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PolyhedralSets

 Display
 dimension of a polyhedral set

 Calling Sequence Display(polyset) Display(polyset, typeset = p)

Parameters

 polyset - polyhedral set p - (optional) boolean; format of printed output

Description

 • This command displays all of the known details for a given set, including the dimension of its ambient space, the dimension of the set, and its defining relations.
 • The Display command will always print the full list of relations of a polyhedral set, while the number of relations printed upon evaluation of a polyhedral set is limited according to PolyhedralSets[PrintLevel].
 • The argument p controls whether the output is rendered as 2-D Math (typeset = true), or 1-D Math (typeset = false).  The default matches the context in which the command is issued.

Examples

 > $\mathrm{with}\left(\mathrm{PolyhedralSets}\right):$

If the PrintLevel has been set to a low number, the list of relations will be truncated.

 > $\mathrm{PrintLevel}\left(1\right):$$c≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right)$
 ${c}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }{1}{,}{\mathrm{and 5 more constraints}}\right]\end{array}$ (1)

Display will show the entire contents of the set, regardless of the current PrintLevel:

 > $\mathrm{Display}\left(c\right)$
 ${\text{PolyhedralSet}}{:}{{}\begin{array}{lll}{\text{Set ID}}& {:}& {728}\\ {\text{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\text{Dimension of Space}}& {:}& {3}\\ {\text{Dimension of Set}}& {:}& {3}\\ {\text{# of Equalities}}& {:}& {0}\\ {\text{# of Inequalities}}& {:}& {6}\\ {\text{Relations}}& {:}& {[}{-1}{\le }{{x}}_{{3}}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{{x}}_{{3}}{\le }{1}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{-1}{\le }{{x}}_{{2}}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{{x}}_{{2}}{\le }{1}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{-1}{\le }{{x}}_{{1}}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{{x}}_{{1}}{\le }{1}{]}\\ {\text{Vertices}}& {:}& {\text{not previously calculated}}\\ {\text{Rays}}& {:}& {\text{not previously calculated}}\\ {\text{Bounded}}& {:}& {\text{not previously calculated}}\\ {\text{Volume}}& {:}& {\text{not previously calculated}}\end{array}$ (2)

Additional details that have been previously calculated are stored with the polyhedral set and printed when the set is displayed.

 > $v,r≔\mathrm{VerticesAndRays}\left(c\right)$
 ${v}{,}{r}{≔}\left[\left[{-1}{,}{-1}{,}{-1}\right]{,}\left[{-1}{,}{-1}{,}{1}\right]{,}\left[{-1}{,}{1}{,}{-1}\right]{,}\left[{-1}{,}{1}{,}{1}\right]{,}\left[{1}{,}{-1}{,}{-1}\right]{,}\left[{1}{,}{-1}{,}{1}\right]{,}\left[{1}{,}{1}{,}{-1}\right]{,}\left[{1}{,}{1}{,}{1}\right]\right]{,}\left[\right]$ (3)
 > $\mathrm{Display}\left(c\right)$
 ${\text{PolyhedralSet}}{:}{{}\begin{array}{lll}{\text{Set ID}}& {:}& {728}\\ {\text{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\text{Dimension of Space}}& {:}& {3}\\ {\text{Dimension of Set}}& {:}& {3}\\ {\text{# of Equalities}}& {:}& {0}\\ {\text{# of Inequalities}}& {:}& {6}\\ {\text{Relations}}& {:}& {[}{-1}{\le }{{x}}_{{3}}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{{x}}_{{3}}{\le }{1}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{-1}{\le }{{x}}_{{2}}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{{x}}_{{2}}{\le }{1}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{-1}{\le }{{x}}_{{1}}{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}{{x}}_{{1}}{\le }{1}{]}\\ {\text{Vertices}}& {:}& {[}\left[{-1}{,}{-1}{,}{-1}\right]{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}\left[{-1}{,}{-1}{,}{1}\right]{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}\left[{-1}{,}{1}{,}{-1}\right]{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}\left[{-1}{,}{1}{,}{1}\right]{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}\left[{1}{,}{-1}{,}{-1}\right]{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}\left[{1}{,}{-1}{,}{1}\right]{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}\left[{1}{,}{1}{,}{-1}\right]{,}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{{[}}\left[{1}{,}{1}{,}{1}\right]{]}\\ {\text{Rays}}& {:}& \left[\right]\\ {\text{Bounded}}& {:}& {\mathrm{true}}\\ {\text{Volume}}& {:}& {\text{not previously calculated}}\end{array}$ (4)

The displayed output can alternatively be rendered as 1-D Math.

 > $\mathrm{Display}\left(c,'\mathrm{typeset}'='\mathrm{false}'\right)$
 Set ID:                 728 Coordinates:            [x, x, x] Number of coordinates:  3 Dimension of set:       3 Number of equalities:   0 Number of inequalities: 6 Relations:              [-x <= 1,                          x <= 1,                          -x <= 1,                          x <= 1,                          -x <= 1,                          x <= 1] Vertices:               [[-1, -1, -1],                          [-1, -1, 1],                          [-1, 1, -1],                          [-1, 1, 1],                          [1, -1, -1],                          [1, -1, 1],                          [1, 1, -1],                          [1, 1, 1]] Rays:                   [] Bounded:                true Volume:                 not previously calculated

Compatibility

 • The PolyhedralSets[Display] command was introduced in Maple 2015.