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{SECT 0 {PARA 0 "" 0 "" {TEXT 257 16 "Utility Routines" }}{PARA 0 "" 
0 "" {TEXT -1 131 "These utility routines are located in the file util
s.p. This file must be read in before using any of these routines.  Fo
r example," }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "read`c:/maple/
utils.p`;" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 6 "Syntax" }}{PARA 0 "
" 0 "" {TEXT 20 60 "NOTE:  Arguments enclosed in angle brackets <> are
 optional." }}{PARA 276 "" 0 "" {TEXT -1 48 "annular_average( expr, co
ords, a, b, paramlist )" }}{PARA 273 "" 0 "" {HYPERLNK 17 "applyfunc" 
2 "utilities,applyfunc" "" }{TEXT 266 50 "( expr, func::\{procedure,fu
nction\}, n::nonnegint )" }}{PARA 273 "" 0 "" {TEXT -1 70 "CombineTrig
( expr::\{algebraic,`=`\}, var1::algebraic, var2::algebraic )" }}
{PARA 275 "" 0 "" {TEXT -1 30 "`CombineTrig/optimize`( expr )" }}
{PARA 286 "" 0 "" {TEXT -1 24 "CombineTrigOpt( expr )  " }{TEXT 262 
22 "(this is an alias for " }{TEXT -1 22 "`CombineTrig/optimize`" }
{TEXT 263 1 ")" }}{PARA 281 "" 0 "" {TEXT -1 56 "common_factor( expr::
algebraic, varlist::\{list,string\} )" }}{PARA 290 "" 0 "" {HYPERLNK 
17 "cosfix" 2 "utilities,cosfix" "" }{TEXT -1 57 "( expr::\{algebraic,
array(1),`=`\}, var::\{algebraic,list\} )" }}{PARA 268 "" 0 "" 
{HYPERLNK 17 "csquare" 2 "utilities,csquare" "" }{TEXT -1 8 "( expr::
" }{TEXT 259 42 "\{algebraic,array,indexed,equation,numeric\}" }{TEXT 
261 2 " \n" }{TEXT -1 17 "         <, var::" }{TEXT 260 36 "\{name,set
,list,`+`,`*`,`^`,function\}" }{TEXT -1 3 "> )" }}{PARA 269 "" 0 "" 
{TEXT 258 51 "debug_print( pname, msg, verbosity_level <, expr> )" }}
{PARA 282 "" 0 "" {HYPERLNK 17 "expansion" 2 "utilities,expansion" "" 
}{TEXT -1 140 "( expression::\{list,set,'array'(1),'array'(2),matrix,`
=`,algebraic\},\n           params::\{set,name,list,function\}, expans
ion_order::integer )" }}{PARA 279 "" 0 "" {HYPERLNK 17 "funcops" 2 "ut
ilities,funcops" "" }{TEXT -1 54 "( expr::`+`, func::procedure, oplist
::\{integer,list\} )" }}{PARA 274 "" 0 "" {TEXT -1 21 "FunctionCalls( \+
expr )" }}{PARA 265 "" 0 "" {TEXT -1 38 "getsqrts( expr::\{algebraic,e
quation\} )" }}{PARA 277 "" 0 "" {TEXT -1 21 "is_real_parts( expr )" }
}{PARA 289 "" 0 "" {HYPERLNK 17 "location" 2 "utilities,location" "" }
{TEXT -1 34 "( expr::anything, term::anything )" }}{PARA 280 "" 0 "" 
{TEXT -1 51 "polytest( expr::algebraic, varlist::\{list,string\} )" }}
{PARA 288 "" 0 "" {HYPERLNK 17 "pullout" 2 "utilities,pullout" "" }
{TEXT -1 66 "( expr::\{`+`,`^`,`*`\}, subexpr::\{name,function,`+`,`*`
,`^`,list\} )" }}{PARA 272 "" 0 "" {TEXT -1 98 "rootfunc( expr::\{alge
braic,equation,list,set,indexed,array\}, \n          func::procedure <
, args> )" }}{PARA 278 "" 0 "" {TEXT -1 41 "RotAxis( theta::algebraic,
 axis::string )" }}{PARA 266 "" 0 "" {TEXT -1 27 "signsqrt( expr::\{`*
`,`^`\} )" }}{PARA 291 "" 0 "" {HYPERLNK 17 "sinfix" 2 "utilities,sinf
ix" "" }{TEXT -1 57 "( expr::\{algebraic,array(1),`=`\}, var::\{algebr
aic,list\} )" }}{PARA 267 "" 0 "" {TEXT -1 100 "small_divisors( expr::
\{algebraic,list(algebraic),array(1)\},\n                varlist::\{li
st,string\} )" }}{PARA 287 "" 0 "" {HYPERLNK 17 "termfunc" 2 "utilitie
s,termfunc" "" }{TEXT 265 19 "( expr::\{algebraic," }{TEXT -1 8 "array
(1)" }{TEXT 264 20 "\}, func::procedure )" }}{PARA 270 "" 0 "" 
{HYPERLNK 17 "tmsg" 2 "utilities,tmsg" "" }{TEXT -1 25 "( proc_name, m
sg <, t0> )" }}{PARA 285 "" 0 "" {TEXT -1 38 "topsqrts( expr::\{algebr
aic,equation\} )" }}{PARA 284 "" 0 "" {TEXT -1 30 "topsqrt( expr::\{`+
`,`*`,`^`\} )" }}{PARA 271 "" 0 "" {TEXT -1 76 "`type/fractional_power
`( expr::\{algebraic,equation,list,set,indexed,array\} )" }}}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 18 "Contact the Author" }}{PARA 15 "" 0 "" 
{TEXT -1 123 "Dr. Marc A. Murison\nAstronomical Applications Dept.\nU.
S. Naval Observatory\n3450 Massachusetts Ave., NW\nWashignton, DC 2039
2" }}{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 4 "" 0 "" {TEXT -1 8 "See Also" }}{PARA 0 "" 0 "" 
{HYPERLNK 17 "AESOP" 2 "AESOP" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "ODE
" 2 "ODE" "" }{TEXT -1 1 " " }}}}{MARK "3 12 1" 19 }{VIEWOPTS 1 1 0 1 
1 1803 }