Preferences - Maple Help

DifferentialGeometry

 Preferences

 Calling Sequence Preferences(keyword) Preferences(keyword, value)

Parameters

 keyword - a string, the name of the particular preference value - the value to be assigned to the preference

Description

 • This command allows the user to control various display conventions used by the DifferentialGeometry package; to specify the LaTeX formatting of DifferentialGeometry objects such as vectors, differential forms and tensors; and to specify how commonly used Maple commands are used internally by DifferentialGeometry procedures.
 • The following are the admissible keywords strings:

 • The  paragraphs below describes the use of each of these keywords.
 • This command is part of the DifferentialGeometry package, and so can be used in the form Preferences(...) only after executing the command with(DifferentialGeometry).  It can always be used in the long form DifferentialGeometry:-Preferences.

Details

"DisplayFrameDefinitions"

This preference controls what information is displayed when the command DGsetup is executed. When this preference is false, no display is displayed.  When this preference is true, the names of the coordinate variables and the labels for the frame vectors and coframe 1-forms are displayed.  The default preference is false.

 > with(DifferentialGeometry):
 > Preferences("DisplayFrameDefinitions");
 ${\mathrm{false}}$ (1)
 > DGsetup([x, y, z], E3);
 ${\mathrm{frame name: E3}}$ (2)
 > Preferences("DisplayFrameDefinitions", true);
 ${\mathrm{false}}$ (3)
 > DGsetup([x, y, z], E3);
 ${\mathrm{The following coordinates have been protected:}}$
 $\left[{x}{,}{y}{,}{z}\right]$
 ${\mathrm{The following vector fields have been defined and protected:}}$
 $\left[{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{E3}}{,}\left[{}\right]\right]{,}\left[\left[\left[{1}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{E3}}{,}\left[{}\right]\right]{,}\left[\left[\left[{2}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{E3}}{,}\left[{}\right]\right]{,}\left[\left[\left[{3}\right]{,}{1}\right]\right]\right]\right)\right]$
 ${\mathrm{The following differential 1-forms have been defined and protected:}}$
 $\left[{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{E3}}{,}{1}\right]{,}\left[\left[\left[{1}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{E3}}{,}{1}\right]{,}\left[\left[\left[{2}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{E3}}{,}{1}\right]{,}\left[\left[\left[{3}\right]{,}{1}\right]\right]\right]\right)\right]$
 ${\mathrm{frame name: E3}}$ (4)
 "ErrorInfoLevel" This preference controls the amount of information provided by an error message from a DifferentialGeometry command.  The default for ErrorInfoLevel is 1.
 "ErrorPrintLength" For many of the error messages returned by the DifferentialGeometry commands, it is not necessary to display all the component information of the vectors, differential forms, and tensors provided as input.  By suppressing the component information, the error messages are generally much easier to read. The ErrorPrintLength preference controls the number of components which will be displayed -- the first k components will be displayed if the sum of their lengths does not exceed the integer specified by the ErrorPrintLength preference.  The length of each component is calculated using the Maple length command.  The default value for this preference is 0 so that no component information is displayed.  To display all component information, set this preference to infinity.

"HistoryDepth"

The Tools command CalculationHistory will store the results of certain critical intermediate computations which the user may wish to view.  The HistoryDepth preference specifies the number of such computations to store.  The default value for this preference is 10.

 > with(DifferentialGeometry):

To illustrate this preference, we create a small procedure called Test and store some values calculated by this program using the CalculationHistory command.

 > Test := proc(n) local i; for i to n do Tools:-CalculationHistory:-Update("Test", [i, i^2]) od; n^2 end:

Run the program Test.

 > Test(25);
 ${625}$ (5)

Retrieve the calculated values.

 > Tools:-CalculationHistory:-Get("Test");
 $\left[\left[{25}{,}{625}\right]{,}\left[{24}{,}{576}\right]{,}\left[{23}{,}{529}\right]{,}\left[{22}{,}{484}\right]{,}\left[{21}{,}{441}\right]{,}\left[{20}{,}{400}\right]{,}\left[{19}{,}{361}\right]{,}\left[{18}{,}{324}\right]{,}\left[{17}{,}{289}\right]{,}\left[{16}{,}{256}\right]\right]$ (6)

Change the HistoryDepth preference to 3.

