LaTeX3 people will give more authoritative answers (particularly they know how to generate variants to \matset which will expand its argument). In the mean time, perhaps this helps (it seems the issues were that you did not use semi-colons to end rows, and there was a problem of expansion).
TeX is a macro language, where the key word is expansion. Even if you use higher abstraction levels like LaTeX2 (which tries to its best to \emph{hide} from the user the programming possibilities) or LaTeX3 (which to the contrary has a very well-thought and sophisticated scheme to make it easier to code, while at the same time clearly separating programmer tasks from end user tools), you can not escape that. It seems that the \matset macro from the code you linked too does not expand its argument. If you try to use it as \matset\MatrixA {\macro{3}}, it will receive \macro{3} and not the semi-colon separated rows it seems to expect. You first need to tell TeX to expand \macro{3} to that list or rows. It would be immediate for a \LaTeX3 programmer to generate the variant of \matset which first expands its argument, as a work-around, \expandafter\matset\expandafter\MatrixA \expandafter{\macro{3}} would do it. Notice that the brace { is part of the input stream and must be jumped over by \expandafter.
%% (to be embedded in the code from [there](https://tex.stackexchange.com/a/112683/34359))
\def\GetRotationMatrix #1{%
cos(#1), -sin(#1), 0;
sin(#1), cos(#1), 0;
0, 0, 1 }
\expandafter\matset\expandafter\transformMatrixA \expandafter
{\GetRotationMatrix {3.141592653}}
\begin{equation}
\mattypeset \transformMatrixA
\end{equation}
Here embedded at the end of the code of Bruno Le Floch
% Programming-level functions: \fpm_new:N, \fpm_set:Nn, \fpm_gset:Nn,
% \fpm_add:NNN, \fpm_sub:NNN, \fp_neg:NN, \fp_transpose:NN, \fp_mul:NNN.
%
% Expandable programming-level functions: \fpm_lines:N, \fpm_columns:N,
% \fpm_get:Nnn.
%
% Document-level functions: \matnew, \matset, \matgset, \matadd,
% \matsub, \matmul, \mattypeset.
%
\RequirePackage{expl3}
{
\ExplSyntaxOn
%
% Programming-level code, for adding, multiplying, matrices. A matrix
% of size |MxN| is stored as a token list of the form
%
% \s__fpm { M } { N } { {a11} ... {a1N} } ... { {aM1} ... {aMN} } ;
%
% where |\s__fpm| is a marker used to recognize matrices, |M| and |N|
% are non-negative integers, and |aij| are floating point numbers.
%
% (1) Variables.
%
\cs_new_eq:NN \s__fpm \scan_stop: % A marker.
\tl_const:Nn \c_empty_fpm { \s__fpm { 0 } { 0 } ; }
\cs_new_eq:NN \l__fpm_tmpa_fpm \c_empty_fpm
\seq_new:N \l__fpm_lines_seq
\int_new:N \l__fpm_lines_A_int
\int_new:N \l__fpm_lines_B_int
\int_new:N \l__fpm_columns_A_int
\int_new:N \l__fpm_columns_B_int
\tl_new:N \l__fpm_matrix_A_tl
\tl_new:N \l__fpm_matrix_B_tl
\tl_new:N \l__fpm_matrix_C_tl
\seq_new:N \l__fpm_matrix_A_seq
\seq_new:N \l__fpm_matrix_B_seq
\seq_new:N \l__fpm_one_line_A_seq
\seq_new:N \l__fpm_one_line_B_seq
\tl_new:N \l__fpm_one_line_A_tl
\int_new:N \l__fpm_tmpa_int
%
% (2) Variants and generic helpers.
%
%
% (3) Storing matrices.
%
\cs_new_protected:Npn \fpm_new:N #1
{ \cs_new_eq:NN #1 \c_empty_fpm }
\cs_new_protected_nopar:Npn \fpm_set:Nn
{ \__fpm_set:NNn \tl_set:Nx }
\cs_new_protected_nopar:Npn \fpm_gset:Nn
{ \__fpm_set:NNn \tl_gset:Nx }
\cs_new_protected:Npn \__fpm_set:NNn #1#2#3
{
\seq_set_split:Nnn \l__fpm_lines_seq { ; } {#3}
\seq_set_filter:NNn \l__fpm_lines_seq \l__fpm_lines_seq
{ ! \tl_if_empty_p:n {##1} }
%
% Now all lines are non-empty.
