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authorNorbert Preining <norbert@preining.info>2023-02-15 03:01:49 +0000
committerNorbert Preining <norbert@preining.info>2023-02-15 03:01:49 +0000
commita7d99429152acee049db679dc26a92e01faf4992 (patch)
treec12bd699dd6c10d6efea6d36cfb71493181d98f5 /macros/luatex/latex/lualinalg/lualinalg.tex
parentdc5dafdd7c01d469b556bc5bef745a6f1c84a5cb (diff)
CTAN sync 202302150301
Diffstat (limited to 'macros/luatex/latex/lualinalg/lualinalg.tex')
-rw-r--r--macros/luatex/latex/lualinalg/lualinalg.tex28
1 files changed, 14 insertions, 14 deletions
diff --git a/macros/luatex/latex/lualinalg/lualinalg.tex b/macros/luatex/latex/lualinalg/lualinalg.tex
index fa7c9fa4ea..99c01d06af 100644
--- a/macros/luatex/latex/lualinalg/lualinalg.tex
+++ b/macros/luatex/latex/lualinalg/lualinalg.tex
@@ -1,6 +1,6 @@
\documentclass{article}
\usepackage{listings,color,parskip,booktabs,longtable,array,
-hyperref,multirow,multicol,url,amsmath,amssymb,framed,graphicx}
+hyperref,multirow,multicol,url,amsmath,amssymb,framed,graphicx,mismath}
\usepackage[top=1.1in, bottom=1.1in, left=1in, right=1in]{geometry}
\hypersetup{colorlinks,urlcolor=blue}
\lstset{frame=none,
@@ -30,7 +30,7 @@ The \verb|lualinalg| package is developed to perform operations on vectors and m
\section{Installation and License}
The installation of the \verb|lualinalg| package is similar to the plain latex package, where the \verb|.sty| file is in the LaTeX directory of the texmf tree. The package can be included with \verb|\usepackage{lualinalg}| command in the preamble of the LaTeX document.
-The \verb|lualinalg| package is released under the LaTeX Project Public License v1.3c or later. The complete license text is available at \url{http://www.latex-project.org/lppl.txt}. It is developed in Lua. Lua is available as a certified open-source software. Its license is simple and liberal, which is compatible with GPL. The package makes use of \verb|complex.lua| file which is available on \url{https://github.com/davidm/lua-matrix/blob/master/lua/matrix.lua}. It is available under the same licensing as that of Lua. The package also loads the \href{https://ctan.org/pkg/luamaths}{luamaths} package, which is available under the LaTeX Project Public License v1.3c or later. This package is loaded to use the standard mathematical functions and for computations on real numbers while performing operations on vectors and matrices.
+The \verb|lualinalg| package is released under the LaTeX Project Public License v1.3c or later. The complete license text is available at \url{http://www.latex-project.org/lppl.txt}. It is developed in Lua. Lua is available as a certified open-source software. Its license is simple and liberal, which is compatible with GPL. The package makes use of \verb|complex.lua| file which is available on \url{https://github.com/davidm/lua-matrix/blob/master/lua/complex.lua}. It is available under the same licensing as that of Lua. The package also loads the \href{https://ctan.org/pkg/luamaths}{luamaths} package, which is available under the LaTeX Project Public License v1.3c or later. This package is loaded to use the standard mathematical functions and for computations on real numbers while performing operations on vectors and matrices.
\section{Defining vectors and performing operations on vectors}
\subsection{Defining Vectors} Vectors are defined with the \verb|\vectornew| command.
\begin{verbatim}
@@ -65,14 +65,14 @@ Table \ref{tbl:luavector} lists commands for operations on vectors.
