{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 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 "Heading 1" 
0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 
0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "restart;\nprintlevel
 := 2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 431 "with(linalg):\nG
 := matrix(['['S[i,j]' $ 'j'=1..6]' $ 'i'=1..6]);\nfor i from 1 to 6 d
o\n  S[i,i] := 1;\nod;\nfor i from 1 to 5 do\n  S[i,i+1] := 1/3;\nod;
\nS[1,6] := 1/3;\nfor i from 2 to 6 do\n  for j from 1 to i-1 do\n    \+
S[i,j] := S[j,i];\n  od;\nod;\neq := \{'S[i,1]+S[i,2]+S[i,3]+S[i,4]+S[
i,5]+S[i,6]=0' $ 'i'=1..6\};\nsol := solve(eq, \{S[1,4],S[2,4],S[2,5],
S[2,6],S[3,6],S[4,6]\});\nG := matrix(['['subs(sol,S[i,j])' $ 'j'=1..6
]' $ 'i'=1..6]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 268 "S[1,3]
 := x;\nS[3,5] := y;\nS[1,5] := z;\nG := matrix(['['subs(sol, S[i,j])'
 $ 'j'=1..6]' $ 'i'=1..6]);\nA := \{1,2,3,4,5,6\};\nF := \{\};\nfor i \+
from 2 to 6 do\n  for j from 1 to i-1 do\n    T := convert(A minus \{i
,j\}, list);\n    F := F union \{det(submatrix(G, T, T))\};\n  od;\nod
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "with(grobner);\nvar :=
 [z, y, x];\nB := gbasis(F, var, plex);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "B := factor(B);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 200 "F1 := \{B[1], B[2], B[4], op(1,B[3])\};\nF2 := \{B[1
], B[2], B[4], op(2,B[3])\};\nF3 := \{B[1], B[2], B[4], op(3,B[3])\};
\nB1 := gbasis(F1, var, plex);\nB2 := gbasis(F2, var, plex);\nB3 := gb
asis(F3, var, plex);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "V1 \+
:= solve(\{op(B1)\});\nV2 := solve(\{op(B2)\});" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 67 "for v in V1 do\n  subs(v, B3);\nod;\nfor v in \+
V2 do\n  subs(v, B3);\nod;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
11 "factor(B3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "with(plo
ts):\nplotsetup(default);" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 5 "Plot
s" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 638 "bigegg := op(1, implic
itplot(B3[3],x=-1..1,y=-1..1,numpoints=4000)):\nsmallegg := op(1, impl
icitplot(B3[3], x=-5..5, y=-5..5, numpoints=4000)):\npoints := POINTS(
[-1/3,-1/3], [-1/3,-7/9], [-7/9,-1/3]):\ntriangle := POLYGONS([[-1,-1]
,[-1,1/3],[1/3,-1]], COLOUR(RGB, 1, 1, 0)):\nline := CURVES([[-5,5-2/3
],[5-2/3,-5]], COLOUR(RGB, 0, 1, 0)):\nstext := TEXT([0.8,-1.2],`y+x+2
/3=0`,ALIGNRIGHT,COLOUR(RGB, 0, 1, 0)), TEXT([2,2],`B3[3]=0`,COLOUR(RG
B, 1, 0, 0)):\nbtext := TEXT([-0.7,-0.7],`B3[3]=0`,COLOUR(RGB, 1, 0, 0
)), TEXT([-0.5,-0.5],`\"boat\"`), POLYGONS([[-0.75,-0.34],[-0.55,-0.48
]],[[-0.35,-0.34],[-0.45,-0.48]],[[-0.34,-0.75],[-0.45,-0.52]]):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "plot1 := PLOT(smallegg, tria
ngle, line, stext, SYMBOL(CIRCLE), AXESLABELS(`x`,`y`)):\nplot1;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "plot2 := PLOT(bigegg, triang
le, points, btext, SYMBOL(CIRCLE), AXESLABELS(`x`,`y`)):\nplot2;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 565 "lift := proc(p)\n  if (type
(p, list)) then\n    [[p[1][1], p[1][2], solve(subs(x = p[1][1], y = p
[1][2], B3[2]))],\n     [p[2][1], p[2][2], solve(subs(x = p[2][1], y =
 p[2][2], B3[2]))]];\n  else\n    NULL;\n  fi;\nend;\nbigegg3D := map(
lift, bigegg):\npoints3D := POINTS([-1/3,-1/3,-7/9],[-1/3,-7/9,-1/3],[
-7/9,-1/3,-1/3],[-1/3,-1/3,-1/3], SYMBOL(CIRCLE)):\ntext3D := TEXT([-0
.5,-0.5,-0.5],`\"boat\"`), TEXT([-0.35,-0.35,-0.35],`\"chair\"`), POLY
GONS([[-0.35,-0.35,-0.75],[-0.48,-0.48,-0.52]],[[-0.35,-0.75,-0.35],[-
0.48,-0.52,-0.48]],[[-0.75,-0.35,-0.35],[-0.52,-0.48,-0.48]]):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 173 "plot3 := PLOT3D(CURVES(op(b
igegg3D), COLOUR(ZHUE), THICKNESS(2)), points3D, text3D, COLOUR(RGB,0,
0,0), AXESSTYLE(BOX), ORIENTATION(-120,80), AXESLABELS(`x`,`y`,`z`)):
\nplot3;" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 \+
0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }