Odtnhj

I have created the following macros in LaTeX:

deftwomate(#1,#2,#3,#4)beginpmatrix#1&#2\#3&#4endpmatrix
defpwr(#1)^#1
deftwoclmn(#1,#2)beginpmatrix#1\#2endpmatrix

Where twomate is a 2x2 matrix, twoclmn creates a 2x1 column vector, and pwr is a command to raise the argument to the power.
However, if I try to do the following:

$$twomate(3epwr(-3t),epwr(2t),-epwr(-3t),-2epwr(2t) )$$

I get an error. However, if I replace the last entry with something that is not a def command:

$$twomate(3epwr(-3t),epwr(2t),-epwr(-3t),5 )$$

The document complies successfully. In addition, the following does not compile successfully:

$$twoclmn(frac625epwr(2t)-frac15tepwr(2t),-frac225epwr(2t) + frac25 t epwr(2t))$$

But the following does:

$$twoclmn(frac625e^2t-frac15te^2t,-frac225e^2t + frac25 t e^2t)$$

So the problem seems to be the nested def commands. How may I nest def commands, without the compiler complaining?

You can use xparse for this job, because the r argument type takes care of nesting.

documentclassarticle
usepackageamsmath
usepackagexparse

NewDocumentCommandtwomate>SplitArgument3,r()%
 maketwomate#1%

NewDocumentCommandmaketwomatemmmm%
 beginpmatrix#1&#2\#3&#4endpmatrix%

NewDocumentCommandpwrr()^#1

begindocument

[
twomate(3epwr(-3t),epwr(2t),-epwr(-3t),-2epwr(2t) )
]

enddocument

However, using () as delimiters doesn't seem a good idea. The following is as clear and behaves better with syntax coloring of front ends.

documentclassarticle
usepackageamsmath
usepackagexparse

NewDocumentCommandtwomate>SplitArgument3,m%
 maketwomate#1%

NewDocumentCommandmaketwomatemmmm%
 beginpmatrix#1&#2\#3&#4endpmatrix%

NewDocumentCommandpwrm^#1

begindocument

[
twomate3epwr-3t,epwr2t,-epwr-3t,-2epwr2t
]

enddocument

Your def contains a very specific sequence defined as the parameter text:

% 1 2 3 4 5
deftwomate(<1>,<2>,<3>,<4>) ... 
% ^ ^ ^ ^ ^
% │ │ │ │ │
% │ └ comma ┘ │
% └─── bracket ───┘

This parameter text is matched exactly in order (almost like a first-come-first-served style) to extract the four arguments <1>, <2>, <3> and <4>. Here's how the elements are grabbed for twomate with the above notation:

% 1 2 3 4 5
twomate(3epwr(-3t),epwr(2t),-epwr(-3t),-2epwr(2t))
% ^ ^ ^ ^ ^
% │ │ │ │ │
% │ └────── comma ────────┘ │
% └───────────────── bracket ──────────────────┘

It should be clear that the last bracket ) isn't properly captured for pwr. The way around it is to hide pwr(.) from twomate:

documentclassarticle

usepackageamsmath

deftwomate(#1,#2,#3,#4)beginpmatrix#1&#2\#3&#4endpmatrix
defpwr(#1)^#1

begindocument

[
 twomate(3epwr(-3t),epwr(2t),-epwr(-3t),-2epwr(2t))
]

enddocument

This solves the problem only temporarily. If you nest elements, you'll run into similar problems because of the parameter text pattern matching. In general, it is safer to group arguments using ....

TeX's delimited parameters parsing doesn't take nesting into account properly. So if you call twomate(3epwr(-3t), ...), the final ) for twomate isn't found at the end of that line but at the end of pwr(-3t). The improperly formed call of pwr then causes trouble.

To hide nested calls of your commands, put them into ... groups (though this probably defeats the purpose):

documentclassarticle
usepackageamsmath

deftwomate(#1,#2,#3,#4)beginpmatrix#1&#2\#3&#4endpmatrix
defpwr(#1)^#1
deftwoclmn(#1,#2)beginpmatrix#1\#2endpmatrix

begindocument
[ twomate(3epwr(-3t),epwr(2t),-epwr(-3t),-2epwr(2t)) ]
enddocument

By the way, don't use $$ ... $$ for display math environments but LaTeX's or amsmath's variants like [ ... ].

original answer

Here is a way to define macros fetching their arguments like "functions" in many programming language.

It is lifted from the xintexpr code.

