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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 256 53 "Images of Parallelograms
 Under Linear Transformations" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the prote
cted names norm and trace have been redefined and unprotected\n" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 261 132 "Load functions to visualize the \+
effects of linear transformations.\nYou may need to customize the foll
owing path to your environment." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "
read  `C:/othermaple/pargrm_image.txt`;" }}{PARA 7 "" 1 "" {TEXT -1 
50 "Warning, the name changecoords has been redefined\n" }}{PARA 6 "" 
1 "" {TEXT -1 15 "Basic Usage is:" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}
{PARA 6 "" 1 "" {TEXT -1 37 "\011\011gr := plot_pargrm_2d([ v1, v2 ], \+
A)" }}{PARA 6 "" 1 "" {TEXT -1 14 "\011\011display(gr);" }}{PARA 6 "" 
1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 60 "where v1 and v2 are \+
vectors in R^2 and A is a 2 by 2 matrix." }}{PARA 6 "" 1 "" {TEXT -1 
0 "" }}{PARA 6 "" 1 "" {TEXT -1 70 "The parallelogram with vertices 0,
 v1, v1+v2, and v2 is drawn in blue." }}{PARA 6 "" 1 "" {TEXT -1 74 "T
he parallelogram with vertices 0, Av1, A(v1+v2), and Av2 is drawn in r
ed." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 24 "Th
ere is also a function" }}{PARA 6 "" 1 "" {TEXT -1 19 "\011 help_pargr
m_3d();" }}{PARA 6 "" 1 "" {TEXT -1 34 "describing the 3 dimensional c
ase." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "vec3 := vector([1,0
]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%vec3G-%'vectorG6#7$\"\"\"\"
\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "vec4 := vector([0,1]
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%vec4G-%'vectorG6#7$\"\"!\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A := matrix(2,2,[.1,.
1,.1,-.1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7$7$$
\"\"\"!\"\"F*7$F*$F,F," }}}{EXCHG {PARA 256 "" 0 "" {TEXT 257 55 "This
 command computes the drawing of one parallelogram." }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 41 "gr1 := plot_pargrm_2d([vec3,vec4],red,2):" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 258 26 "This actually displays it." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "display(gr1);" }}{PARA 13 "" 1 "" 
{GLPLOT2D 254 254 254 {PLOTDATA 2 "6#-%)POLYGONSG6%7&7$$\"\"!F)F(7$$\"
\"\"F)F(7$F+F+7$F(F+-%'COLOURG6&%$RGBG$\"*++++\"!\")F(F(-%*THICKNESSG6
#\"\"#" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve
 1" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT 259 80 "This computes a graphic
 structure for both the original and image parallelogram." }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 38 "gr2 := pargrm_image_2d([vec3,vec4],A):" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 260 11 "Display it." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 33 "display(gr2,scaling=constrained);" }}{PARA 13 "" 1 
"" {GLPLOT2D 254 254 254 {PLOTDATA 2 "6%-%)POLYGONSG6%7&7$$\"\"!F)F(7$
$\"\"\"F)F(7$F+F+7$F(F+-%'COLOURG6&%$RGBGF(F($\"*++++\"!\")-%*THICKNES
SG6#\"\"$-F$6%7&F'7$$F,!\"\"F>7$$\"\"#F?F(7$F>$F?F?-F06&F2F3F(F(F6-%(S
CALINGG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 132 }
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