{VERSION 3 0 "DEC ALPHA UNIX" "3.0" } {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 "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 0 561 "coplanar:=proc()\n \+ local i,P,V,Delta;\n if nargs<4 then \n ERROR(`expected 4 a rguments, but received`,args) \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 arg ument to be a list or a \n vector but received`,args) \n fi\n od;\n for i to 3 do V[i]:=evalm(P[i]-P[4]) od;\n \+ Delta:=linalg[det](linalg[augment](V[1],V[2],V[3]));\n userinfo(2, `coplanar`,Normalizer(Delta));\n evalb(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):" }}}{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+s in(theta)^2*b)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "coplana r(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:=readlib(`combine/trig`);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+NormalizerGR6#%\"xG6\"6#%aoCopyright~(c)~1990~b y~the~University~of~Waterloo.~All~rights~reserved.GF(--%(readlibG6#%,t rig/reduceG6#9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "co planar(a,b,c,d);" }}{PARA 6 "" 1 "" {TEXT -1 13 "coplanar: 0" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "a:=[a1,a2,a3]:\nb:=[b1,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 "coplanar: a1*b2*c3-a1*c2*b3-a2*b1* c3+a2*c1*b3+a3*b1*c2-a3*c1*b2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&fal seG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "expand(linalg[dotpro d](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" 0 }{VIEWOPTS 1 1 0 1 1 1803 }