I had a bit forgotten the details, and left the code comments of XINT_isbalanced_a for those interested.

now that things come back more to my memory: of course comma separation of arguments will cause further issues. The xintexpr parser does not use at all this mechanism for implementing comma separated arguments of "functions". The mechanism as here is applied only for things such as seq(<expression>, x=1..10) where the <expression> if fetched as delimited by a comma, and then the balancing test is applied to it in case it was for example seq(myfunction(x,x^2),x=1..10) where the first comma would have been intially mistakendly taken as delimiter, but then the code realizes it is not balanced so it goes further.

thus, now that I think about it, nesting here would need checking the arguments picked up by comma delimited macros are balanced with respect to parentheses. I have not applied it yet, as the poor man approach here is still very low-weight and is enough for the OP use cases

See below how applyfunction is to be used.

(but as I explained in paragraphs above this is not provided as a nestable thing, only "functions" with 1 argument can be nested inside others; perhaps I will edit later to provide fuller solution).

Thus this is a no-package solution.

documentclassarticle

% copy over some utility code from package xintexpr
catcode`_ 11

makeatletter
letxint_c_monem@ne
letxint_c_z@
letxint_c_i@ne
longdefxint_bye #1xint_bye %
makeatother
% % endmacrocode
% subsubsectioncshXINT_isbalanced_a for cshnolabelXINT_expr_onliteral_seq_a
% lverb|Expands to xint_c_mone in case a closing ) had no opening ( matching
% it, to @ne if opening ( had no closing ) matching it, to z@ if expression
% was balanced.|
% beginmacrocode
% use as XINT_isbalanced_a relax #1(xint_bye)xint_bye
defXINT_isbalanced_a #1(XINT_isbalanced_b #1)xint_bye %
defXINT_isbalanced_b #1)#2%
 xint_bye #2XINT_isbalanced_cxint_byeXINT_isbalanced_error %
% endmacrocode
% lverb|if #2 is not xint_bye, a ) was found, but there was no (. Hence error -> -1|
% beginmacrocode
defXINT_isbalanced_error #1)xint_bye xint_c_mone%
% endmacrocode
% lverb|#2 was xint_bye, was there a ) in original #1?|
% beginmacrocode
defXINT_isbalanced_cxint_byeXINT_isbalanced_error #1%
 xint_bye #1XINT_isbalanced_yesxint_byeXINT_isbalanced_d #1%
% endmacrocode
% lverb|#1 is xint_bye, there was never ( nor ) in original #1, hence OK.|
% beginmacrocode
defXINT_isbalanced_yesxint_byeXINT_isbalanced_dxint_bye )xint_bye xint_c_ %
% endmacrocode
% lverb|#1 is not xint_bye, there was indeed a ( in original #1. We check if
% we see a ). If we do, we then loop until no ( nor ) is to be found.|
% beginmacrocode
defXINT_isbalanced_d #1)#2%
 xint_bye #2XINT_isbalanced_noxint_byeXINT_isbalanced_a #1#2%
% endmacrocode
% lverb|#2 was xint_bye, we did not find a closing ) in original #1. Error.|
% beginmacrocode
defXINT_isbalanced_noxint_bye #1xint_byexint_bye xint_c_i %

% Define a utility to apply a "function", comma separated arguments
defapplyfunction #1(#2)%
%
 ifcaseXINT_isbalanced_a relax #1#2(xint_bye)xint_bye
 expandafterapplyfunction_doit
 orexpandafterapplyfunction_again
 elseexpandafterwe_are_doomed
 fi #1#2%
%
defapplyfunction_doit #1#1,
defapplyfunction_again #1applyfunction #1)(

catcode`_ 8

usepackageamsmath


makeatletter

% function wrappers
deftwomateapplyfunctiontwomate@csv
defpwrapplyfunctionpwr@csv
deftwoclmnapplyfunctiontwoclmn@csv

% define macros with comma delimited arguments
deftwomate@csv#1,#2,#3,#4,beginpmatrix#1&#2\#3&#4endpmatrix
defpwr@csv#1,^#1
deftwoclmn@csv#1,#2,beginpmatrix#1\#2endpmatrix
% 

makeatother

begindocument

[
 twomate(3epwr(-3t),epwr(2t),-epwr(-3t),-2epwr(2t))
]
[
 twoclmn(frac625epwr(2t)-frac15tepwr(2t),-frac225epwr(2t)
 + frac25 t epwr(2t))
]
enddocument

updated answer

Original code allowed only nesting of "function" with one-argument inside other "functions".

Updated code makes more general nesting possible, we will test it with this input

foo(Bar(3,5,7),Bar(9,foo(a,Bar(W,X,Y),c,d),13),Bar(15,17,19),Bar(21,23,25))

and it works.

Notice that this code works only by expansion.

