Visualization - Maple Help

 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

 > $\mathrm{with}\left(\mathrm{plots}\right):$$\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathrm{inequal}\left(\left\{{x}^{2}-y<0,{x}^{2}+{y}^{2}<9,0<3y-x-2\right\},x=-2..2,y=0..3,\mathrm{color}="Niagara 1"\right)$

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

Example

 > $\mathrm{ineqs}:=\left[\left[\frac{4}{9}
 > $\mathrm{i1}:=\mathrm{inequal}\left({\mathrm{ineqs}}_{1},x=-2..2,y=0..3,\mathrm{color}="Niagara 1"\right):$$\mathrm{i2}:=\mathrm{inequal}\left({\mathrm{ineqs}}_{2},x=-2..2,y=0..3,\mathrm{color}="Niagara 2"\right):\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$$\mathrm{i3}:=\mathrm{inequal}\left({\mathrm{ineqs}}_{3},x=-2..2,y=0..3,\mathrm{color}="Niagara 3"\right):$$\mathrm{i4}:=\mathrm{inequal}\left({\mathrm{ineqs}}_{4},x=-2..2,y=0..3,\mathrm{color}="Niagara 4"\right):$$\mathrm{display}\left(\mathrm{i1},\mathrm{i2},\mathrm{i3},\mathrm{i4}\right)$

Multiple inequality regions can also be plotted using one command:

Example

 > $\mathrm{inequal}\left(\mathrm{map}\left(t→\left[{t}_{\left[\right]},0\le y-2x-1\right],\mathrm{ineqs}\right),x=-2..2,y=0..3,\mathrm{optionsfeasible}=\left[\left[\mathrm{color}="Niagara 1"\right],\left[\mathrm{color}="Niagara 2"\right],\left[\mathrm{color}="Niagara 3"\right],\left[\mathrm{color}="Niagara 4"\right]\right],\mathrm{optionsopen}=\left[\mathrm{color}="Mono 2",\mathrm{thickness}=1\right],\mathrm{optionsclosed}=\left[\mathrm{color}="Mono 1",\mathrm{thickness}=3\right],\mathrm{optionsexcluded}=\left[\mathrm{color}="Mono 5"\right]\right)\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$

Group Theory: Drawing Cayley Tables

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

Example

 >
 >

Example

$\mathrm{DrawSubgroupLattice}\left(\mathrm{DicyclicGroup}\left(3\right)\right)$

$\mathrm{DrawSubgroupLattice}\left(\mathrm{ElementaryGroup}\left(3,2\right)\right)$

Branch Cuts of Mathematical Expressions

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

Example

 >

 $\left[{\mathrm{arcsin}}{}\left({2}{}{z}{}\sqrt{{-}{{z}}^{{2}}{+}{1}}\right){,}{\mathrm{And}}{}\left({z}{=}{-}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{-}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({1}{,}{\mathrm{∞}}\right)\right){,}{\mathrm{And}}{}\left({z}{=}{-}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{-}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({-}{\mathrm{∞}}{,}{-}{1}\right)\right){,}{\mathrm{And}}{}\left({z}{=}{-}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{+}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({1}{,}{\mathrm{∞}}\right)\right){,}{\mathrm{And}}{}\left({z}{=}{-}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{+}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({-}{\mathrm{∞}}{,}{-}{1}\right)\right){,}{\mathrm{And}}{}\left({z}{=}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{-}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({1}{,}{\mathrm{∞}}\right)\right){,}{\mathrm{And}}{}\left({z}{=}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{-}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({-}{\mathrm{∞}}{,}{-}{1}\right)\right){,}{\mathrm{And}}{}\left({z}{=}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{+}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({1}{,}{\mathrm{∞}}\right)\right){,}{\mathrm{And}}{}\left({z}{=}\frac{{1}}{{2}}{}\sqrt{{1}{+}{\mathrm{α}}}{+}\frac{{1}}{{2}}{}\sqrt{{1}{-}{\mathrm{α}}}{,}{\mathrm{α}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{∈}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{RealRange}}{}\left({-}{\mathrm{∞}}{,}{-}{1}\right)\right){,}{\mathrm{And}}{}\left({\mathrm{ℑ}}{}\left({z}\right){=}{0}{,}{1}{<}{\mathrm{ℜ}}{}\left({z}\right)\right){,}{z}{<}{-}{1}\right]$ (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

 > $\mathrm{plot3d}\left(\mathrm{sin}\left(x\right)+\mathrm{cos}\left(y\right),x=-5..5,y=-5..5\right)$