{VERSION 2 3 "APPLE_PPC_MAC" "2.3" }
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1 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
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1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 
256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 
-1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 
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-1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 52 "Vector Spaces, I -- Lif
e in Two and Three Dimensions" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" 
{TEXT -1 202 "\nVectors are denoted in Maple with commas separating th
eir entries and enclosed by square brackets as shown by the cell below
.   Notice that calculations with vectors are done in Maple by the pro
cedure " }{TEXT 257 6 "evalm " }{TEXT -1 18 "as shown below.   " }
{TEXT 258 22 "Evaluate that cell now" }{TEXT -1 2 ". " }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "evalm([
1, 2] + [3, 4]);\n  \nevalm(3 * [1, 2]);\n\nevalm([1, 2, 3] + [4, 5, 6
]);\n\nevalm(5 * [1, -1, 2]); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 135 "For some of the exercises in this mo
dule you will want to plot points.  The following cell illustrates how
 this can be done in Maple.  " }{TEXT 259 27 "Evaluate the next cell n
ow." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 93 "plot([[1,2], [3, 1]], -4..4, -4..4, \n   \+
    scaling=CONSTRAINED, style=POINT, symbol=CIRCLE);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "Notice th
e ranges for the x- and y-axes are specified in the form" }}{PARA 257 
"" 0 "" {TEXT -1 2 "\n\n" }{TEXT 260 28 "xlow .. xhigh, ylow .. yhigh
" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 7 "\nwith  " }{TEXT 261 
4 "xlow" }{TEXT -1 7 "  and  " }{TEXT 262 5 "xhigh" }{TEXT -1 57 "  de
noting the low and high end of the x-axis range and  " }{TEXT 263 4 "y
low" }{TEXT -1 7 "  and  " }{TEXT 264 5 "yhigh" }{TEXT -1 52 " denotin
g the low and high end of the y-axis range.\n" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 164 "You may also want to \+
use the procedures below from the previous section to display and mani
pulate images.  Each image is represented by a list of points of the f
orm" }}{PARA 258 "" 0 "" {TEXT -1 2 "\n\n" }{TEXT 265 34 "[[x1, y1], [
x2, y2], ... [xn, yn]]" }{TEXT -1 2 "\n\n" }}{PARA 0 "" 0 "" {TEXT -1 
89 "and is drawn by connecting the points by lines.\n\nYou will use th
e following procedures:\n\n" }{TEXT 266 18 "plotcurve(list, n)" }
{TEXT -1 118 " -- This procedure displays one image represented by a l
ist of points as described above.  The x- and y-axes run from " }
{TEXT 267 2 "-n" }{TEXT -1 4 " to " }{TEXT 268 1 "n" }{TEXT -1 3 ".\n
\n" }{TEXT 269 27 "plotcurves(list1, list2, n)" }{TEXT -1 104 " -- Thi
s procedure displays two images represented by two lists of points.  t
he x- and y-axes run from  " }{TEXT 270 2 "-n" }{TEXT -1 5 "  to " }
{TEXT 271 1 "n" }{TEXT -1 84 ".  The first image is displayed in black
 and the second image is displayed in red.\n\n" }{TEXT 272 12 "mirror(
list)" }{TEXT -1 85 " -- This procedure computes the reflection in the
 x-axis of the image represented by " }{TEXT 273 5 "list\n" }{TEXT -1 
2 "\nt" }{TEXT 274 15 "rans(list, a, b" }{TEXT -1 54 ") -- This proced
ure translates the image represnted by" }{TEXT 275 6 " list " }{TEXT 
-1 3 "by " }{TEXT 276 2 "a " }{TEXT -1 23 "units horizontally and " }
{TEXT 277 1 "b" }{TEXT -1 20 " units vertically.\n\n" }{TEXT 278 16 "r
ot(list, theta)" }{TEXT -1 52 " -- This procedure rotates the image re
presented by " }{TEXT 279 5 "list " }{TEXT -1 3 "by " }{TEXT 280 5 "th
eta" }{TEXT -1 46 " radians counterclockwise around the origin.\n\n" }
{TEXT 281 15 "dilate(list, a)" }{TEXT -1 50 " -- This procedure dilate
s an image represented by" }{TEXT 282 5 " list" }{TEXT -1 15 " by the \+
factor " }{TEXT 283 1 "a" }{TEXT -1 3 ".\n\n" }{TEXT 284 12 "ident(lis
t) " }{TEXT -1 49 "-- This procedure leaves the image represented by" 
}{TEXT 285 5 " list" }{TEXT -1 9 " alone.\n\n" }{TEXT 286 26 "Evaluate
 the next cell now" }{TEXT -1 2 ".\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 839 "with('plots'):\n\n  plotcurve := proc(lst, n)\n     \+
plot(lst, -n..n, -n..n, scaling = CONSTRAINED)\n  end: \n\n  mirrorpt \+
:= x -> [x[1], -x[2]]:\n  transpt  := (x, a, b) -> [x[1] + a, x[2] + b
]:\n  rotpt    := (x, theta) -> [x[1] * cos(theta) - x[2] * sin(theta)
,\n                           x[1] * sin(theta) + x[2] * cos(theta)]:
\n  dilatept := (x, a) -> [x[1] * a, x[2] * a]:\n  identpt  := x -> x:
\n\n  mirror   := x -> [seq(mirrorpt(j), j=x)]:\n  trans    := (x, a, \+
b)  -> [seq(transpt(j, a, b), j=x)]:\n  rot      := (x, theta) -> [seq
(rotpt(j, theta), j=x)]:\n  dilate   := (x, a) -> [seq(dilatept(j, a),
 j=x)]:\n  ident    := x -> x:\n\n  plotcurves  := proc(x, y, n) local
 blk, rd;\n     blk := plot(x, -n..n, -n..n, scaling=CONSTRAINED, colo
r=black);\n     rd  := plot(y, -n..n, -n..n, scaling=CONSTRAINED, colo
r=red);\n     display([blk, rd]);\n  end:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "The next cell illustrates
 how these procedures are used to work with images.  " }{TEXT 287 16 "
Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 114 "a := [[1,2], [2,1], [3,2]]:\n\n  plotcurve(a
, 3);\n\n  plotcurves(a, mirror(a), 3);\n\n  plotcurves(a, dilate(a, 2
), 8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0
" 23 }{VIEWOPTS 1 1 0 1 1 1803 }