%
\tl_clear:N \l__fpm_matrix_A_tl
\int_zero:N \l__fpm_lines_A_int
\int_zero:N \l__fpm_columns_A_int
\seq_map_inline:Nn \l__fpm_lines_seq
{
\int_incr:N \l__fpm_lines_A_int
\seq_set_from_clist:Nn \l__fpm_one_line_A_seq {##1}
\int_set:Nn \l__fpm_tmpa_int { \seq_count:N \l__fpm_one_line_A_seq }
\int_compare:nNnT \l__fpm_columns_A_int = \c_zero
{ \int_set_eq:NN \l__fpm_columns_A_int \l__fpm_tmpa_int }
\int_compare:nNnF \l__fpm_tmpa_int = \l__fpm_columns_A_int
{ \seq_map_break:n { \msg_error:nn { fpm } { invalid-size } } }
\tl_put_right:Nx \l__fpm_matrix_A_tl
{ { \seq_map_function:NN \l__fpm_one_line_A_seq \__fpm_set_aux:n } }
}
#1 #2
{
\s__fpm
{ \int_use:N \l__fpm_lines_A_int }
{ \int_use:N \l__fpm_columns_A_int }
\l__fpm_matrix_A_tl
;
}
}
\cs_new:Npn \__fpm_set_aux:n #1 { { \fp_to_tl:n {#1} } }
%
% (4) Extracting the size of a matrix, and its contents.
% |#1| is the matrix, |#2|, |#3| integer variables receiving the
% number of lines and of columns, and |#4| a token list receiving the
% contents of the matrix.
%
\cs_new_protected:Npn \__fpm_get_parts:NNNN #1#2#3#4
{ \exp_after:wN \__fpm_get_parts:NnnwNNN #1 #2 #3 #4 }
\cs_new_protected:Npn \__fpm_get_parts:NnnwNNN \s__fpm #1#2#3 ; #4#5#6
{
\int_set:Nn #4 {#1}
\int_set:Nn #5 {#2}
\tl_set:Nn #6 {#3}
}
%
% (5) Some expandable functions: getting one entry, getting the size.
%
\cs_new:Npn \fpm_lines:N #1
{ \exp_after:wN \__fpm_lines:NnnwN #1 \use_i:nn }
\cs_new:Npn \fpm_columns:N #1
{ \exp_after:wN \__fpm_lines:NnnwN #1 \use_ii:nn }
\cs_new:Npn \__fpm_lines:NnnwN \s__fpm #1#2#3 ; #4 { #4 {#1} {#2} }
\cs_new:Npn \fpm_get:Nnn #1#2#3
{ \exp_after:wN \__fpm_get:Nnnwnn #1 #2 #3 }
\cs_new:Npn \__fpm_get:Nnnwnn \s__fpm #1#2#3 ; #4#5
{ \exp_args:Nf \tl_item:nn { \tl_item:nn {#3} {#4} } {#5} }
%
% (6) Summing matrices
%
\cs_new_protected_nopar:Npn \fpm_add:NNN { \__fpm_add:NNNN + }
\cs_new_protected_nopar:Npn \fpm_sub:NNN { \__fpm_add:NNNN - }
\cs_new_protected:Npn \__fpm_add:NNNN #1#2#3#4
{
\tl_set:Nn \l__fpm_sign_tl {#1}
\__fpm_get_parts:NNNN #3
\l__fpm_lines_A_int \l__fpm_columns_A_int \l__fpm_matrix_A_tl
\__fpm_get_parts:NNNN #4
\l__fpm_lines_B_int \l__fpm_columns_B_int \l__fpm_matrix_B_tl
\int_compare:nNnTF \l__fpm_lines_A_int = \l__fpm_lines_B_int
{
\int_compare:nNnTF \l__fpm_columns_A_int = \l__fpm_columns_B_int
{ \__fpm_add:N #2 }
{ \msg_error:nn { fpm } { invalid-size } }
}
{ \msg_error:nn { fpm } { invalid-size } }
}
\cs_new_protected:Npn \__fpm_add:N #1
{
\seq_set_split:NnV \l__fpm_matrix_A_seq { } \l__fpm_matrix_A_tl
\seq_set_split:NnV \l__fpm_matrix_B_seq { } \l__fpm_matrix_B_tl
\tl_clear:N \l__fpm_matrix_C_tl
\seq_mapthread_function:NNN
\l__fpm_matrix_A_seq
\l__fpm_matrix_B_seq
\__fpm_add_lines:nn
\tl_set:Nx #1
{
\s__fpm
{ \int_use:N \l__fpm_lines_A_int }
{ \int_use:N \l__fpm_columns_A_int }
\l__fpm_matrix_C_tl
;
}
}
\cs_new_protected:Npn \__fpm_add_lines:nn #1#2
{
\seq_set_split:Nnn \l__fpm_one_line_A_seq { } {#1}
\seq_set_split:Nnn \l__fpm_one_line_B_seq { } {#2}
\tl_put_right:Nx \l__fpm_matrix_C_tl
{
{
\seq_mapthread_function:NNN
\l__fpm_one_line_A_seq
\l__fpm_one_line_B_seq
\__fpm_add_entries:nn
}
}
}
\cs_new:Npn \__fpm_add_entries:nn #1#2
{ { \fp_to_tl:n { #1 \l__fpm_sign_tl #2 } } }
%
% (7) Negating all entries.
