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0 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 
"" 0 514 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 515 1 {CSTYLE "" 
-1 -1 "Helvetica" 1 14 0 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 "" 0 516 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 
0 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 
"" 3 518 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 4 519 1 {CSTYLE "" 
-1 -1 "Helvetica" 0 1 0 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 "" 4 520 1 {CSTYLE "" -1 -1 "Helvetica" 0 1 0 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 "" 
4 521 1 {CSTYLE "" -1 -1 "Helvetica" 0 1 0 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 "" 0 522 1 {CSTYLE "" -1 -1 "
Times" 0 1 0 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 "" 0 523 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 524 1 
{CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 525 1 {CSTYLE "" -1 -1 "Helvet
ica" 1 14 0 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 "" 0 526 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 527 1 
{CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 528 1 {CSTYLE "" -1 -1 "Helvet
ica" 1 14 0 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 "" 0 529 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 530 1 
{CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 531 1 {CSTYLE "" -1 -1 "Helvet
ica" 1 14 0 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 "" 0 532 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 533 1 
{CSTYLE "" -1 -1 "Helvetica" 1 14 0 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 "" 0 534 1 {CSTYLE "" -1 -1 "Helvet
ica" 1 14 0 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 "" 0 535 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 522 "" 0 "" {TEXT -1 1 " " }{TEXT -1 0 "" }{TEXT 257 30 "A Short
 Introduction to Maple " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{SECT 1 {PARA 259 "" 0 "" {TEXT -1 22 " Arithmetic Operations" }}
{EXCHG {PARA 535 "" 0 "" {TEXT -1 21 " Variable Assignement" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a := 100;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"aG\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 9 "b := 200;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"$+#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a+b;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"$+$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "a mo
d 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 6 "12*23;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$w#
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "12^23;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\":G,76qB\\pEPZi'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "30!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"B+++![3jje5>
7)fGDl#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "100/20;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "100/30;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#5\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "trunc(100/30);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "round(100/30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "trunc(-4.3);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
"round(-4.3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "floor(2.3); floor(-2.3);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"
$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "ceil(2.3); ceil(-2.3);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "abs(-
4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}}{SECT 1 {PARA 3 "" 
0 "" {TEXT 301 30 "Quotes, Concatenation operator" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 5 "a:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"a
G\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:='a';" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sqrt(s^2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#*$*$)%\"sG\"\"#\"\"\"#F(F'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 25 "assume(s>0);   sqrt(s^2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%#s|irG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "a
ssume(s<0);   sqrt(s^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#s|irG!
\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "s:='s';" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"sGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 11 "a:=(x+y)^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG*$),&%\"x
G\"\"\"%\"yGF)\"\"$F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }
{TEXT 302 52 "In Maple 5, the concatenation operator was the dot. " }}
{PARA 523 "" 0 "" {TEXT -1 65 " In Maple 6, the concatenation operator
 is the two vertical bars." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
5 "a||1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#a1G" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "a||1||2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
$a12G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 303 21 "Definit
ion of strings" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "c:=\"abcd
\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cGQ%abcd6\"" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 296 26 "Interface, Code Generati
on" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 297 28 "Customize t
he user interface" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "interf
ace(version);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%^pMaple~Worksheet~In
