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{SECT 0 {PARA 260 "" 0 "" {HYPERLNK 17 "Utility Routines" 2 "utilities
" "" }{TEXT -1 12 " \226 csquare()" }}{SECT 0 {PARA 5 "" 0 "" {TEXT 
-1 6 "Syntax" }}{PARA 0 "" 0 "" {TEXT 260 8 "csquare(" }{TEXT 265 1 " \+
" }{TEXT 263 106 "expr::\{algebraic,array,indexed,equation,numeric\} \+
\n         <, var::\{name,set,list,`+`,`*`,`^`,function\}> )" }}}
{SECT 0 {PARA 5 "" 0 "" {TEXT -1 7 "Purpose" }}{PARA 0 "" 0 "" {TEXT 
-1 158 "Complete the square in the (optional) variable var in the (2nd
 degree in var) polynomial expr.  This is routine is more general than
 student[completesquare]. " }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 9 "Arg
uments" }}{PARA 15 "" 0 "" {TEXT 257 4 "expr" }{TEXT -1 30 "    An exp
ression or equation." }}{PARA 15 "" 0 "" {TEXT 258 7 "var    " }{TEXT 
-1 139 "A name, a function, a `+`, `*`, or `^` expression, or a set or
 \n          list of functions, variable names, and `+`, `*`, `^` expr
essions." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 8 "Examples" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "e1 := (a*c+b^2-d)*(a*c+b^2+d) = 0:
\ne2 := (t*u+p*q+r*s)*(t*u-p*q-r*s):\ne3 := 9*sin(x)^2 + 24*sin(x) + 1
6 = f(x):\ne4 := x^2 - 2*x*a + a^2 + y^2 -2*y*b + b^2 = F:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "csquare(e1,b^2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/,&*$,&*$%\"bG\"\"#\"\"\"*&%\"aGF*%\"cGF*F*F)F**$%\"d
GF)!\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "csquare(e4
,[x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$,&%\"yG\"\"\"%\"bG!\"
\"\"\"#F(*$,&%\"xGF(%\"aGF*F+F(%\"FG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "M := array([[e1,e2],[e3,e4]]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"MG-%'MATRIXG6#7$7$/*&,(*&%\"aG\"\"\"%\"cGF/F/*$%\"b
G\"\"#F/%\"dG!\"\"F/,(F-F/F1F/F4F/F/\"\"!*&,(*&%\"tGF/%\"uGF/F/*&%\"pG
F/%\"qGF/F/*&%\"rGF/%\"sGF/F/F/,(F:F/F=F5F@F5F/7$/,(*$-%$sinG6#%\"xGF3
\"\"*FH\"#C\"#;F/-%\"fGFJ/,.*$FKF3F/*&FKF/F.F/!\"#*$F.F3F/*$%\"yGF3F/*
&FXF/F2F/FUF1F/%\"FG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "csq
uare( M, [p*q,b^2,x,y,sin(x)] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
'MATRIXG6#7$7$/,&*$,&*$%\"bG\"\"#\"\"\"*&%\"aGF/%\"cGF/F/F.F/*$%\"dGF.
!\"\"\"\"!,&*$,&*&%\"pGF/%\"qGF/F/*&%\"rGF/%\"sGF/F/F.F5*&%\"tGF.%\"uG
F.F/7$/,$*$,&-%$sinG6#%\"xGF/#\"\"%\"\"$F/F.\"\"*-%\"fGFJ/,&*$,&%\"yGF
/F-F5F.F/*$,&FKF/F1F5F.F/%\"FG" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 
18 "Contact the Author" }}{PARA 15 "" 0 "" {TEXT -1 123 "Dr. Marc A. M
urison\nAstronomical Applications Dept.\nU.S. Naval Observatory\n3450 \+
Massachusetts Ave., NW\nWashignton, DC 20392" }}{PARA 15 "" 0 "" 
{TEXT 256 29 "murison@riemann.usno.navy.mil" }}{PARA 15 "" 0 "" {TEXT 
256 37 "http://riemann.usno.navy.mil/murison/" }}}{SECT 0 {PARA 5 "" 
0 "" {TEXT -1 8 "See Also" }}{PARA 0 "" 0 "" {HYPERLNK 17 "utilities" 
2 "utilities" "" }{TEXT -1 1 " " }}}}{MARK "4" 0 }{VIEWOPTS 1 1 0 1 1 
1803 }