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
Group Theory: Drawing Cayley Tables
Branch Cuts of Mathematical Expressions
Automatic Axes on 3-D Plots
See Also
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:inequalx2−y<0,x2+y2<9,0<3y−x−2,x=−2..2,y=0..3,color=Niagara 1
Multiple inequality plots can be combined with plots[display]:
ineqs:=49<y,y<1,−y<x,x<3y−2,1<y,y<35+18610,−y<x,x<y,35+18610<y,y<−12+1372,−y<x,x<y,−12+1372<y,y<3,−−y2+9<x,x<−y2+9:
i1:=inequalineqs1,x=−2..2,y=0..3,color=Niagara 1:i2:=inequalineqs2,x=−2..2,y=0..3,color=Niagara 2:i3:=inequalineqs3,x=−2..2,y=0..3,color=Niagara 3:i4:=inequalineqs4,x=−2..2,y=0..3,color=Niagara 4:displayi1,i2,i3,i4
Multiple inequality regions can also be plotted using one command:
inequalmapt→t,0≤y−2x−1,ineqs,x=−2..2,y=0..3,optionsfeasible=color=Niagara 1,color=Niagara 2,color=Niagara 3,color=Niagara 4,optionsopen=color=Mono 2,thickness=1,optionsclosed=color=Mono 1,thickness=3,optionsexcluded=color=Mono 5
The Group Theory package features new visualizations for drawing Cayley tables and subgroup lattices of finite groups.
withGroupTheory: DrawCayleyTableAlternatingGroup4, colors=ColorToolsGetPalettegeneric, labels=letters
DrawCayleyTableAlternatingGroup3, colors=ColorToolsGetPaletteresene, labels=numbers
DrawSubgroupLatticeDicyclicGroup3
DrawSubgroupLatticeElementaryGroup3,2
Exploring branch cuts in mathematical expressions is easier using new plot options in the FunctionAdvisor command.
FunctionAdvisorbranch_cuts,arcsin2z1−z2, plot=`3D`
arcsin2z−z2+1,Andz=−121+α−121−α,α∈RealRange1,∞,Andz=−121+α−121−α,α∈RealRange−∞,−1,Andz=−121+α+121−α,α∈RealRange1,∞,Andz=−121+α+121−α,α∈RealRange−∞,−1,Andz=121+α−121−α,α∈RealRange1,∞,Andz=121+α−121−α,α∈RealRange−∞,−1,Andz=121+α+121−α,α∈RealRange1,∞,Andz=121+α+121−α,α∈RealRange−∞,−1,Andℑz=0,1<ℜz,z<−1
By popular demand, 3-D plots in the Standard Worksheet will now appear with a default axis setting of "boxed".
plot3dsinx+cosy,x=−5..5,y=−5..5
plots[inequal] command, GroupTheory[DrawCayleyTable] command, GroupTheory[DrawSubgroupLattice] command, Options for 3-D Plots, Branch Cuts
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