How do I use \newcommand to print a matrix everytime I input 6 values?

Question

I'm relatively new to LaTeX and I still don't really know how to use the \newcommand feature at all (new to stackexchange as well). I've been trying to find out how to print something like this

I've tried various ways and so far the code with the least number of errors is this:

\newcommand{\xmatrix}[6]{
\begin{vmatrix}
    $i & j & k$\\
    {u1} & {u2} & {u3}\\
    {v1} & {v2} & {v3}
\end{vmatrix}}

I'm pretty sure I'm just using the \newcommand part wrong but I want to be able to print the unit vectors in bold in the first row and the next 6 numbers are input. Thank you for any advice!

score 2 · Accepted Answer · answered Sep 25 '20 at 11:47

You want to define a macro with six arguments: those six arguments are represented by #1, ..., #6 in the macro code. Since vmatrix is always in math mode there is no need to use $ dollar signs within it. You could therefore do something like this:

\documentclass{article}
\usepackage{amsmath} % for vmatrix
\newcommand{\xmatrix}[6]{%
\begin{vmatrix}
    \mathbf{i} & \mathbf{j} & \mathbf{k} \
    #1 & #2 & #3\
    #4 & #5 & #6
\end{vmatrix}}
\begin{document}
[
\xmatrix{u1}{u2}{u3}{v1}{v2}{v3}
]
\end{document}

However, I find a macro taking six arguments a little bit unpleasant and prone to errors. I propose an alternative definition with two arguments, each of them being a comma-separated list.

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\newcommand*{\xmatrix}[2]{{%
   \def@xmatrix##1,##2,##3,##4\relax{##1 & ##2 & ##3}%
   \begin{vmatrix}
    \mathbf{i} & \mathbf{j} & \mathbf{k} \
    @xmatrix#1,,,\relax\
    @xmatrix#2,,,\relax
   \end{vmatrix}%
}}
\makeatother
\begin{document}
[
\xmatrix{u1,u2,u3}{v1,v2,v3}
\quad
\xmatrix{u1}{,v2,v3} % just as example
]
\end{document}

Thank you so much! I'm a bit confused as to what the \makeatletter and \makeatother do. Also what does the % and the @ do in this case? — msun5040, Sep 25 '20 at 12:05
@msun5040 See What do \makeatletter and \makeatother do? and What is the use of percent signs (%) at the end of lines?. The % are not really necessary here (spaces are ignored in math mode) but they are an habit. — campa, Sep 25 '20 at 12:09

score 2 · Answer 2 · answered Sep 25 '20 at 12:23

You can do much better than defining a macro with six arguments. I propose just two arguments, representing the coefficients of the vectors as comma separated lists.

We can also define a variant that actually computes the cross product.

\documentclass{article}
\usepackage{amsmath,xparse}
\ExplSyntaxOn
\NewDocumentCommand{\crossproduct}{s m m}
 {% #1 = optional *
  % #2 = first vector as comma list
  % #3 = second vector as comma list
  \IfBooleanTF{#1}
   {% *-variant, compute the product
    \msun_crossproduct_compute:nn { #2 } { #3 }
   }
   {% normal, typeset in determinant form
    \msun_crossproduct_symbolic:nn { #2 } { #3 }
   }
 }
\fp_new:N \l_msun_crossproduct_i_fp
\fp_new:N \l_msun_crossproduct_j_fp
\fp_new:N \l_msun_crossproduct_k_fp
\cs_new_protected:Nn \msun_crossproduct_compute:nn
 {
  \fp_set:Nn \l_msun_crossproduct_i_fp
   {
    \clist_item:nn { #1 } { 2 } * \clist_item:nn { #2 } { 3 }
    -
    \clist_item:nn { #1 } { 3 } * \clist_item:nn { #2 } { 2 }
   }
  \fp_set:Nn \l_msun_crossproduct_j_fp
   {
    \clist_item:nn { #1 } { 3 } * \clist_item:nn { #2 } { 1 }
    -
    \clist_item:nn { #1 } { 1 } * \clist_item:nn { #2 } { 3 }
   }
  \fp_set:Nn \l_msun_crossproduct_k_fp
   {
    \clist_item:nn { #1 } { 1 } * \clist_item:nn { #2 } { 2 }
    -
    \clist_item:nn { #1 } { 2 } * \clist_item:nn { #2 } { 1 }
   }
  \fp_use:N \l_msun_crossproduct_i_fp \mathbf{i}
  \fp_compare:nF { \l_msun_crossproduct_j_fp < \c_zero_fp } { + }
  \fp_use:N \l_msun_crossproduct_j_fp \mathbf{j}
  \fp_compare:nF { \l_msun_crossproduct_k_fp < \c_zero_fp } { + }
  \fp_use:N \l_msun_crossproduct_k_fp \mathbf{k}
 }
\cs_new_protected:Nn \msun_crossproduct_symbolic:nn
 {
  \begin{vmatrix}
  \mathbf{i} & \mathbf{j} & \mathbf{k}
  \
  \clist_item:nn { #1 } { 1 } & \clist_item:nn { #1 } { 2 } & \clist_item:nn { #1 } { 3 }
  \
  \clist_item:nn { #2 } { 1 } & \clist_item:nn { #2 } { 2 } & \clist_item:nn { #2 } { 3 }
  \end{vmatrix}
 }
\ExplSyntaxOff
\begin{document}
[
\crossproduct{0,1,-2}{3,0,-4}=
\crossproduct*{0,1,-2}{3,0,-4}
]
\end{document}

How do I use \newcommand to print a matrix everytime I input 6 values?

2 Answers2