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Visualization

 

Visualization improvements in Maple 17 include:

• 

Enhanced Plot Builder lets you easily embed interactive plots with parameters controlled by sliders directly into your document

• 

Improved plotting of inequalities now supports the plotting of non-linear inequalities, and makes it easier to specify the style of the plotted region and combine plots of multiple regions

• 

Easy visualization of branch cuts in 2-D and 3-D plots

• 

New visualizations for drawing Cayley tables and subgroup lattices of finite groups

• 

Automatic "boxed" 3-D axes for all 3-D plots, by default

Plotting Inequalities

As of Maple 17 the inequality plotting command in the plots package is greatly improved.  Most notably, it now supports the plotting of non-linear inequalities, but it also has improved the interface for specifying the style of the plotted region and for combining plots of multiple regions.

 

Example

withplots&colon;inequalx2y<0&comma;x2&plus;y2<9&comma;0<3yx2&comma;x&equals;2..2&comma;y&equals;0..3&comma;color&equals;Niagara 1

 

 

Multiple inequality plots can be combined with plots[display]:

Example

ineqs:=49<y&comma;y<1&comma;y<x&comma;x<3y2&comma;1<y&comma;y<35&plus;18610&comma;y<x&comma;x<y&comma;35&plus;18610<y&comma;y<12&plus;1372&comma;y<x&comma;x<y&comma;12&plus;1372<y&comma;y<3&comma;y2&plus;9<x&comma;x<y2&plus;9&colon;

i1:=inequalineqs1&comma;x&equals;2..2&comma;y&equals;0..3&comma;color&equals;Niagara 1&colon;i2:=inequalineqs2&comma;x&equals;2..2&comma;y&equals;0..3&comma;color&equals;Niagara 2&colon;i3:=inequalineqs3&comma;x&equals;2..2&comma;y&equals;0..3&comma;color&equals;Niagara 3&colon;i4:=inequalineqs4&comma;x&equals;2..2&comma;y&equals;0..3&comma;color&equals;Niagara 4&colon;displayi1&comma;i2&comma;i3&comma;i4

 

 

Multiple inequality regions can also be plotted using one command:

Example

inequalmapt&rarr;t&comma;0y2x1&comma;ineqs&comma;x&equals;2..2&comma;y&equals;0..3&comma;optionsfeasible&equals;color&equals;Niagara 1&comma;color&equals;Niagara 2&comma;color&equals;Niagara 3&comma;color&equals;Niagara 4&comma;optionsopen&equals;color&equals;Mono 2&comma;thickness&equals;1&comma;optionsclosed&equals;color&equals;Mono 1&comma;thickness&equals;3&comma;optionsexcluded&equals;color&equals;Mono 5

 

 

Group Theory: Drawing Cayley Tables

The Group Theory package features new visualizations for drawing Cayley tables and subgroup lattices of finite groups.

 

Example

withGroupTheory&colon; DrawCayleyTableAlternatingGroup4&comma; colors&equals;ColorToolsGetPalettegeneric&comma; labels&equals;letters

DrawCayleyTableAlternatingGroup3&comma; colors&equals;ColorToolsGetPaletteresene&comma; labels&equals;numbers

 

Example

DrawSubgroupLatticeDicyclicGroup3

DrawSubgroupLatticeElementaryGroup3&comma;2

Branch Cuts of Mathematical Expressions

Exploring branch cuts in mathematical expressions is easier using new plot options in the FunctionAdvisor command.

 

Example

FunctionAdvisorbranch_cuts&comma;arcsin2z1z2&comma; plot&equals;`3D`

arcsin2zz2&plus;1&comma;Andz&equals;121&plus;&alpha;121&alpha;&comma;&alpha;&in;RealRange1&comma;&infin;&comma;Andz&equals;121&plus;&alpha;121&alpha;&comma;&alpha;&in;RealRange&infin;&comma;1&comma;Andz&equals;121&plus;&alpha;&plus;121&alpha;&comma;&alpha;&in;RealRange1&comma;&infin;&comma;Andz&equals;121&plus;&alpha;&plus;121&alpha;&comma;&alpha;&in;RealRange&infin;&comma;1&comma;Andz&equals;121&plus;&alpha;121&alpha;&comma;&alpha;&in;RealRange1&comma;&infin;&comma;Andz&equals;121&plus;&alpha;121&alpha;&comma;&alpha;&in;RealRange&infin;&comma;1&comma;Andz&equals;121&plus;&alpha;&plus;121&alpha;&comma;&alpha;&in;RealRange1&comma;&infin;&comma;Andz&equals;121&plus;&alpha;&plus;121&alpha;&comma;&alpha;&in;RealRange&infin;&comma;1&comma;And&Im;z&equals;0&comma;1<&real;z&comma;z<1

(3.1)

Automatic Axes on 3-D Plots

By popular demand, 3-D plots in the Standard Worksheet will now appear with a default axis setting of "boxed".

 

Example

plot3dsinx&plus;cosy&comma;x&equals;5..5&comma;y&equals;5..5

 

See Also

plots[inequal] command, GroupTheory[DrawCayleyTable] command, GroupTheory[DrawSubgroupLattice] command, Options for 3-D Plots, Branch Cuts


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