Code:

documentclassarticle
usepackageamsmath

% copy over some utility code from package xintexpr
catcode`_ 11

makeatletter
letxint_c_monem@ne
letxint_c_z@
letxint_c_i@ne
longdefxint_bye #1xint_bye %
makeatother
% NOTICE THAT ALL MACROS NEXT SHOULD BE MADE `long` ARGUABLY
% IT WAS NOT NEEDED IN XINTEXPR CONTEXT
% % endmacrocode
% subsubsectioncshXINT_isbalanced_a for cshnolabelXINT_expr_onliteral_seq_a
% lverb|Expands to xint_c_mone in case a closing ) had no opening ( matching
% it, to @ne if opening ( had no closing ) matching it, to z@ if expression
% was balanced.|
% beginmacrocode
% use as XINT_isbalanced_a relax #1(xint_bye)xint_bye
defXINT_isbalanced_a #1(XINT_isbalanced_b #1)xint_bye %
defXINT_isbalanced_b #1)#2%
 xint_bye #2XINT_isbalanced_cxint_byeXINT_isbalanced_error %
% endmacrocode
% lverb|if #2 is not xint_bye, a ) was found, but there was no (. Hence error -> -1|
% beginmacrocode
defXINT_isbalanced_error #1)xint_bye xint_c_mone%
% endmacrocode
% lverb|#2 was xint_bye, was there a ) in original #1?|
% beginmacrocode
defXINT_isbalanced_cxint_byeXINT_isbalanced_error #1%
 xint_bye #1XINT_isbalanced_yesxint_byeXINT_isbalanced_d #1%
% endmacrocode
% lverb|#1 is xint_bye, there was never ( nor ) in original #1, hence OK.|
% beginmacrocode
defXINT_isbalanced_yesxint_byeXINT_isbalanced_dxint_bye )xint_bye xint_c_ %
% endmacrocode
% lverb|#1 is not xint_bye, there was indeed a ( in original #1. We check if
% we see a ). If we do, we then loop until no ( nor ) is to be found.|
% beginmacrocode
defXINT_isbalanced_d #1)#2%
 xint_bye #2XINT_isbalanced_noxint_byeXINT_isbalanced_a #1#2%
% endmacrocode
% lverb|#2 was xint_bye, we did not find a closing ) in original #1. Error.|
% beginmacrocode
defXINT_isbalanced_noxint_bye #1xint_byexint_bye xint_c_i %

% New utility (expandable)
longdefapplyfunction #1#2)%
%
 ifcaseXINT_isbalanced_a relax #1#2)(xint_bye)xint_bye
 expandafterapplyfunction_b
 orexpandafterapplyfunction_again
 elseexpandafterwe_are_doomed
 fi #1#2%
%
longdefapplyfunction_again #1applyfunction #1)%
longdefmy_bbye #1my_bbye %
longdefapplyfunction_b #1applyfunction_c #1,my_bbye,%
longdefapplyfunction_c #1(applyfunction_d #1%
% we will take care of brace removal another day
longdefapplyfunction_d #1#2#3#4,%
%
 ifcaseXINT_isbalanced_a relax #3#4(xint_bye)xint_bye
 expandafterapplyfunction_e
 orexpandafterapplyfunction_d_again
 elseexpandafterwe_are_doomed
 fi #1#2#3#4%
%
longdefapplyfunction_d_again #1#2#3#4%
%
 applyfunction_d #1#2#3#4,%
%
longdefapplyfunction_e #1#2#3#4%
%
 my_bbye#4applyfunction_finishmy_bbye
 applyfunction_g #1#2#3#4%
%
longdefapplyfunction_g #1#2#3applyfunction_d #1#2#3%
longdefapplyfunction_finishmy_bbyeapplyfunction_g #1#2#3#1#2%

catcode`_ 8

%% USAGE
% "functions" to be used as foo(a,b,c,...)
% Syntax: applyfunctionnondelimitedmacro
% Number of arguments is determined dynamically (at most 9)
makeatletter
newcommandtwomateapplyfunctiontwomate@macro
newcommandpwrapplyfunctionpwr@macro
newcommandtwoclmnapplyfunctiontwoclmn@macro
% define here the **non-delimited** auxiliary macros
newcommandtwomate@macro[4]beginpmatrix#1&#2\#3&#4endpmatrix
newcommandpwr@macro[1]^#1
newcommandtwoclmn@macro[2]beginpmatrix#1\#2endpmatrix
makeatother


%% TESTING NESTING
makeatletter
newcommandfooapplyfunctionfoo@macro
newcommandfoo@macro[4]left[#1+#2+#3+#4right]
letBarrelax
newcommandBarapplyfunctionBar@macro
newcommandBar@macro[3]left(#1*#2*#3right)
makeatother

delimiterfactor1001

begindocument

[
 twomate(3epwr(-3t),epwr(2t),-epwr(-3t),-2epwr(2t))
]
[
 twoclmn(frac625epwr(2t)-frac15tepwr(2t),-frac225epwr(2t)
 + frac25 t epwr(2t))
]
[foo(Bar(3,5,7),Bar(9,foo(a,Bar(W,X,Y),c,d),13),Bar(15,17,19),Bar(21,23,25))]
enddocument