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28 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small201" -1 207 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "He lp Italic" -1 42 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small202204208" -1 208 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Output Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Maple Name" -1 35 "Times" 1 12 104 64 92 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Emphasized" -1 22 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Time s" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small202204" -1 209 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Underlin ed Italic" -1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold" -1 5 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "restart; # cubic pol ynomial, C0 4 node line element (L4_C0)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(linalg):\n" }{MPLTEXT 1 0 62 "P:=matrix(1,4,[1,x ,x^2,x^3]); # complete cubic polynomial in x" }}{PARA 7 "" 1 "" {TEXT 210 79 "Warning, the protected names norm and trace have been redefine d and unprotected" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"F&;F& \"\"%E\\[l%6$F&\"\"#I\"xGF#6$F&F(*$)F,\"\"$F&6$F&F&F&6$F&F0*$)F,F+F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "# coordinate system, 0 <= x <= L for two identities in G below" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "G:=matrix(4,4,[[1, 0, 0, 0],[1,L/3,L^2/9,L^3/27],\n \+ [1,2*L/3,4*L^2/9,8*L^3/27],[1, L, L^2, L^3]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"%F%E\\[l16$F'\"\"$*$)I\"LGF# \"\"#F&6$F*F&F&6$F.F',$*&#F&\"#FF&)F-F*F&F&6$F&F.\"\"!6$F'F.F-6$F.F*,$ *&#F&\"\"*F&F,F&F&6$F&F'F76$F.F.,$*&#F&F*F&F-F&F&6$F&F&F&6$F'F'*$F5F&6 $F.F&F&6$F'F&F&6$F*F.,$*&#F.F*F&F-F&F&6$F&F*F76$F*F*,$*&#F'F=F&F,F&F&6 $F*F',$*&#\"\")F4F&F5F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "G_inv:=evalm(inverse(G)); # exists for valid interpolations" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "N:=linalg[multiply](P,G_inv);" }} {PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"%F%E\\[l16$F'\"\"$,$*&# \"#F\"\"#F&)I\"LGF#F*!\"\"F26$F*F&,$*&\"\"*F&)F1F/F2F&6$F/F'*$F1F26$F& F/\"\"!6$F'F/,$F,F&6$F/F*,$*&#F6F/F&F1F2F26$F&F'F;6$F/F/,$*&F6F&F1F2F& 6$F&F&F&6$F'F',$*&FAF&F0F2F&6$F/F&,$*&#\"#6F/F&F1F2F26$F'F&,$FIF26$F*F /,$*&#\"#XF/F&F7F2F26$F&F*F;6$F*F*,$*&\"#=F&F7F2F&6$F*F',$*&FAF&F7F2F2 " }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"F&;F&\"\"%E\\[l%6$F&\" \"#,(*(\"\"*F&I\"xGF#F&I\"LGF#!\"\"F&*(#\"#XF+F&)F/F+F&)F0F+F1F1*(#\"# FF+F&)F/\"\"$F&)F0F;F1F&6$F&F(,(*&F/F&F0F1F&*(#F.F+F&F5F&F6F1F1*(FAF&F :F&F " 0 "" {MPLTEXT 1 0 21 "sum('N[1,k]',k=1..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Load := map(int ,transpose(N), x = 0..L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\" \"\"\"%;F&F&E\\[l%6$\"\"$F&,$*&#F+\"\")F&I\"LGF#F&F&6$F&F&,$*&#F&F/F&F 0F&F&6$\"\"#F&F,6$F'F&F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "B:= map (diff,N,x); # B is dN/dx" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"F&;F&\"\"%E\\[ l%6$F&\"\"#,(*&\"\"*F&I\"LGF#!\"\"F&*(\"#XF&I\"xGF#F&)F/F+F0F0*(#\"#\" )F+F&)F3F+F&)F/\"\"$F0F&6$F&F(,(*$F/F0F&*(F.F&F3F&F4F0F0*(#\"#FF+F&F8F &F9F0F&6$F&F&,(*&#\"#6F+F&F/F0F0*(\"#=F&F3F&F4F0F&F?F06$F&F:,(*&#F.F+F &F/F0F0*(\"#OF&F3F&F4F0F&F5F0" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Typesetting:-mrow(Typesetting:-mi(\"\"), Typesetting:-mspace(heigh t = \"0.0 ex\", width = \"0.0 em\", depth = \"0.0 ex\", linebreak = \" newline\"), Typesetting:-mi(\"\"), Typesetting:-mrow(Typesetting:-mi( \"sum\"), Typesetting:-mo(\"(\", form = \"prefix\", fence = \"true\", \+ separator = \"false\", lspace = \"thinmathspace\", rspace = \"thinmath space\", stretchy = \"true\", symmetric = \"false\", maxsize = \"infin ity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\" , accent = \"false\"), Typesetting:-mo(\"'\", form = \"postfix\", fenc e = \"false\", separator = \"false\", lspace = \"verythinmathspace\", \+ rspace = \"0em\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\"), Typesetting:-mi(\"B\"), Typesetting:- mo(\"[\", form = \"prefix\", fence = \"true\", separator = \"false\", \+ lspace = \"thinmathspace\", rspace = \"thinmathspace\", stretchy = \"t rue\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\"), \+ Typesetting:-mn(\"1\"), Typesetting:-mo(\",\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rspace = \"veryt hickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize \+ = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \+ \"false\", accent = \"false\"), Typesetting:-mi(\"k\"), Typesetting:-m o(\"]\", form = \"postfix\", fence = \"true\", separator = \"false\", \+ lspace = \"thinmathspace\", rspace = \"verythinmathspace\", stretchy = \"true\", symmetric = \"false\", maxsize = \"infinity\", minsize = \" 1\", largeop = \"false\", movablelimits = \"false\", accent = \"false \"), Typesetting:-mo(\"'\", form = \"postfix\", fence = \"false\", sep arator = \"false\", lspace = \"verythinmathspace\", rspace = \"0em\", \+ stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", m insize = \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"false\"), Typesetting:-mo(\",\", form = \"infix\", fence = \"fals e\", separator = \"true\", lspace = \"0em\", rspace = \"verythickmaths pace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infin ity\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\" , accent = \"false\"), Typesetting:-mi(\"k\"), Typesetting:-mo(\"=\", \+ form = \"infix\", fence = \"false\", separator = \"false\", lspace = \+ \"thickmathspace\", rspace = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", large op = \"false\", movablelimits = \"false\", accent = \"false\"), Typese tting:-mn(\"1\"), Typesetting:-mo(\"..\", form = \"postfix\", fence = \+ \"false\", separator = \"false\", lspace = \"mediummathspace\", rspace = \"0em\", stretchy = \"false\", symmetric = \"false\", maxsize = \"i nfinity\", minsize = \"1\", largeop = \"false\", movablelimits = \"fal se\", accent = \"false\"), Typesetting:-mn(\"4\"), Typesetting:-mo(\") \", form = \"postfix\", fence = \"true\", separator = \"false\", lspac e = \"thinmathspace\", rspace = \"verythinmathspace\", stretchy = \"tr ue\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", \+ largeop = \"false\", movablelimits = \"false\", accent = \"false\"), T ypesetting:-mo(\";\", form = \"infix\", fence = \"false\", separator = \"true\", lspace = \"0em\", rspace = \"thickmathspace\", stretchy = \+ \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \" 1\", largeop = \"false\", movablelimits = \"false\", accent = \"false \")), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Typesetti ngGI(_syslibGF'6'-I#miGF$6#Q!F'-I'mspaceGF$6&/%'heightGQ'0.0~exF'/%&wi dthGQ'0.0~emF'/%&depthGF4/%*linebreakGQ(newlineF'F+-F#64-F,6#Q$sumF'-I #moGF$6/Q\"(F'/%%formGQ'prefixF'/%&fenceGQ%trueF'/%*separatorGQ&falseF '/%'lspaceGQ.thinmathspaceF'/%'rspaceGFQ/%)stretchyGFK/%*symmetricGFN/ %(maxsizeGQ)infinityF'/%(minsizeGQ\"1F'/%(largeopGFN/%.movablelimitsGF N/%'accentGFN-FC6/Q\"'F'/FGQ(postfixF'/FJFNFL/FPQ2verythinmathspaceF'/ FSQ$0emF'/FUFNFVFXFenFhnFjnF\\o-F,6#Q\"BF'-FC6/Q\"[F'FFFIFLFOFRFTFVFXF enFhnFjnF\\o-I#mnGF$6#Fgn-FC6/Q\",F'/FGQ&infixF'Fco/FMFK/FPFgo/FSQ3ver ythickmathspaceF'FhoFVFXFenFhnFjnF\\o-F,6#Q\"kF'-FC6/Q\"]F'FaoFIFLFO/F SFeoFTFVFXFenFhnFjnF\\oF^oFbpF[q-FC6/Q\"=F'FepFcoFL/FPQ/thickmathspace F'/FSFfqFhoFVFXFenFhnFjnF\\oF_p-FC6/Q#..F'FaoFcoFL/FPQ0mediummathspace F'FfoFhoFVFXFenFhnFjnF\\o-F`p6#Q\"4F'-FC6/Q\")F'FaoFIFLFOFaqFTFVFXFenF hnFjnF\\o-FC6/Q\";F'FepFcoFgpFhpFgqFhoFVFXFenFhnFjnF\\oF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "L:=1 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