot mu%
  \kern-0.6\wd\z@%
%    \end{macrocode}
% Place radical adding extra kernings |\mafx@root@preskip| and
% |\mafx@root@endskip|:
%    \begin{macrocode}
  \mkern\mafx@root@preskip\sqrtsign{#2\mskip\mafx@root@endskip}%
%    \end{macrocode}
% Add a closing bar to the radical,
% see \url{http://en.wikibooks.org/wiki/LaTeX/Mathematics}.
% If |\mafx@root@close| is empty, ignore.
% Determine the thickness of the rule as font dimension x8.
% Draw a vertical rule starting from relative height |\mafx@root@close|
% of the radical:
%    \begin{macrocode}
  \ifx\mafx@root@close\@empty\else%
  \setlength\dimen@{\fontdimen8\mafx@tmp@fontsel3}%
  \lower\dimen@\hbox{%
    \vrule width\dimen@ height\ht\z@ depth -\mafx@root@close\ht\z@}%
  \fi%
%    \end{macrocode}
% Finally, add kerning |\mafx@root@postskip|:
%    \begin{macrocode}
  \mkern\mafx@root@postskip}}
%    \end{macrocode}

% \macro{root}
% Implement replacement |\sqrt| and |\root|:
%    \begin{macrocode}
\define@key{mafx@}{root}[]{
  \let\sqrt=\mafx@sqrt
  \let\@sqrt=\mafx@@sqrt
  \let\root=\mafx@root
  \let\r@@t=\mafx@r@@t
}
%    \end{macrocode}

% \macro{rootclose}
% \macro{rootclass}
% \macro{rootskipend}
% \macro{rootskippre}
% \macro{rootskipbefore}
% Define configurable parameters for alternative root:
%    \begin{macrocode}
\define@key{mafx@}{rootclose}[0.8]{\def\mafx@root@close{#1}}
\define@key{mafx@}{rootclass}{\def\mafx@root@class{#1}}
\define@key{mafx@}{rootskipend}{\def\mafx@root@endskip{#1}}
\define@key{mafx@}{rootskippre}{\def\mafx@root@preskip{#1}}
\define@key{mafx@}{rootskippost}{\def\mafx@root@postskip{#1}}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Space Representing Multiplication.}
%
% \macro{\.}
% Define |\.| to represent a thin math skip when in math mode.
% Retain original definition as an accent in text mode.
% Switch is performed by temporarily storing the appropriate macro
% which is subsequently issued so that the correct number of
% arguments are fetched:
%    \begin{macrocode}
\let\mafx@old@dot=\.
\def\mafx@dot@skip{\thinmuskip}
\def\mafx@dot{\mskip\mafx@dot@skip}
\def\mafx@per@dot{\begingroup\ifmmode\def\mafx@tmp{\mafx@dot}\else%
  \def\mafx@tmp{\mafx@old@dot}\fi\expandafter\endgroup\mafx@tmp}
%    \end{macrocode}

% \macro{multskip}
% Implement definition of |\.|:
%    \begin{macrocode}
\define@key{mafx@}{multskip}[\thinmuskip]{%
  \let\.=\mafx@per@dot
  \def\mafx@dot@skip{#1}%
}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Italic Capital Greek Letters.}
%
% \macro{\Gamma}
% \macro{...}
% Define capital Greek letters as letters
% (instead of the default assignment as operators).
% This implementation follows the package \textsf{fixmath}:
%    \begin{macrocode}
\DeclareMathSymbol{\mafx@Gamma}{\mathalpha}{letters}{0}
\DeclareMathSymbol{\mafx@Delta}{\mathalpha}{letters}{1}
\DeclareMathSymbol{\mafx@Theta}{\mathalpha}{letters}{2}
\DeclareMathSymbol{\mafx@Lambda}{\mathalpha}{letters}{3}
\DeclareMathSymbol{\mafx@Xi}{\mathalpha}{letters}{4}
\DeclareMathSymbol{\mafx@Pi}{\mathalpha}{letters}{5}
\DeclareMathSymbol{\mafx@Sigma}{\mathalpha}{letters}{6}
\DeclareMathSymbol{\mafx@Upsilon}{\mathalpha}{letters}{7}
\DeclareMathSymbol{\mafx@Phi}{\mathalpha}{letters}{8}
\DeclareMathSymbol{\mafx@Psi}{\mathalpha}{letters}{9}
\DeclareMathSymbol{\mafx@Omega}{\mathalpha}{letters}{10}
%    \end{macrocode}

