{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Headi ng 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 4 "" 0 "" {TEXT -1 49 "The Gram-Schmidt Process \+ and the QR Decomposition" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "First \+ load the Linear Algebra package." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }{TEXT -1 0 "" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 7 "Example" }}{PARA 0 "" 0 "" {TEXT -1 45 "Ap ply the Gram-Schmidt process to the vectors" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 47 "v1 := <2,-1,0>: v2 := <-1,2,1>: v3 := <0,-1,2>:" }} }{EXCHG {PARA 5 "" 0 "" {TEXT -1 8 "Solution" }}{PARA 0 "" 0 "" {TEXT -1 13 "First vector:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "w1 \+ := v1: q1 := Normalize(w1,Euclidean);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q1G-%'RTABLEG6%\"*?F(o8-%'MATRIXG6#7%7#,$*(\"\"#\"\"\"\"\"&!\"\" F2#F1F0F17#,$*&F2F3F2F4F37#\"\"!&%'VectorG6#%'columnG" }}}{EXCHG } {EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Second vector:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "w2 := v2 - (v2.w1)/(w1.w1)*w1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#w2G-%'RTABLEG6%\"*O39P\"-%'MATRIXG6 #7%7##\"\"$\"\"&7##\"\"'F07#\"\"\"&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "q2 := Normalize(w2,Euclidean);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q2G-%'RTABLEG6%\"*Gc;P\"-%'MATRIXG6 #7%7#,$*(\"\"$\"\"\"\"#q!\"\"F2#F1\"\"#F17#,$*(F0F1\"#NF3F2F4F17#,$*& \"#9F3F2F4F1&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Third vector:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "w3 := \+ v3 - (v3.w1)/(w1.w1)*w1 - (v3.w2)/(w2.w2)*w2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#w3G-%'RTABLEG6%\"*s&>u8-%'MATRIXG6#7%7##!\"%\"\"(7## !\")F07##\"#7F0&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "q3:=Normalize(w3,Euclidean);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q3G-%'RTABLEG6%\"*C+WP\"-%'MATRIXG6#7%7#,$*&\"#9!\" \"F0#\"\"\"\"\"#F17#,$*&\"\"(F1F0F2F17#,$*(\"\"$F3F0F1F0F2F3&%'VectorG 6#%'columnG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Maple can do this \+ all in one step." }}{PARA 0 "" 0 "" {TEXT -1 83 "Either to get the vec tors w1, w2, and w3 which are orthogonal but not unit vectors:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "GramSchmidt([v1,v2,v3]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7%-%'RTABLEG6%\"*#*R/N\"-%'MATRIXG6#7% 7#\"\"#7#!\"\"7#\"\"!&%'VectorG6#%'columnG-F%6%\"*O]^P\"-F)6#7%7##\"\" $\"\"&7##\"\"'F?7#\"\"\"F2-F%6%\"*+saP\"-F)6#7%7##!\"%\"\"(7##!\")FN7# #\"#7FNF2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "or to get the orthon ormal set q1, q2, and q3 (orthogonal and unit vectors):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "GramSchmidt([v1,v2,v3], normalized) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%-%'RTABLEG6%\"*k@kN\"-%'MATRIXG 6#7%7#,$*(\"\"#\"\"\"\"\"&!\"\"F1#F0F/F07#,$*&F1F2F1F3F27#\"\"!