The first calling sequence Browse() returns the call sequences for all the tables in the DifferentialGeometry Library.

Each table in the Library is uniquely specified by its call sequence author, n.  The second call sequence Browse(author, n) returns all the indices for the table specified by the given call sequence.

The third call sequence Browse(author, n, indexlist, options) displays all the table entries for the given list of table indices.  These indices match the reference scheme used by the author in the original source article or book.

When a table of Lie algebras of vector fields is to be browsed, the argument manifold = M is required.  Here M is the name of the manifold upon which the vector fields are to be defined.

The command Browse is part of the DifferentialGeometry:-Library package.  It can be used in the form Browse(...) only after executing the commands with(DifferentialGeometry) and with(Library), but can always be used by executing DifferentialGeometry:-Library:-Browse(...).

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{Library}\right)\:$

$\mathrm{Browse}\left(\right)$

$\left[\left[''Gong''\,1\right]\,\left[''Gonzalez-Lopez''\,1\right]\,\left[''Kamke''\,1\right]\,\left[''Morozov''\,1\right]\,\left[''Mubarakyzanov''\,1\right]\,\left[''Mubarakyzanov''\,2\right]\,\left[''Mubarakyzanov''\,3\right]\,\left[''Olver''\,1\right]\,\left[''Petrov''\,1\right]\,\left[''Turkowski''\,1\right]\,\left[''Turkowski''\,2\right]\,\left[''USU''\,2\right]\,\left[''USU''\,''2D''\right]\,\left[''Winternitz''\,1\right]\right]$

$L≔\mathrm{Browse}\left(''Winternitz''\,1\right)$

$L≔\left[\left[3\,0\right]\,\left[3\,1\right]\,\left[3\,2\right]\,\left[3\,3\right]\,\left[3\,4\right]\,\left[3\,5\right]\,\left[3\,6\right]\,\left[3\,7\right]\,\left[3\,8\right]\,\left[3\,9\right]\,\left[4\,0\right]\,\left[4\,1\right]\,\left[4\,2\right]\,\left[4\,3\right]\,\left[4\,4\right]\,\left[4\,5\right]\,\left[4\,6\right]\,\left[4\,7\right]\,\left[4\,8\right]\,\left[4\,9\right]\,\left[4\,10\right]\,\left[4\,11\right]\,\left[4\,12\right]\,\left[5\,0\right]\,\left[5\,1\right]\,\left[5\,2\right]\,\left[5\,3\right]\,\left[5\,4\right]\,\left[5\,5\right]\,\left[5\,6\right]\,\left[5\,7\right]\,\left[5\,8\right]\,\left[5\,9\right]\,\left[5\,10\right]\,\left[5\,11\right]\,\left[5\,12\right]\,\left[5\,13\right]\,\left[5\,14\right]\,\left[5\,15\right]\,\left[5\,16\right]\,\left[5\,17\right]\,\left[5\,18\right]\,\left[5\,19\right]\,\left[5\,20\right]\,\left[5\,21\right]\,\left[5\,22\right]\,\left[5\,23\right]\,\left[5\,24\right]\,\left[5\,25\right]\,\left[5\,26\right]\,\left[5\,27\right]\,\left[5\,28\right]\,\left[5\,29\right]\,\left[5\,30\right]\,\left[5\,31\right]\,\left[5\,32\right]\,\left[5\,33\right]\,\left[5\,34\right]\,\left[5\,35\right]\,\left[5\,36\right]\,\left[5\,37\right]\,\left[5\,38\right]\,\left[5\,39\right]\,\left[5\,40\right]\,\left[6\,1\right]\,\left[6\,2\right]\,\left[6\,3\right]\,\left[6\,4\right]\,\left[6\,5\right]\,\left[6\,6\right]\,\left[6\,7\right]\,\left[6\,8\right]\,\left[6\,9\right]\,\left[6\,10\right]\,\left[6\,11\right]\,\left[6\,12\right]\,\left[6\,13\right]\,\left[6\,14\right]\,\left[6\,15\right]\,\left[6\,16\right]\,\left[6\,17\right]\,\left[6\,18\right]\,\left[6\,19\right]\,\left[6\,20\right]\,\left[6\,21\right]\,\left[6\,22\right]\right]$