%
\cs_new_protected:Npn \fpm_neg:NN #1#2
{ \tl_set:Nx #1 { \exp_after:wN \__fpm_neg:Nnnw #2 } }
\cs_new:Npn \__fpm_neg:Nnnw \s__fpm #1#2#3 ;
{ \s__fpm {#1} {#2} \tl_map_function:nN {#3} \__fpm_neg_aux:n ; }
\cs_new:Npn \__fpm_neg_aux:n #1
{ { \tl_map_function:nN {#1} \__fpm_neg_auxii:n } }
\cs_new:Npn \__fpm_neg_auxii:n #1
{ { \fp_to_tl:n { - #1 } } }
%
% (8) Transposing a matrix.
%
\cs_new_protected:Npn \fpm_transpose:NN #1#2
{
\__fpm_get_parts:NNNN #2
\l__fpm_lines_A_int \l__fpm_columns_A_int \l__fpm_matrix_A_tl
\seq_set_split:NnV \l__fpm_matrix_A_seq { } \l__fpm_matrix_A_tl
\tl_clear:N \l__fpm_matrix_B_tl
\prg_replicate:nn { \l__fpm_columns_A_int }
{
\tl_put_right:Nx \l__fpm_matrix_B_tl
{ { \seq_map_function:NN \l__fpm_matrix_A_seq \__fpm_wrap_head:n } }
\seq_set_map:NNn \l__fpm_matrix_A_seq \l__fpm_matrix_A_seq
{ \tl_tail:n {##1} }
}
\tl_set:Nx #1
{
\s__fpm
{ \int_use:N \l__fpm_columns_A_int }
{ \int_use:N \l__fpm_lines_A_int }
\l__fpm_matrix_B_tl
;
}
}
\cs_new:Npn \__fpm_wrap_head:n #1 { { \tl_head:n {#1} } }
%
% (9) Multiplying matrices.
%
\cs_new_protected:Npn \fpm_mul:NNN #1#2#3
{
\int_compare:nNnTF { \fpm_columns:N #2 } = { \fpm_lines:N #3 }
{
\fpm_transpose:NN \l__fpm_tmpa_fpm #3
\__fpm_get_parts:NNNN #2
\l__fpm_lines_A_int \l__fpm_columns_A_int \l__fpm_matrix_A_tl
\__fpm_get_parts:NNNN #3
\l__fpm_lines_B_int \l__fpm_columns_B_int \l__fpm_matrix_B_tl
\tl_set:Nx #1
{
\s__fpm
{ \int_use:N \l__fpm_lines_A_int }
{ \int_use:N \l__fpm_columns_B_int }
\tl_map_function:NN \l__fpm_matrix_A_tl \__fpm_mul_line:n
;
}
}
{ \msg_error:nn { fpm } { invalid-size } }
}
\cs_new:Npn \__fpm_mul_line:n #1
{ { \exp_after:wN \__fpm_mul_line:Nnnwn \l__fpm_tmpa_fpm {#1} } }
\cs_new:Npn \__fpm_mul_line:Nnnwn \s__fpm #1#2#3 ; #4
{ \__fpm_mul_line:nn {#4} #3 \q_recursion_tail \q_recursion_stop }
\cs_new:Npn \__fpm_mul_line:nn #1#2
{
\quark_if_recursion_tail_stop:n {#2}
{
\fp_to_tl:n
{
\__fpm_mul_one:nwn #1 \use_none_delimit_by_q_stop:w
\q_mark #2 \q_nil \q_stop
0
}
}
\__fpm_mul_line:nn {#1}
}
\cs_new:Npn \__fpm_mul_one:nwn #1#2 \q_mark #3
{ #1 * #3 + \__fpm_mul_one:nwn #2 \q_mark }
%
%
% Messages.