&%'Vect orG6#%'columnG-F%6%\"*o=hP\"-F)6#7%7#,$*(\"\"$F0\"#qF2FGF3F07#,$*(FFF0 \"#NF2FGF3F07#,$*&\"#9F2FGF3F0F9-F%6%\"*k!Rw8-F)6#7%7#,$*&FOF2FOF3F27# ,$*&\"\"(F2FOF3F27#,$*(FFF0FOF2FOF3F0F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 7 "Example" }} {PARA 0 "" 0 "" {TEXT -1 154 "Consider the vector space of polynomials of degree 2 with the inner product of two polynomials f and g defined by integrating the product f*g from 0 to 1:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "ip := proc(f,g) int(f*g,x=0..1); end:" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "For example:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ip(x+1,x^2-x+2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6##\"#6\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Ap ply the GramSchmidt process to" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "v1 := 1: v2 := x: v3 := x^2:" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 8 "Solution" }}{PARA 0 "" 0 "" {TEXT -1 17 "First polynomial:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "w1 := v1: q1 := w1/sqrt(ip(w 1,w1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q1G\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Note" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "ip(w1,w1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\" " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "so w1 is already normalized a nd q1 = w1." }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Se cond polynomial:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "w2 := v 2 - ip(v2,w1)/ip(w1,w1)*w1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#w2G, &%\"xG\"\"\"#F'\"\"#!\"\"" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Normalize:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "q1 := w2/ sqrt(ip(w2,w2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q1G,$*(\"\"#\" \"\",&%\"xGF(#F(F'!\"\"F(\"\"$#F(F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "ip(q1,q1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\" " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Third polynomial:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "w3 := v3 - ip(v3,w1)/ip(w1,w1)*w1 - ip(v3,w2)/ip(w2,w2)*w2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#w3G,(*$ )%\"xG\"\"#\"\"\"F*#F*\"\"'F*F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Normalize:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "q3 := \+ w3/sqrt(ip(w3,w3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q3G,$*(\"\"' \"\"\",(*$)%\"xG\"\"#F(F(#F(F'F(F,!\"\"F(\"\"&#F(F-F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "ip(q3,q3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 240 "So an o rthonormal basis for teh space spaced by v1 = 1, v2 = x and v3 = x^2 ( which is the entire vector space of polynomials fo degree 2) with re spect to this inner product is: q1 = 1, q2 = 2*sqrt(3)(x-1/2) and q3 \+ = 6*sqrt(5)(x^2-x+1/6)." }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 "QR D ecomposition" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 243 "To find the QR decomposition of a matrix A, first apply the Gr am-Schmidt process to the columns of A = [ a_1 |...| a_n ] to get Q = \+ [ q_1 |...| q_n ], then get the upper triangular matrix R = [ r_ij ] f rom the inner products r_ij = q_i . a_j ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 7 "Example" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 29 "A1 := <1,2,3>: A2 := <4,5,6>:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A := ;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\"*!3wX8-%'MATRIXG6#7%7$\"\"\"\"\"% 7$\"\"#\"\"&7$\"\"$\"\"'%'MatrixG" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 39 "GS := GramSchmidt([A1,A2], normalized);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#GSG7$-%'RTABLEG6%\"*s\"f[8-%'MATRIX G6#7%7#,$*&\"#9!