$\mathrm{Browse}\left(''Winternitz''\,1\,\left[\left[4\,2\right]\right]\right)$

$''Winternitz''\,1\,\left[4\,2\right]$

$\left[\left[\mathrm{e1}\,\mathrm{e4}\right]\=a\mathrm{e1}\,\left[\mathrm{e2}\,\mathrm{e4}\right]\=\mathrm{e2}\,\left[\mathrm{e3}\,\mathrm{e4}\right]\=\mathrm{e2}\+\mathrm{e3}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{ListTools}\left[\mathrm{Search}\right]\left(\left[5\,0\right]\,L\right),\mathrm{ListTools}\left[\mathrm{Search}\right]\left(\left[5\,5\right]\,L\right)$

$24\,29$

$\mathrm{Browse}\left(''Winternitz''\,1\,L\left[24..29\right]\right)$

$''Winternitz''\,1\,\left[5\,0\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Winternitz''\,1\,\left[5\,1\right]$

$\left[\left[\mathrm{e3}\,\mathrm{e5}\right]\=\mathrm{e1}\,\left[\mathrm{e4}\,\mathrm{e5}\right]\=\mathrm{e2}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Winternitz''\,1\,\left[5\,2\right]$

$\left[\left[\mathrm{e2}\,\mathrm{e5}\right]\=\mathrm{e1}\,\left[\mathrm{e3}\,\mathrm{e5}\right]\=\mathrm{e2}\,\left[\mathrm{e4}\,\mathrm{e5}\right]\=\mathrm{e3}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Winternitz''\,1\,\left[5\,3\right]$

$\left[\left[\mathrm{e3}\,\mathrm{e4}\right]\=\mathrm{e2}\,\left[\mathrm{e3}\,\mathrm{e5}\right]\=\mathrm{e1}\,\left[\mathrm{e4}\,\mathrm{e5}\right]\=\mathrm{e3}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Winternitz''\,1\,\left[5\,4\right]$

$\left[\left[\mathrm{e2}\,\mathrm{e4}\right]\=\mathrm{e1}\,\left[\mathrm{e3}\,\mathrm{e5}\right]\=\mathrm{e1}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Winternitz''\,1\,\left[5\,5\right]$

$\left[\left[\mathrm{e2}\,\mathrm{e5}\right]\=\mathrm{e1}\,\left[\mathrm{e3}\,\mathrm{e4}\right]\=\mathrm{e1}\,\left[\mathrm{e3}\,\mathrm{e5}\right]\=\mathrm{e2}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{L2}≔\mathrm{Browse}\left(''Gonzalez-Lopez''\,1\right)$

$\mathrm{L2}≔\left[\left[1\right]\,\left[2\right]\,\left[3\right]\,\left[4\right]\,\left[5\right]\,\left[6\right]\,\left[7\right]\,\left[8\right]\,\left[9\right]\,\left[10\right]\,\left[11\right]\,\left[12\right]\,\left[13\right]\,\left[14\right]\,\left[15\right]\,\left[16\right]\,\left[17\right]\,\left[18\right]\,\left[19\right]\,\left[20\,1\right]\,\left[20\,2\right]\,\left[20\,3\right]\,\left[20\,4\right]\,\left[20\,5\right]\,\left[21\,1\right]\,\left[21\,2\right]\,\left[21\,3\right]\,\left[21\,4\right]\,\left[21\,5\right]\,\left[22\,1\right]\,\left[22\,2\right]\,\left[22\,3\right]\,\left[22\,4\right]\,\left[22\,5\right]\,\left[22\,6\right]\,\left[22\,7\right]\,\left[22\,8\right]\,\left[22\,9\right]\,\left[22\,10\right]\,\left[22\,11\right]\,\left[22\,12\right]\,\left[22\,13\right]\,\left[22\,14\right]\,\left[22\,15\right]\,\left[22\,16\right]\,\left[22\,17\right]\,\left[22\,18\right]\,\left[22\,19\right]\,\left[22\,20\right]\,\left[22\,21\right]\,\left[22\,22\right]\,\left[22\,23\right]\,\left[22\,24\right]\,\left[22\,25\right]\,\left[22\,26\right]\,\left[22\,27\right]\,\left[22\,28\right]\,\left[22\,29\right]\,\left[22\,30\right]\,\left[22\,31\right]\,\left[22\,32\right]\,\left[22\,33\right]\,\left[22\,34\right]\,\left[22\,35\right]\,\left[22\,36\right]\,\left[22\,37\right]\,\left[23\,1\right]\,\left[23\,2\right]\,\left[23\,3\right]\,\left[23\,4\right]\,\left[23\,5\right]\,\left[23\,6\right]\,\left[23\,7\right]\,\left[23\,8\right]\,\left[23\,9\right]\,\left[23\,10\right]\,\left[23\,11\right]\,\left[23\,12\right]\,\left[23\,13\right]\,\left[23\,14\right]\,\left[23\,15\right]\,\left[23\,16\right]\,\left[23\,17\right]\,\left[23\,18\right]\,\left[23\,19\right]\,\left[23\,20\right]\,\left[23\,21\right]\,\left[23\,22\right]\,\left[23\,23\right]\,\left[23\,24\right]\,\left[23\,25\right]\,\left[23\,26\right]\,\left[23\,27\right]\,\left[23\,28\right]\,\left[23\,29\right]\,\left[23\,30\right]\,\left[23\,31\right]\,\left[23\,32\right]\,\left[23\,33\right]\,\left[23\,34\right]\,\left[23\,35\right]\,\left[23\,36\right]\,\left[23\,37\right]\,\left[24\,1\right]\,\left[24\,2\right]\,\left[24\,3\right]\,\left[24\,4\right]\,\left[24\,5\right]\,\left[25\,1\right]\,\left[25\,2\right]\,\left[25\,3\right]\,\left[25\,4\right]\,\left[25\,5\right]\,\left[26\,1\right]\,\left[26\,2\right]\,\left[26\,3\right]\,\left[26\,4\right]\,\left[26\,5\right]\,\left[27\,1\right]\,\left[27\,2\right]\,\left[27\,3\right]\,\left[27\,4\right]\,\left[27\,5\right]\,\left[28\,1\right]\,\left[28\,2\right]\,\left[28\,3\right]\,\left[28\,4\right]\,\left[28\,5\right]\right]$