 > Preferences("HistoryDepth", 3);
 ${10}$ (7)

 • Rerun the program Test and retrieve the calculated values.  This time only 3 values are stored.
 > Test(25);
 ${625}$ (8)
 > Tools:-CalculationHistory:-Get("Test");
 $\left[\left[{25}{,}{625}\right]{,}\left[{24}{,}{576}\right]{,}\left[{23}{,}{529}\right]\right]$ (9)

"JetNotation"

In the mathematical literature, there are two standard index notations for representing derivatives of a function.  For example, if u = u(x, y) then we have:

JetNotation1: u[1] = u_x, u[2] = u_y, u[1, 1] = u_xx, u[1, 2] = u_xy, u[2, 2] = u_yy, u[1, 1, 1] = u_xxx, u[1, 1, 2] = u_xxy, u[1, 2, 2] = u_xyy, u[2, 2, 2] = u_yyy.

JetNotation2: u[1, 0] = u_x, u[0, 1] = u_y, u[2, 0] = u_xx, u[1, 1] = u_xy, u[0, 2] = u_yy, u[3, 0] = u_xxx, u[2, 1] = u_xxy, u[1, 2] = u_xyy, u[0, 3] = u_yyy.

 • The JetNotation preference determines which notation is used by the DifferentialGeometry package (and the JetCalculus subpackage).  The default is JetNotation1.
 > with(DifferentialGeometry):
 > Preferences("JetNotation");
 ${"JetNotation1"}$ (10)
 > DGsetup([x,y], [u], Jet, 3, verbose);
 ${\mathrm{The following coordinates have been protected:}}$
 $\left[{x}{,}{y}{,}{u}\left[\right]{,}{{u}}_{{1}}{,}{{u}}_{{2}}{,}{{u}}_{{1}{,}{1}}{,}{{u}}_{{1}{,}{2}}{,}{{u}}_{{2}{,}{2}}{,}{{u}}_{{1}{,}{1}{,}{1}}{,}{{u}}_{{1}{,}{1}{,}{2}}{,}{{u}}_{{1}{,}{2}{,}{2}}{,}{{u}}_{{2}{,}{2}{,}{2}}\right]$
 ${\mathrm{The following vector fields have been defined and protected:}}$
 $\left[{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{1}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{2}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{3}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{4}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{5}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{6}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{7}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{8}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{9}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{10}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{11}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{12}\right]{,}{1}\right]\right]\right]\right)\right]$
 ${\mathrm{The following differential 1-forms have been defined and protected:}}$
 $\left[{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{1}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{2}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{3}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{4}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{5}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{6}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{7}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{8}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{9}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{10}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{11}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"form"}{,}{\mathrm{Jet}}{,}{1}\right]{,}\left[\left[\left[{12}\right]{,}{1}\right]\right]\right]\right)\right]$
 ${\mathrm{The following type \left[1,0\right] biforms have been defined and protected::}}$
 $\left[{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{1}{,}{0}\right]\right]{,}\left[\left[\left[{1}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{1}{,}{0}\right]\right]{,}\left[\left[\left[{2}\right]{,}{1}\right]\right]\right]\right)\right]$
 ${\mathrm{The following type \left[0,1\right] biforms \left(contact 1-forms\right) have been defined and protected::}}$
 $\left[{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{3}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{4}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{5}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{6}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{7}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{8}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{9}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{10}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{11}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"biform"}{,}{\mathrm{Jet}}{,}\left[{0}{,}{1}\right]\right]{,}\left[\left[\left[{12}\right]{,}{1}\right]\right]\right]\right)\right]$
 ${\mathrm{frame name: Jet}}$ (11)
 > Preferences("JetNotation", "JetNotation2");
 ${"JetNotation1"}$ (12)
 > DGsetup([x, y], [u], Jet, 3, verbose);
 ${\mathrm{The following coordinates have been protected:}}$
 $\left[{x}{,}{y}{,}{{u}}_{{0}{,}{0}}{,}{{u}}_{{1}{,}{0}}{,}{{u}}_{{0}{,}{1}}{,}{{u}}_{{2}{,}{0}}{,}{{u}}_{{1}{,}{1}}{,}{{u}}_{{0}{,}{2}}{,}{{u}}_{{3}{,}{0}}{,}{{u}}_{{2}{,}{1}}{,}{{u}}_{{1}{,}{2}}{,}{{u}}_{{0}{,}{3}}\right]$
 ${\mathrm{The following vector fields have been defined and protected:}}$
 $\left[{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{1}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}{,}\left[{}\right]\right]{,}\left[\left[\left[{2}\right]{,}{1}\right]\right]\right]\right){,}{\mathrm{_DG}}{}\left(\left[\left[{"vector"}{,}{\mathrm{Jet}}\right]\right]\right)\right]$