\"\"F1#\"\"\"\"\"#F47#,$*&\"\"(F2F1F3F47#,$*(\"\"$F4F1 F2F1F3F4&%'VectorG6#%'columnG-F'6%\"*W9=N\"-F+6#7%7#,$*(\"\"%F4\"#@F2F LF3F47#,$*&FLF2FLF3F47#,$*(F5F4FLF2FLF3F2F>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Q1 := GS[1]: Q2 := GS[2]:" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Q := ;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"QG-%'RTABLEG6%\"*cWbM\"-%'MATRIXG6#7%7$,$*&\"#9! \"\"F0#\"\"\"\"\"#F3,$*(\"\"%F3\"#@F1F8F2F37$,$*&\"\"(F1F0F2F3,$*&F8F1 F8F2F37$,$*(\"\"$F3F0F1F0F2F3,$*(F4F3F8F1F8F2F1%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "R := < | >;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'RTABLEG6%\"*'Hck8-%'MATRIXG 6#7$7$*$\"#9#\"\"\"\"\"#,$*(\"#;F1\"\"(!\"\"F/F0F17$\"\"!,$*(\"\"$F1F6 F7\"#@F0F1%'MatrixG" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "Q.R;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*_!Q(Q\"-%'MA TRIXG6#7%7$\"\"\"\"\"%7$\"\"#\"\"&7$\"\"$\"\"'%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "In one step:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "QRDecomposition(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6%\"*o&fp8-%'MATRIXG6#7%7$,$*&\"#9!\"\"F.#\"\"\"\"\"#F 1,$*(\"\"%F1\"#@F/F6F0F17$,$*&\"\"(F/F.F0F1,$*&F6F/F6F0F17$,$*(\"\"$F1 F.F/F.F0F1,$*(F2F1F6F/F6F0F/%'MatrixG-F$6%\"*'f=p8-F(6#7$7$*$F.F0,$*( \"#;F1F:F/F.F0F17$\"\"!,$*(F@F1F:F/F6F0F1FC" }}}{EXCHG }{SECT 0 {PARA 5 "" 0 "" {TEXT -1 7 "Example" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "A1 := <2,-1,0>: A2 := <-1,2,-1>: A3 := <0,-1,2>:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "A := ;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\"*O)3d8-%'MATRIXG6#7%7%\"\"#! \"\"\"\"!7%F/F.F/7%F0F/F.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "GS := GramSchmidt([A1,A2,A3],normalized);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#GSG7%-%'RTABLEG6%\"*oj`R\"-%'MATRIXG6#7%7 #,$*(\"\"#\"\"\"\"\"&!\"\"F3#F2F1F27#,$*&F3F4F3F5F47#\"\"!&%'VectorG6# %'columnG-F'6%\"*?mSQ\"-F+6#7%7#,$*(\"\"$F2\"#qF4FIF5F27#,$*(FHF2\"#NF 4FIF5F27#,$*&\"#9F4FIF5F4F;-F'6%\"*W&)**Q\"-F+6#7%7#,$*&FQF4FQF5F27#,$ *&\"\"(F4FQF5F27#,$*(FHF2FQF4FQF5F2F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Q1 := GS[1]: Q2 := GS[2]: Q3 := GS[3]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Q := ;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"QG-%'RTABLEG6%\"*k@?N\"-%'MATRIXG6#7%7%,$*( \"\"#\"\"\"\"\"&!\"\"F2#F1F0F1,$*(\"\"$F1\"#qF3F8F4F1,$*&\"#9F3F;F4F17 %,$*&F2F3F2F4F3,$*(F7F1\"#NF3F8F4F1,$*&\"\"(F3F;F4F17%\"\"!,$*&F;F3F8F 4F3,$*(F7F1F;F3F;F4F1%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "R := < | | >;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'RTABLEG6%\"*KedQ\"-%'MATRIX G6#7%7%*$\"\"&#\"\"\"\"\"#,$*(\"\"%F1F/!\"\"F/F0F6,$*&F/F6F/F0F17%\"\" !,$*&F/F6\"#qF0F1,$*(\"\")F1\"#NF6F=F0F67%F:F:,$*(F2F1\"\"(F6\"#9F0F1% 'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "Q.R;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*St " 0 "" {MPLTEXT 1 0 19 "QRDecomposition(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6$-%'RTABLEG6%\"*CFnN\"-%'MATRIXG6#7%7%,$*(\"\"#\"\"\"\"\"&!