\vectorGetCoordinate{vector}{i}
\end{lstlisting}
&
-Gives the \(i^{th}\) coordinate of vector. \\
+Gives the \(i\)th coordinate of vector. \\
\midrule
\begin{lstlisting}
\vectorSetCoordinate
{vector}{i}{val}
\end{lstlisting}
&
-Sets the \(i^{th}\) coordinate of vector as \verb|val|. \\
+Sets the \(i\)th coordinate of vector as \verb|val|. \\
\midrule
\begin{lstlisting}
\vectorCopy{v}{w}
@@ -137,7 +137,7 @@ Defines a new vector obtained by evaluating an expression. The expression suppor
\begin{lstlisting}
\vectorGetAngle{v}{w}
\end{lstlisting}&
-Gives the angle between two vectors \(v\) and \(w\) in radians. If \(v\) and \(w \) are defined over the field of real numbers, then it is evaluated as \(\cos^{-1}\left(\frac{v \cdot w}{|v| |w|}\right)\). If they are defined over the field of complex numbers, then it is evaluated as \(\cos^{-1}\left(\frac{Re (v \cdot w) }{|v| |w|}\right)\). Here \(v \cdot w\) denotes the dot product of vectors \(v\) and \(w\), \(Re (v \cdot w)\) denotes real part of the dot product \(v \cdot w\), and \(|v|\) and \(|w|\) denote Euclidean norms of vectors \(v\) and \(w\) respectively. \\
+Gives the angle between two vectors \(v\) and \(w\) in radians. If \(v\) and \(w \) are defined over the field of real numbers, then it is evaluated as \(\cos^{-1}\left(\frac{v \cdot w}{|v| |w|}\right)\). If they are defined over the field of complex numbers, then it is evaluated as \(\cos^{-1}\left(\frac{\Re (v \cdot w) }{|v| |w|}\right)\). Here \(v \cdot w\) denotes the dot product of vectors \(v\) and \(w\), \(\Re (v \cdot w)\) denotes real part of the dot product \(v \cdot w\), and \(|v|\) and \(|w|\) denote Euclidean norms of vectors \(v\) and \(w\) respectively. \\
\midrule
\begin{lstlisting}
\vectorParse{vector}
@@ -471,7 +471,7 @@ Gives the number of columns in a matrix.\\
\matrixGetElement{matrix}{i}{j}
\end{lstlisting}
&
-Gives an entry of matrix in the \(i^{th} \) row and the \(j^{th} \) column. \\
+Gives an entry of matrix in the \(i\)th row and the \(j\)th column. \\
\midrule
\multicolumn{2}{c}{Algebraic operations on matrices} \\
\midrule
@@ -498,7 +498,7 @@ Defines a new matrix obtained by multiplying matrix m1 by matrix m2. The number
\begin{lstlisting}
\matrixPow{matrix}{m1}{power}
\end{lstlisting}&
-Defines a new matrix obtained by taking the \(i^{th}\) power of matrix m11 (multiplying matrix1 \(i\) times with itself). \\
+Defines a new matrix obtained by taking the \(i\)th power of matrix m1 (multiplying matrix m1 \(i\) times with itself). \\
\midrule
\begin{lstlisting}
\matrixInvert{matrix}{matrix1}
@@ -564,7 +564,7 @@ Defines a new matrix obtained by taking the transpose of matrix m1. \\
\matrixSetElement{matrix}{i}{j}{val}
\end{lstlisting}
&
-Set entry of a matrix in the \(i^{th} \) row and \(j^{th} \) column as \verb|val|. \\
+Set entry of a matrix in the \(i\)th row and \(j\)th column as \verb|val|. \\
\midrule
\begin{lstlisting}
\matrixSubmatrix{sm}{m}{i}{j}{k}{l}
@@ -602,34 +602,34 @@ Creates a new matrix m with random numbers. Here \(i,j\) denotes the number of r
\begin{lstlisting}
\matrixSwapRows{mtx}{m1}{i}{j}
\end{lstlisting}&
-Defines a new matrix mtx obtained by swapping the \(i^{th}\) and \(j^{th}\) rows of matrix m1. \\
+Defines a new matrix mtx obtained by swapping the \(i\)th and \(j\)th rows of matrix m1. \\
\midrule
\begin{lstlisting}
\matrixMulRow{matrix}{m}{i}{no}
\end{lstlisting}&
-Defines a new matrix obtained by multiplying the \(i^{th}\) row of matrix1 by a real or complex number. \\
+Defines a new matrix obtained by multiplying the \(i\)th row of matrix1 by a real or complex number. \\
\midrule
\begin{lstlisting}
\matrixMulAddRow{mtx}{m}{i}{no}{j}
\end{lstlisting}&
-Defines a new matrix mtx obtained by multiplying the \(i^{th}\) row of matrix1 by a real or complex number and adding it to the \(j^{th}\) row. \\
+Defines a new matrix mtx obtained by multiplying the \(i\)th row of matrix1 by a real or complex number and adding it to the \(j\)th row. \\
\midrule
\multicolumn{2}{c}{Elementary column operations on matrices} \\
\midrule
\begin{lstlisting}
\matrixSwapCols{mtx}{m}{i}{j}
\end{lstlisting}&
-Defines a new matrix mtx obtained by swapping the \(i^{th}\) and \(j^{th}\) columns of matrix m. \\
+Defines a new matrix mtx obtained by swapping the \(i\)th and \(j\)th columns of matrix m. \\
\midrule
\begin{lstlisting}
\matrixMulCol{matrix}{m}{i}{no}
\end{lstlisting}&
-Defines a new matrix obtained by multiplying the \(i^{th}\) column of matrix1 by a real or complex number. \\
+Defines a new matrix obtained by multiplying the \(i\)th column of matrix1 by a real or complex number. \\
\midrule
\begin{lstlisting}
\matrixMulAddCol{mtx}{m}{i}{no}{j}
\end{lstlisting}&
-Defines a new matrix mtx obtained by multiplying the \(i^{th}\) column of matrix1 by a real or complex number and adding it to the \(j^{th}\) column. \\
+Defines a new matrix mtx obtained by multiplying the \(i\)th column of matrix1 by a real or complex number and adding it to the \(j\)th column. \\
\midrule
\multicolumn{2}{c}{Reduced row echelon form of matrix} \\
\midrule