$\mathrm{DGsetup}\left(\left[x\,y\right]\,M\right)\:$

$\mathrm{Browse}\left(''Gonzalez-Lopez''\,1\,\left[\left[5\right]\right]\,\mathrm{manifold}=M\right)$

$''Gonzalez-Lopez''\,1\,\left[5\right]$

$\left[\mathrm{D\_x}\,\mathrm{D\_y}\,x\mathrm{D\_x}-y\mathrm{D\_y}\,y\mathrm{D\_x}\,x\mathrm{D\_y}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{Browse}\left(''Gonzalez-Lopez''\,1\,\mathrm{L2}\left[7..10\right]\,\mathrm{manifold}=M\right)$

$''Gonzalez-Lopez''\,1\,\left[7\right]$

$\left[\mathrm{D\_x}\,\mathrm{D\_y}\,x\mathrm{D\_x}\+y\mathrm{D\_y}\,y\mathrm{D\_x}-x\mathrm{D\_y}\,\left(x^2-y^2\right)\mathrm{D\_x}\+2xy\mathrm{D\_y}\,2xy\mathrm{D\_x}\+\left(y^2-x^2\right)\mathrm{D\_y}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Gonzalez-Lopez''\,1\,\left[8\right]$

$\left[\mathrm{D\_x}\,\mathrm{D\_y}\,x\mathrm{D\_x}\,y\mathrm{D\_x}\,x\mathrm{D\_y}\,y\mathrm{D\_y}\,x^2\mathrm{D\_x}\+xy\mathrm{D\_y}\,xy\mathrm{D\_x}\+y^2\mathrm{D\_y}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Gonzalez-Lopez''\,1\,\left[9\right]$

$\left[\mathrm{D\_x}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$''Gonzalez-Lopez''\,1\,\left[10\right]$

$\left[\mathrm{D\_x}\,x\mathrm{D\_x}\right]$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$

$\mathrm{L3}≔\mathrm{Browse}\left(''Kamke''\,1\right)\:$

$\mathrm{nops}\left(\mathrm{L3}\right)$

$1548$

$\mathrm{L3}\left[755\right]$

$\left[2\,153\right]$

$\mathrm{Browse}\left(''Kamke''\,1\,\left[\left[2\,153\right]\right]\right)\:$

$''Kamke''\,1\,\left[2\,153\right]$

$x^2\left(\frac{{\ⅆ}^2}{\ⅆx^2}y\left(x\right)\right)\+\left(\mathrm{a1}{x}^2-\mathrm{\ν}\left(\mathrm{\ν}-1\right)\right)y\left(x\right)$

$\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}$