%
\msg_new:nnn { fpm } { invalid-size }
{ Sizes~of~matrices~or~lines~don't~match. }
}
\RequirePackage{amsmath, siunitx}
{
\ExplSyntaxOn
%
% Turning matrices into arrays for display.
%
\cs_new_protected:Npn \fpm_to_array:N #1
{
\begin{pmatrix}
\exp_after:wN \__fpm_to_array:Nnnw #1
\end{pmatrix}
}
\cs_new_eq:NN \__fpm_newline: ? % Dummy def.
\cs_new_protected:Npn \__fpm_to_array:Nnnw \s__fpm #1#2#3 ;
{
\cs_gset_nopar:Npn \__fpm_newline:
{ \cs_gset_nopar:Npn \__fpm_newline: { \\ } }
\tl_map_inline:nn {#3}
{
\__fpm_newline:
\seq_set_split:Nnn \l__fpm_one_line_A_seq { } {##1}
\seq_set_map:NNn \l__fpm_one_line_A_seq \l__fpm_one_line_A_seq
{ \__fpm_to_array_entry:n {####1} }
\seq_use:Nnnn \l__fpm_one_line_A_seq { & } { & } { & }
}
}
\cs_new_protected:Npn \__fpm_to_array_entry:n #1
{
\str_case:nnn {#1}
{
{ nan } { \text{nan} }
{ inf } { \infty }
{ -inf } { -\infty }
}
{ \num{#1} }
}
}
\RequirePackage{xparse}
\ExplSyntaxOn
%
% Document-level functions.
%
\NewDocumentCommand { \matnew } { m } { \fpm_new:N #1 }
\NewDocumentCommand { \matset } { mm } { \fpm_set:Nn #1 {#2} }
\NewDocumentCommand { \matgset } { mm } { \fpm_gset:Nn #1 {#2} }
\NewDocumentCommand { \matadd } { mmm } { \fpm_add:NNN #1 #2 #3 }
\NewDocumentCommand { \matsub } { mmm } { \fpm_sub:NNN #1 #2 #3 }
\NewDocumentCommand { \matneg } { mm } { \fpm_neg:NN #1 #2 }
\NewDocumentCommand { \mattranspose } { mm } { \fpm_transpose:NN #1 #2 }
\NewDocumentCommand { \matmul } { mmm } { \fpm_mul:NNN #1 #2 #3 }
\NewDocumentCommand { \mattypeset } { m }
{ \fpm_to_array:N #1 }
\ExplSyntaxOff
\documentclass{article}
\begin{document}
\matnew \X
\matnew \Y
\matnew \Z
\matset \X { 1 , 2 + 3 ; 4 , 3.4e22 }
\matset \Y { 3 , 4 ; -5 , 6 }
\begin{align}
\matadd \Z \X \Y
\mattypeset \Z & = \mattypeset \X + \mattypeset \Y \\
\matsub \Z \X \Y
\mattypeset \Z & = \mattypeset \X - \mattypeset \Y \\
\matmul \Z \X \Y
\mattypeset \Z & = \mattypeset \X \times \mattypeset \Y \\
\matmul \Z \Y \X
\mattypeset \Z & = \mattypeset \Y \times \mattypeset \X
\end{align}
\def\GetRotationMatrix #1{%
cos(#1), -sin(#1), 0;
sin(#1), cos(#1), 0;
0, 0, 1 }
\expandafter\matset\expandafter\transformMatrixA \expandafter
{\GetRotationMatrix {3.141592653}}
\begin{equation}
\mattypeset \transformMatrixA
\end{equation}
\end{document}
The first four equations are the ones from the original code
\matnewand\matset? Could you include in your post what you've tried...? Perhaps that'll make things more clear. – Werner Nov 06 '13 at 17:52