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DEtools

 zoom
 zoom in/out 2-D or 3-D plots

 Calling Sequence zoom(P, a..b, c..d) zoom(P, a..b, c..d, e..f) zoom(P, 1=a..b, 3=c..d, 2=e..f)

Parameters

 P - a 2-D or 3-D plot structure

Description

 • zoom allows for changing the ranges of the display of a given 2-D or 3-D plot without having to recalculate it, thus saving time and memory resources.
 • Two different syntaxes are available. In the first one, the first argument (a plot) is followed by ranges. The first range will be used as horizontal range in 2-D plots, or as the "first" range in 3-D plots. The second range will be the vertical range in 2-D plots or the second horizontal range in 3-D plots. When using this syntax, all the ranges must be given; that is, two ranges for 2-D plots and three for 3-D plots.
 • The second syntax, a bit more flexible, permits the zooming of some (or all) of the coordinates. For example, zoom just one coordinate by indicating it with a number from the list [1,2,3]. The original ranges for the other coordinates will remain unchanged.
 • This function is part of the DEtools package, and so it can be used in the form zoom(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[zoom](..).

Examples

 > $\mathrm{with}\left(\mathrm{DEtools}\right):$
 > $H≔\frac{1\left({\mathrm{p1}}^{2}+{\mathrm{p2}}^{2}\right)}{2}+\frac{1\left({ⅇ}^{2\mathrm{q2}+2\sqrt{3}\mathrm{q1}}+{ⅇ}^{2\mathrm{q2}-2\sqrt{3}\mathrm{q1}}+{ⅇ}^{-4\mathrm{q2}}\right)}{24}-\frac{1}{8}$
 ${H}{:=}\frac{{1}}{{2}}{}{{\mathrm{p1}}}^{{2}}{+}\frac{{1}}{{2}}{}{{\mathrm{p2}}}^{{2}}{+}\frac{{1}}{{24}}{}{{ⅇ}}^{{2}{}{\mathrm{q2}}{+}{2}{}\sqrt{{3}}{}{\mathrm{q1}}}{+}\frac{{1}}{{24}}{}{{ⅇ}}^{{2}{}{\mathrm{q2}}{-}{2}{}\sqrt{{3}}{}{\mathrm{q1}}}{+}\frac{{1}}{{24}}{}{{ⅇ}}^{{-}{4}{}{\mathrm{q2}}}{-}\frac{{1}}{{8}}$ (1)

Create a 3-D plot of the surface-of-section.

 > $\mathrm{plot1}≔\mathrm{poincare}\left(H,t=-100..100,\left\{\left[0,0.1,1.4,0.1,0\right]\right\},\mathrm{stepsize}=0.1,\mathrm{iterations}=2,3\right)$

Now, zoom the plot above; it is possible to cut a slice (a small range for the third axis) and display the 2-D surface-of-section.

 > $\mathrm{zoom}\left(\mathrm{plot1},3=-0.1..0.1\right)$
 > $P≔\mathrm{plot3d}\left(\left\{\mathrm{sin}\left(xy\right),x+2y\right\},x=-\mathrm{π}..\mathrm{π},y=-\mathrm{π}..\mathrm{π}\right):$
 > $\mathrm{zoom}\left(P,-2..2,-3..3,-1..1\right)$
 > $\mathrm{zoom}\left(P,2=-4..4,1=-1..1,3=-9..9\right)$