{VERSION 2 3 "DEC ALPHA UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warni ng" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "X[1]:=vector([1,2,3] ):\nX1:=vector([1,2,3]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "linalg[augment](X[1],X[1]);" }}{PARA 8 "" 1 "" {TEXT -1 46 "Error, (i n linalg[vectdim]) expecting a vector" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "linalg[augment](X1,X1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7$\"\"\"F(7$\"\"#F*7$\"\"$F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 549 "coplanar:=proc()\n local i,P,V,Delta;\n \+ if nargs<4 then \n ERROR(`expected 4 arguments, but received`,a rgs) \n fi;\n for i to 4 do \n if type(args[i],list) then P .i:=vector(args[i])\n elif type(args[i],vector) then P.i:=args[i] \n else ERROR(`expected its`,i,`th argument to be a list or a \n \+ vector but received`,args)\n fi\n od;\n fo r i to 3 do V.i:=evalm(P.i-P4) od;\n Delta:=linalg[det](linalg[augm ent](V1,V2,V3));\n userinfo(2,`coplanar`,Normalizer(Delta));\n e valb(Normalizer(Delta)=0)\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "a:=[1,2,3]:\nb:=[-1,2,3]:\nc:=[0,1,1]:\nd:=evalm((2*a+b-c)/2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG-%'VECTORG6#7%#\"\"\"\"\"## \"\"&F+\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coplanar(a, b,c,d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "a:=[1,2,3]:\nb:=[-1,2,3]:\nc:=[0,3,1]:\nd:= evalm((x*a+y*b+z*c)/(x+y+z)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coplanar(a,b,c,d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "a:=[1,2,3]:\nb:=[-1,2,3]: \nc:=[0,3,1]:\nd:=evalm((cos(theta)^2*a+sin(theta)^2*b)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coplanar(a,b,c,d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "infolevel[coplanar]:=2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coplanar(a,b,c,d);" }}{PARA 6 "" 1 "" {TEXT -1 47 "coplanar: - 14+14*cos(theta)^2+14*sin(theta)^2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# %&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Normalizer:=rea dlib(`combine/trig`);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+Normalizer G:6#%\"xG6\"6#%aoCopyright~(c)~1990~by~the~University~of~Waterloo.~All ~rights~reserved.GF(--%(readlibG6#%,trig/reduceG6#9$F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coplanar(a,b,c,d);" }}{PARA 6 "" 1 "" {TEXT -1 13 "coplanar: 0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%tru eG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "a:=[a1,a2,a3]:\nb:=[b 1,b2,b3]:\nc:=[c1,c2,c3]:\nd:=[0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coplanar(a,b,c,d);" }}{PARA 6 "" 1 "" {TEXT -1 65 "co planar: a1*b2*c3-a1*c2*b3-a2*b1*c3+a2*c1*b3+a3*b1*c2-a3*c1*b2" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "expand(linalg[dotprod](linalg[crossprod](a,b),c));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*(%#a1G\"\"\"%#b2GF&%#c3GF&F&*(F%F& %#c2GF&%#b3GF&!\"\"*(%#a2GF&%#b1GF&F(F&F,*(F.F&%#c1GF&F+F&F&*(%#a3GF&F /F&F*F&F&*(F3F&F1F&F'F&F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 }