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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 256 3 "\011\011\011" }{TEXT 257 
22 "\011Parallelopiped Images" }}}{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 262 132 "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`;" }{TEXT -1 1 "\n" }}{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 "wher
e 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 "The parallelogram with vertices 0, Av1, A(v1+v2), and A
v2 is drawn in red." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "
" {TEXT -1 24 "There is also a function" }}{PARA 6 "" 1 "" {TEXT -1 
19 "\011 help_pargrm_3d();" }}{PARA 6 "" 1 "" {TEXT -1 34 "describing \+
the 3 dimensional case." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 23 "Stand
ard Basis Vectors." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "e1 :=vector(3
,[1,0,0]); e2 :=vector(3,[0,1,0]); e3 :=vector(3,[0,0,1]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#e1G-%'vectorG6#7%\"\"\"\"\"!F*" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#e2G-%'vectorG6#7%\"\"!\"\"\"F)" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#e3G-%'vectorG6#7%\"\"!F)\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "A := matrix(3,3,[[2,1,0],[1,
2,0],[0,0,1/2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6
#7%7%\"\"#\"\"\"\"\"!7%F+F*F,7%F,F,#F+F*" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 259 81 "This computes a graphic structure for both the original \+
and image parallelopiped." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gr1 :=
 pargrm_image_3d([e1,e2,e3],A):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 
105 "The default display is hidden line and not satisfactory - this co
uld be corrected with the\noptions panel." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "display(gr1);" }}{PARA 13 "" 1 "" {GLPLOT3D 237 180 
180 {PLOTDATA 3 "6$-%)POLYGONSG6*7&7%$\"\"!F)F(F(7%$\"\"\"F)F(F(7%F+F+
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F5F37&F*F-F5F0-%'COLOURG6&%$RGBGF(F($\"*++++\"!\")-%*THICKNESSG6#\"\"$
-F$6*7&F'7%$\"\"#F)F+F(7%$FBF)FJF(7%F+FGF(7&F'FF7%FGF+$\"+++++]!#57%F(
F(FN7&F'FK7%F+FGFNFQ7&FQFM7%FJFJFNFS7&FKFIFUFS7&FFFIFUFM-F96&F;F<F(F(F
?" 1 2 0 1 10 0 2 1 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "
Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 46 "Or just immediately \+
specify some good options." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "displ
ay(gr1,style=wireframe,scaling=constrained, axes=boxed);" }}{PARA 13 "
" 1 "" {GLPLOT3D 284 231 231 {PLOTDATA 3 "6'-%)POLYGONSG6*7&7%$\"\"!F)
F(F(7%$\"\"\"F)F(F(7%F+F+F(7%F(F+F(7&F'F*7%F+F(F+7%F(F(F+7&F'F.7%F(F+F
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\"!\")-%*THICKNESSG6#\"\"$-F$6*7&F'7%$\"\"#F)F+F(7%$FBF)FJF(7%F+FGF(7&
F'FF7%FGF+$\"+++++]!#57%F(F(FN7&F'FK7%F+FGFNFQ7&FQFM7%FJFJFNFS7&FKFIFU
FS7&FFFIFUFM-F96&F;F<F(F(F?-%&STYLEG6#%%LINEG-%*AXESSTYLEG6#%$BOXG-%(S
CALINGG6#%,CONSTRAINEDG" 1 6 0 1 10 0 2 1 1 2 1 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" 
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