{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {CSTYLE "" 18 256 "Helvetica" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "interface(imaginaryu nit=_i):\nwith(PolynomialIdeals):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "h1 := x2-u3; \nh2 := (x1-u1)*u3-u2*u3;\nh3 := x1*x4-x 2*x3;\nh4 := u3*(u1-x3)-x4*(u1-u2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#h1G,&%#x2G\"\"\"%#u3G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h 2G,&*&,&%#x1G\"\"\"%#u1G!\"\"F)%#u3GF)F)*&%#u2GF)F,F)F+" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#h3G,&*&%#x1G\"\"\"%#x4GF(F(*&%#x2GF(%#x3GF(! \"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h4G,&*&%#u3G\"\"\",&%#u1GF( %#x3G!\"\"F(F(*&%#x4GF(,&F*F(%#u2GF,F(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "g1 := x3^2+x4^2 - ((x1-x3)^2+(x2-x4)^2);\ng2 := (u1-x 3)^2+x4^2 - ((x3-u2)^2+(x4-u3)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#g1G,**$)%#x3G\"\"#\"\"\"F**$)%#x4GF)F*F**$),&%#x1GF*F(!\"\"F)F*F2*$ ),&%#x2GF*F-F2F)F*F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2G,**$),&% #u1G\"\"\"%#x3G!\"\"\"\"#F*F**$)%#x4GF-F*F**$),&F+F*%#u2GF,F-F*F,*$),& F0F*%#u3GF,F-F*F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "I := < h1,h2,h3,h4>;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"IG-%$<,>G6&,**&%# u3G\"\"\"%#u1GF+F+*&F*F+%#x3GF+!\"\"*&%#x4GF+F,F+F/*&F1F+%#u2GF+F+,&%# x2GF+F*F/,(*&F*F+%#x1GF+F+F)F/*&F3F+F*F+F/,&*&F8F+F1F+F+*&F5F+F.F+F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Note, by default, all uknowns a re treated as variables, not parameters, so " }{XPPEDIT 18 0 "`subset` (I,Q);" "6#-%'subsetG6$%\"IG%\"QG" }{TEXT -1 1 "[" }{XPPEDIT 18 0 "x1, x2,x3,x4,u1,u2,u3;" "6)%#x1G%#x2G%#x3G%#x4G%#u1G%#u2G%#u3G" }{TEXT -1 2 "]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "IdealInfo[Variable s](I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<)%#x2G%#u3G%#x1G%#u1G%#u2G% #x4G%#x3G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "IdealInfo[Para meters](I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "The test if g1 and g2 are in I is false" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "IdealMembership(g1,I);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "IdealMembership(g2,I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "The test if the y are in " }{XPPEDIT 18 0 "sqrt(I);" "6#-%%sqrtG6#%\"IG" }{TEXT -1 12 " also fails" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "R :=