% \macro{greekcaps}
% Implement italic capital Greek letters.
% The optional argument is used as a prefix for the definitions:
%    \begin{macrocode}
\define@key{mafx@}{greekcaps}[]{%
  \expandafter\let\csname #1Gamma\endcsname=\mafx@Gamma
  \expandafter\let\csname #1Delta\endcsname=\mafx@Delta
  \expandafter\let\csname #1Theta\endcsname=\mafx@Theta
  \expandafter\let\csname #1Lambda\endcsname=\mafx@Lambda
  \expandafter\let\csname #1Xi\endcsname=\mafx@Xi
  \expandafter\let\csname #1Pi\endcsname=\mafx@Pi
  \expandafter\let\csname #1Sigma\endcsname=\mafx@Sigma
  \expandafter\let\csname #1Upsilon\endcsname=\mafx@Upsilon
  \expandafter\let\csname #1Phi\endcsname=\mafx@Phi
  \expandafter\let\csname #1Psi\endcsname=\mafx@Psi
  \expandafter\let\csname #1Omega\endcsname=\mafx@Omega
}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Lowercase Greek Letters in Standard Math Type.}
%
% \macro{\alpha}
% \macro{...}
% Define lowercase Greek letters in standard type |\mathalpha|
% (instead of the default assiment |\mathord|).
% This implementation follows the package \textsf{fixmath}:
%    \begin{macrocode}
\DeclareMathSymbol{\mafx@alpha}{\mathalpha}{letters}{11}
\DeclareMathSymbol{\mafx@beta}{\mathalpha}{letters}{12}
\DeclareMathSymbol{\mafx@gamma}{\mathalpha}{letters}{13}
\DeclareMathSymbol{\mafx@delta}{\mathalpha}{letters}{14}
\DeclareMathSymbol{\mafx@epsilon}{\mathalpha}{letters}{15}
\DeclareMathSymbol{\mafx@zeta}{\mathalpha}{letters}{16}
\DeclareMathSymbol{\mafx@eta}{\mathalpha}{letters}{17}
\DeclareMathSymbol{\mafx@theta}{\mathalpha}{letters}{18}
\DeclareMathSymbol{\mafx@iota}{\mathalpha}{letters}{19}
\DeclareMathSymbol{\mafx@kappa}{\mathalpha}{letters}{20}
\DeclareMathSymbol{\mafx@lambda}{\mathalpha}{letters}{21}
\DeclareMathSymbol{\mafx@mu}{\mathalpha}{letters}{22}
\DeclareMathSymbol{\mafx@nu}{\mathalpha}{letters}{23}
\DeclareMathSymbol{\mafx@xi}{\mathalpha}{letters}{24}
\DeclareMathSymbol{\mafx@pi}{\mathalpha}{letters}{25}
\DeclareMathSymbol{\mafx@rho}{\mathalpha}{letters}{26}
\DeclareMathSymbol{\mafx@sigma}{\mathalpha}{letters}{27}
\DeclareMathSymbol{\mafx@tau}{\mathalpha}{letters}{28}
\DeclareMathSymbol{\mafx@upsilon}{\mathalpha}{letters}{29}
\DeclareMathSymbol{\mafx@phi}{\mathalpha}{letters}{30}
\DeclareMathSymbol{\mafx@chi}{\mathalpha}{letters}{31}
\DeclareMathSymbol{\mafx@psi}{\mathalpha}{letters}{32}
\DeclareMathSymbol{\mafx@omega}{\mathalpha}{letters}{33}
\DeclareMathSymbol{\mafx@varepsilon}{\mathalpha}{letters}{34}
\DeclareMathSymbol{\mafx@vartheta}{\mathalpha}{letters}{35}
\DeclareMathSymbol{\mafx@varpi}{\mathalpha}{letters}{36}
\DeclareMathSymbol{\mafx@varphi}{\mathalpha}{letters}{39}
\DeclareMathSymbol{\mafx@varrho}{\mathalpha}{letters}{37}
\DeclareMathSymbol{\mafx@varsigma}{\mathalpha}{letters}{38}
%    \end{macrocode}

% \macro{greeklower}
% Implement standard type lowercase Greek letters.
% The optional argument is used as a prefix for the definitions:
%    \begin{macrocode}
\define@key{mafx@}{greeklower}[]{%
  \expandafter\let\csname #1alpha\endcsname=\mafx@alpha
  \expandafter\let\csname #1beta\endcsname=\mafx@beta
  \expandafter\let\csname #1gamma\endcsname=\mafx@gamma
  \expandafter\let\csname #1delta\endcsname=\mafx@delta
  \expandafter\let\csname #1epsilon\endcsname=\mafx@epsilon
  \expandafter\let\csname #1zeta\endcsname=\mafx@zeta
  \expandafter\let\csname #1eta\endcsname=\mafx@eta
  \expandafter\let\csname #1theta\endcsname=\mafx@theta
  \expandafter\let\csname #1iota\endcsname=\mafx@iota
  \expandafter\let\csname #1kappa\endcsname=\mafx@kappa
  \expandafter\let\csname #1lambda\endcsname=\mafx@lambda
  \expandafter\let\csname #1mu\endcsname=\mafx@mu
  \expandafter\let\csname #1nu\endcsname=\mafx@nu
  \expandafter\let\csname #1xi\endcsname=\mafx@xi
  \expandafter\let\csname #1pi\endcsname=\mafx@pi
  \expandafter\let\csname #1rho\endcsname=\mafx@rho
  \expandafter\let\csname #1sigma\endcsname=\mafx@sigma
  \expandafter\let\csname #1tau\endcsname=\mafx@tau
  \expandafter\let\csname #1upsilon\endcsname=\mafx@upsilon
  \expandafter\let\csname #1phi\endcsname=\mafx@phi
  \expandafter\let\csname #1chi\endcsname=\mafx@chi
  \expandafter\let\csname #1psi\endcsname=\mafx@psi
  \expandafter\let\csname #1omega\endcsname=\mafx@omega
  \expandafter\let\csname #1varepsilon\endcsname=\mafx@varepsilon
  \expandafter\let\csname #1vartheta\endcsname=\mafx@vartheta
  \expandafter\let\csname #1varpi\endcsname=\mafx@varpi
  \expandafter\let\csname #1varphi\endcsname=\mafx@varphi
  \expandafter\let\csname #1varrho\endcsname=\mafx@varrho
  \expandafter\let\csname #1varsigma\endcsname=\mafx@varsigma
}
%    \end{macrocode}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \paragraph{Package Options.}
%
% \macro{\ProvideMathFix}
% Implement a particular fix or option:
%    \begin{macrocode}
\newcommand{\ProvideMathFix}[1]{\setkeys{mafx@}{#1}}
%    \end{macrocode}

% Pass undeclared options on to \textsf{keyval} processing:
%    \begin{macrocode}
\DeclareOption*{\expandafter\ProvideMathFix\expandafter{\CurrentOption}}
%    \end{macrocode}
%
% Process package options:
%    \begin{macrocode}
\ProcessOptions
%    \end{macrocode}

%\iffalse
%</package>
%\fi
%
\endinput