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Plots Library for TI-Nspire

## Plots Library for TI-Nspire

This library document contains a collection of useful programs and functions which may be used to create and support a range of plot options:

Dual GridsThe functionsdualgridx(min,xmax,ymin,ymax) anddualgridy(min,xmax,ymin,ymax) may be used to set up a scatter plot which simulates two side-by-side axes. These may then be used to compare graphs of functions, matrices, even complex mappings.

Step 1: It is most useful to begin by storing the axes parameters as variables (right-click on each on a graph page and choose

Storefrom the contextual menu).Step 2: Define variables such as dgx:=

dualgridx(min,xmax,ymin,ymax) and dgy:=dualgridy(min,xmax,ymin,ymax). This can be done in Calculator or, even more easily, in Lists & Spreadsheet.Step 3: Set up a scatter plot using dgx and dgy, and then choose Attributes. Change Point Size to the smallest option, and change to connected. All done!

Now that your dual grids are in place, use the following functions to place functions, matrices, complex lists and other objects on either right or left:

shiftlandshiftrwill take objects like matrices and functions (entered as strings) and plot them to left or right.shiftxlandshiftylwill plot lists to the left, whileshiftxrandshiftyrwill plot them to the right.

Complex GridsThe dualgrid functions are very useful for studying the effects of complex mappings or transformations upon complex lists or polygons. Three options are available here:

2.1

complex_map(clist,z-map) is a program which takes a complex list and a transformation in z and returns the transformed complex list. e.g.complex_map({2+3, -3+2i, 2-3i},zi^{2}-2z).2.2

complex(clist, z-map) andcomplexy(clist,z-map) are functions which take a complex list and return the real and imaginary components of the transformed list.2.3

cplotx(clist) andcploty(clist) are functions which simply take a complex list and return real and imaginary components for plotting.

Matrix PlotsMatrices may be plotted using the programmatrix_plot(matrix) or the functionsmplotx(matrix) andmploy(matrix).

matrix_plot(matrix), when run in Calculator, generates two lists,xv and iv, which when used as the basis for a connected scatter plot, plot the polygon represented by the matrix. Subsequent applications of this program will plot further polygons, until the programresetm()is run to clear settings. This way, such studies as the effects of repeated transformations can be observed.

Thus, the program matrix_plot is cumulative: successive matrices will be plotted on the same axes until the resetm() program is run. This program also plots a closed polygon, while the mplotx and mploty functions simply plot the x- and y-coordinates as lists.

3D PlotsA simulation of a 3D grid is created using the functionsgrid3dx(min,xmax,xtick,ymin,ymax,ytick) and

grid3dy(min,xmax,xtick,ymin,ymax,ytick).Set attributes to show points as crosses, and the plot as connected.

Use with

vector3dx(list) andvector3dy(list).These create a scatter plot which, when connected, joins x, y and z-coordinates. Overlay these with segments for best effect.

Conic PlotsPart of the Polynomial Toolkit, the functionconic_plotwill take a string and plot the conic in x and y.If the program

par("x,y") is run first, then the conic may be entered directly in the Calculator, without the need for quotes. For graphing, though, the string is required.

Isometric PlotsUsing the program

isometric(min,xmax,xtick,ymin,ymax,ytick)

or the functionsisox(min,xmax,xtick,ymin,ymax,ytick) and

isoy(xmin,xmax,xtick,ymin,ymax,ytick)

an isometric grid can be created using scatter plots.

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