Browse - Maple Help

Library[Browse] - display a list of entries from a table in the DifferentialGeometry library

Calling Sequences

Browse()

Browse(author, n)

Browse(author, n, indexlist, options)

Parameters

author    - the author of a table in the DifferentialGeometry Library

n         - an integer

indexlist - the indices for the table specified by the call sequence author, n

options   - other arguments, which depend upon the nature of the table being browsed

Description

 • 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(...).

Examples

 > $\mathrm{with}\left(\mathrm{DifferentialGeometry}\right):$$\mathrm{with}\left(\mathrm{Library}\right):$
 > $\mathrm{Browse}\left(\right)$
 $\left[\left[{"Gong"}{,}{1}\right]{,}\left[{"Gonzalez-Lopez"}{,}{1}\right]{,}\left[{"Kamke"}{,}{1}\right]{,}\left[{"Morozov"}{,}{1}\right]{,}\left[{"Mubarakyzanov"}{,}{1}\right]{,}\left[{"Mubarakyzanov"}{,}{2}\right]{,}\left[{"Mubarakyzanov"}{,}{3}\right]{,}\left[{"Olver"}{,}{1}\right]{,}\left[{"Petrov"}{,}{1}\right]{,}\left[{"Turkowski"}{,}{1}\right]{,}\left[{"Turkowski"}{,}{2}\right]{,}\left[{"USU"}{,}{2}\right]{,}\left[{"USU"}{,}{"2D"}\right]{,}\left[{"Winternitz"}{,}{1}\right]\right]$ (2.1)

Example 1.

Obtain the indices for the ["Winternitz", 1] table.  This table contains a list of all Lie algebras of dimension less than or equal to 5 and a list of nilpotent Lie algebras of dimension 6.

 > $L≔\mathrm{Browse}\left("Winternitz",1\right)$
 ${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]$ (2.2)

Display the entry for the index [4, 2].

 > $\mathrm{Browse}\left("Winternitz",1,\left[\left[4,2\right]\right]\right)$
 ${"Winternitz"}{,}{1}{,}\left[{4}{,}{2}\right]$ $\left[\left[{\mathrm{e1}}{,}{\mathrm{e4}}\right]{=}{a}{}{\mathrm{e1}}{,}\left[{\mathrm{e2}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e2}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e2}}{+}{\mathrm{e3}}\right]$ ${\mathrm{___________________}}$ (2.3)

Display the entries for the indices [5, 0]..[5, 5].  We first use the ListTools[Search] command to locate the position of the indices [5, 0] and [5, 5]] in L.

 > ${\mathrm{ListTools}}_{\mathrm{Search}}\left(\left[5,0\right],L\right),{\mathrm{ListTools}}_{\mathrm{Search}}\left(\left[5,5\right],L\right)$
 ${24}{,}{29}$ (2.4)
 > $\mathrm{Browse}\left("Winternitz",1,{L}_{24..29}\right)$
 ${"Winternitz"}{,}{1}{,}\left[{5}{,}{0}\right]$ $\left[{}\right]$ ${\mathrm{___________________}}$ ${"Winternitz"}{,}{1}{,}\left[{5}{,}{1}\right]$ $\left[\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e2}}\right]$ ${\mathrm{___________________}}$ ${"Winternitz"}{,}{1}{,}\left[{5}{,}{2}\right]$ $\left[\left[{\mathrm{e2}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e2}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e3}}\right]$ ${\mathrm{___________________}}$ ${"Winternitz"}{,}{1}{,}\left[{5}{,}{3}\right]$ $\left[\left[{\mathrm{e3}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e2}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e4}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e3}}\right]$ ${\mathrm{___________________}}$ ${"Winternitz"}{,}{1}{,}\left[{5}{,}{4}\right]$ $\left[\left[{\mathrm{e2}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e1}}\right]$ ${\mathrm{___________________}}$ ${"Winternitz"}{,}{1}{,}\left[{5}{,}{5}\right]$ $\left[\left[{\mathrm{e2}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e4}}\right]{=}{\mathrm{e1}}{,}\left[{\mathrm{e3}}{,}{\mathrm{e5}}\right]{=}{\mathrm{e2}}\right]$ ${\mathrm{___________________}}$ (2.5)

Example 2.