\"\"F0#F/F .F/,$*(\"\"$F/\"#qF1F6F2F/,$*&\"#9F1F9F2F/7%,$*&F0F1F0F2F1,$*(F5F/\"#N F1F6F2F/,$*&\"\"(F1F9F2F/7%\"\"!,$*&F9F1F6F2F1,$*(F5F/F9F1F9F2F/%'Matr ixG-F$6%\"*+MdP\"-F(6#7%7%*$F0F2,$*(\"\"%F/F0F1F0F2F1,$*&F0F1F0F2F/7%F D,$*&F0F1F6F2F/,$*(\"\")F/F?F1F6F2F17%FDFD,$*(F.F/FBF1F9F2F/FI" }}} {EXCHG }}{EXCHG }}}{EXCHG }{EXCHG }}{MARK "6" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 136872720 137140836 137165628 137419572 137440024 135043992 137515036 137547200 135642164 137611868 137639064 134576080 134859172 135181444 134554456 136456296 138738052 136959568 136918596 135708836 139536368 138406620 138998544 135202164 138575832 138177340 135672724 137573400 }{RTABLE M7R0 I6RTABLE_SAVE/136872720X*%)anythingG6"6"[gl!#%!!!"$"$,$*$""&#"""""##F,F),$F(#!" "F)""!F& } {RTABLE M7R0 I6RTABLE_SAVE/137140836X*%)anythingG6"6"[gl!#%!!!"$"$#""$""&#""'F)"""F& } {RTABLE M7R0 I6RTABLE_SAVE/137165628X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#q#"""""##""$F),$F(#F ."#N,$F(#F+"#9F& } {RTABLE M7R0 I6RTABLE_SAVE/137419572X*%)anythingG6"6"[gl!#%!!!"$"$#!"%""(#!")F)#"#7F)F& } {RTABLE M7R0 I6RTABLE_SAVE/137440024X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#9#"""""##!""F),$F(#F .""(,$F(#""$F)F& } {RTABLE M7R0 I6RTABLE_SAVE/135043992X*%)anythingG6"6"[gl!#%!!!"$"$""#!""""!F& } {RTABLE M7R0 I6RTABLE_SAVE/137515036X*%)anythingG6"6"[gl!#%!!!"$"$#""$""&#""'F)"""F& } {RTABLE M7R0 I6RTABLE_SAVE/137547200X*%)anythingG6"6"[gl!#%!!!"$"$#!"%""(#!")F)#"#7F)F& } {RTABLE M7R0 I6RTABLE_SAVE/135642164X*%)anythingG6"6"[gl!#%!!!"$"$,$*$""&#"""""##F,F),$F(#!" "F)""!F& } {RTABLE M7R0 I6RTABLE_SAVE/137611868X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#q#"""""##""$F),$F(#F ."#N,$F(#F+"#9F& } {RTABLE M7R0 I6RTABLE_SAVE/137639064X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#9#"""""##!""F),$F(#F .""(,$F(#""$F)F& } {RTABLE M7R0 I6RTABLE_SAVE/134576080X,%)anythingG6"6"[gl!"%!!!#'"$"#"""""#""$""%""&""'F& } {RTABLE M7R0 I6RTABLE_SAVE/134859172X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#9#"""""##F+F),$F(#F+ ""(,$F(#""$F)F& } {RTABLE M7R0 I6RTABLE_SAVE/135181444X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#@#"""""##""%F),$F(#F +F),$F(#!"#F)F& } {RTABLE M7R0 I6RTABLE_SAVE/134554456X,%)anythingG6"6"[gl!"%!!!#'"$"#,$*$"#9#"""""##F+F),$F(# F+""(,$F(#""$F),$*$"#@F*#""%F6,$F5#F+F6,$F5#!"#F6F& } {RTABLE M7R0 I6RTABLE_SAVE/136456296X,%)anythingG6"6"[gl!"%!!!#%"#"#*$"#9#"""""#""!,$F'#"#;" "(,$*$"#@F)#""$F0F& } {RTABLE M7R0 I6RTABLE_SAVE/138738052X,%)anythingG6"6"[gl!"%!!!#'"$"#"""""#""$""%""&""'F& } {RTABLE M7R0 I6RTABLE_SAVE/136959568X,%)anythingG6"6"[gl!"%!!!#'"$"#,$*$"#9#"""""##F+F),$F(# F+""(,$F(#""$F),$*$"#@F*#""%F6,$F5#F+F6,$F5#!"#F6F& } {RTABLE M7R0 I6RTABLE_SAVE/136918596X,%)anythingG6"6"[gl!"%!!!#%"#"#*$"#9#"""""#""!,$F'#"#;" "(,$*$"#@F)#""$F0F& } {RTABLE M7R0 I6RTABLE_SAVE/135708836X,%)anythingG6"6"[gl!"%!!!#*"$"$""#!""""!F(F'F(F)F(F'F& } {RTABLE M7R0 I6RTABLE_SAVE/139536368X*%)anythingG6"6"[gl!#%!!!"$"$,$*$""&#"""""##F,F),$F(#!" "F)""!F& } {RTABLE M7R0 I6RTABLE_SAVE/138406620X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#q#"""""##""$F),$F(#F ."#N,$F(#!"""#9F& } {RTABLE M7R0 I6RTABLE_SAVE/138998544X*%)anythingG6"6"[gl!#%!!!"$"$,$*$"#9#"""""##F+F),$F(#F+ ""(,$F(#""$F)F& } {RTABLE M7R0 I6RTABLE_SAVE/135202164X,%)anythingG6"6"[gl!"%!!!#*"$"$,$*$""&#"""""##F,F),$F(# !""F)""!,$*$"#qF*#""$F4,$F3#F6"#N,$F3#F0"#9,$*$F#F+""(,$F>#F6F#F+""(,$F>#F6F