Obtain the indices for the ["Gonzalez-Lopez", 1] table.  This table contains a list of all Lie algebras of vector fields in the plane.

 > $\mathrm{L2}≔\mathrm{Browse}\left("Gonzalez-Lopez",1\right)$
 ${\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]$ (2.6)

To browse this table, one must first define a two dimensional manifold and pass the name of this manifold to the Browse command.

 > $\mathrm{DGsetup}\left(\left[x,y\right],M\right):$
 M > $\mathrm{Browse}\left("Gonzalez-Lopez",1,\left[\left[5\right]\right],\mathrm{manifold}=M\right)$
 ${"Gonzalez-Lopez"}{,}{1}{,}\left[{5}\right]$ $\left[{\mathrm{D_x}}{,}{\mathrm{D_y}}{,}{x}{}{\mathrm{D_x}}{-}{y}{}{\mathrm{D_y}}{,}{y}{}{\mathrm{D_x}}{,}{x}{}{\mathrm{D_y}}\right]$ ${\mathrm{___________________}}$ (2.7)
 M > $\mathrm{Browse}\left("Gonzalez-Lopez",1,{\mathrm{L2}}_{7..10},\mathrm{manifold}=M\right)$
 ${"Gonzalez-Lopez"}{,}{1}{,}\left[{7}\right]$ $\left[{\mathrm{D_x}}{,}{\mathrm{D_y}}{,}{x}{}{\mathrm{D_x}}{+}{y}{}{\mathrm{D_y}}{,}{y}{}{\mathrm{D_x}}{-}{x}{}{\mathrm{D_y}}{,}\left({{x}}^{{2}}{-}{{y}}^{{2}}\right){}{\mathrm{D_x}}{+}{2}{}{x}{}{y}{}{\mathrm{D_y}}{,}{2}{}{x}{}{y}{}{\mathrm{D_x}}{+}\left({{y}}^{{2}}{-}{{x}}^{{2}}\right){}{\mathrm{D_y}}\right]$ ${\mathrm{___________________}}$ ${"Gonzalez-Lopez"}{,}{1}{,}\left[{8}\right]$ $\left[{\mathrm{D_x}}{,}{\mathrm{D_y}}{,}{x}{}{\mathrm{D_x}}{,}{y}{}{\mathrm{D_x}}{,}{x}{}{\mathrm{D_y}}{,}{y}{}{\mathrm{D_y}}{,}{{x}}^{{2}}{}{\mathrm{D_x}}{+}{x}{}{y}{}{\mathrm{D_y}}{,}{x}{}{y}{}{\mathrm{D_x}}{+}{{y}}^{{2}}{}{\mathrm{D_y}}\right]$ ${\mathrm{___________________}}$ ${"Gonzalez-Lopez"}{,}{1}{,}\left[{9}\right]$ $\left[{\mathrm{D_x}}\right]$ ${\mathrm{___________________}}$ ${"Gonzalez-Lopez"}{,}{1}{,}\left[{10}\right]$ $\left[{\mathrm{D_x}}{,}{x}{}{\mathrm{D_x}}\right]$ ${\mathrm{___________________}}$ (2.8)

Example 3.

Obtain the number of indices for the ["Kamke", 1] table (The list is too long to show here).  This table contains a list of all ordinary differential equations in Kamke's book.

 M > $\mathrm{L3}≔\mathrm{Browse}\left("Kamke",1\right):$
 M > $\mathrm{nops}\left(\mathrm{L3}\right)$
 ${1548}$ (2.9)
 M > ${\mathrm{L3}}_{755}$
 $\left[{2}{,}{153}\right]$ (2.10)
 M > $\mathrm{Browse}\left("Kamke",1,\left[\left[2,153\right]\right]\right):$
 ${"Kamke"}{,}{1}{,}\left[{2}{,}{153}\right]$ ${{x}}^{{2}}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{y}{}\left({x}\right)\right){+}\left({\mathrm{a1}}{}{{x}}^{{2}}{-}{\mathrm{ν}}{}\left({\mathrm{ν}}{-}{1}\right)\right){}{y}{}\left({x}\right)$ ${\mathrm{___________________}}$ (2.11)