terface,~Maple~8.00,~IBM~INTEL~LINUX,~Apr~22~2002~Build~ID~110847G" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "interface(screenwidth=100);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "interface( quiet=true);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "interface( quiet=false)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "interface( verboseproc
 = 2 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eval(isprime);" 
}}{PARA 12 "" 1 "" {XPPMATH 20 "6#f*6#%\"nG6&%%btorG%#nrG%\"pG%\"rG6%%
)rememberG%'systemG%ipCopyright~(c)~1993~Gaston~Gonnet,~Wissenschaftli
ches~Rechnen,~ETH~Zurich.~All~rights~reserved.G6\"C$@$4-%%typeG6$9$.%(
integerG@%-F46$F6.%(numericGYQ<argument~must~be~an~integerF/O.-%(ispri
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\"FqgvJt9-JvC%=b%R'zc0BF6\"\"\"FH2F6\"&,-\"FM0-FP6$\"fbl8r'y#f\"*GXCx/
v@mp?Z1qWkXfJ,j*fAg*>DM'y$oi+bGAA[))H7vW?spIY$o&fDh'en;3EvQ!ROOPaRFE-C
tD\\\\i[/iyk18JjIP*)pp=d\")ySk$*yltE68uwvmI'H'zt$)Hs'Q#o(4DQL*\\h)G!o'
=r\"py4v84&4tZp!44Rp2F$*Q?UjUX:hOF$*[meig#f'*\\t=4*RB`5\"=MB*[pp\\)F6F
SFH2F6\"(\"3=5FMC*>8%-FP6$\"-++55%3%,&F6FSFS!\"\">Fhn-FP6$*$)Fhn\"\"&F
SF\\o>8'-%%iquoG6$F\\oFhn>8$-%%modpG6$-.%&powerG6$FGFeoF6@$555/-%2ispr
ime/cyclotestG6&F6FjoFGFeoFH3/-%%iremG6$Fhn\"\"$\"\"!/-Fhp6&F6FjoF_qFe
oFH3/-F]q6$FhnFcoF`q/-Fhp6&F6FjoFcoFeoFH3/-F]q6$Fhn\"\"(F`q/-Fhp6&F6Fj
oF_rFeoFHOFH@$/*$)-%&isqrtGFDFGFSF6OFH?(8&F_qFSF/0-&%*numtheoryG6#%'ja
cobiG6$,&*$)F\\sFGFSFS\"\"%F]oF6F]oF/-%&evalbG6#/-%3isprime/TraceModQF
G6%F\\s,&F6FSFSFSF67$FGF\\sF/F/F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
1 " " }{TEXT 298 15 "LaTeX interface" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "expr:=expand((x+y)^10);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%%exprG,8*$)%\"xG\"#5\"\"\"F**(F)F*)F(\"\"*F*%\"yGF*F**(\"#XF*)
F(\"\")F*)F.\"\"#F*F**(\"$?\"F*)F(\"\"(F*)F.\"\"$F*F**(\"$5#F*)F(\"\"'
F*)F.\"\"%F*F**(\"$_#F*)F(\"\"&F*)F.FDF*F**(F<F*)F(F@F*)F.F>F*F**(F6F*
)F(F:F*)F.F8F*F**(F0F*)F(F4F*)F.F2F*F**(F)F*F(F*)F.F-F*F**$)F.F)F*F*" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "latex(expr);" }}{PARA 6 "
" 1 "" {TEXT -1 91 "\{x\}^\{10\}+10\\,\{x\}^\{9\}y+45\\,\{x\}^\{8\}\{y
\}^\{2\}+120\\,\{x\}^\{7\}\{y\}^\{3\}+210\\,\{x\}^\{6\}\{y\}^\{4\}+252
\\,\{x\}^\{" }}{PARA 6 "" 1 "" {TEXT -1 90 "5\}\{y\}^\{5\}+210\\,\{x\}
^\{4\}\{y\}^\{6\}+120\\,\{x\}^\{3\}\{y\}^\{7\}+45\\,\{x\}^\{2\}\{y\}^
\{8\}+10\\,x\{y\}^\{9\}+\{y\}^\{10\}" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 1 " " }{TEXT 299 29 "C and Fortran code generation" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(codegen);" }}{PARA 7 "" 1 "" 
{TEXT -1 70 "Warning, the protected name MathML has been redefined and
 unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7>%\"CG%%GRADG%)GRAD
IENTG%(HESSIANG%)JACOBIANG%'MathMLG%&WebEQG%%costG%(declareG%+dontretu
rnG%$eqnG%(fortranG%'hornerG%-intrep2mapleG%*joinprocsG%+makeglobalG%*
makeparamG%)makeprocG%)makevoidG%-maple2intrepG%)optimizeG%)packargsG%
+packlocalsG%+packparamsG%+prep2transG%*renamevarG%&splitG%)swapargsG
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "C(1-x/2+3*x^2-x^3+x^4);
" }}{PARA 6 "" 1 "" {TEXT -1 43 "      t0 = 1.0-x/2.0+3.0*x*x-x*x*x+x*
x*x*x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fortran(1-x/2+3*x
^2-x^3+x^4);" }}{PARA 6 "" 1 "" {TEXT -1 33 "      t0 = 1-x/2+3*x**2-x
**3+x**4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "C([a=10.3*x-y,b
=z/t*log(z)]);" }}{PARA 6 "" 1 "" {TEXT -1 22 "      a = 0.103E2*x-y;
" }}{PARA 6 "" 1 "" {TEXT -1 21 "      b = z/t*log(z);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "fortran([a=10.3*x-y,b=z/t*log(z)]);
" }}{PARA 6 "" 1 "" {TEXT -1 21 "      a = 0.103D2*x-y" }}{PARA 6 "" 
1 "" {TEXT -1 20 "      b = z/t*log(z)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "cost(expand((x+y)^5));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&*&\"\"&\"\"\"%*additionsGF&F&*&\"#GF&%0multiplicationsGF&F&" }
}}}{SECT 1 {PARA 260 "" 0 "" {TEXT -1 33 " Types  (whattype, type, has
type)" }}{EXCHG {PARA 261 "" 0 "" {TEXT -1 1 " " }{TEXT 264 59 "Maple \+
has a type system. Using it is not obligatory though." }}}{EXCHG 
{PARA 262 "> " 0 "" {MPLTEXT 1 0 18 "a:=1; whattype(a);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"aG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
%(integerG" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 20 "b:=1.2; wha
ttype(b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"#7!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%&floatG" }}}{PARA 11 "" 1 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 266 "> " 0 "" {MPLTEXT 1 0 22 "c:=2-3*I; whatty
pe(c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG^$\"\"#!\"$" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%(complexG" }}}{EXCHG {PARA 267 "> " 0 "" 
{MPLTEXT 1 0 23 "c:=cos(x); whattype(c);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"cG-%$cosG6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)functi
onG" }}}{EXCHG {PARA 268 "> " 0 "" {MPLTEXT 1 0 14 "whattype(1/2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%)fractionG" }}}{EXCHG {PARA 269 "> " 
0 "" {MPLTEXT 1 0 12 "whattype(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
%'symbolG" }}}{EXCHG {PARA 270 "" 0 "" {TEXT -1 2 "  " }{TEXT 265 55 "
For lazy typists, there is an alias mechanism in Maple." }}}{EXCHG 
{PARA 271 "> " 0 "" {MPLTEXT 1 0 18 "alias(w=whattype);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%\"wG" }}}{EXCHG {PARA 272 "> " 0 "" {MPLTEXT 1 
0 7 "w(a+b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&floatG" }}}{EXCHG 
{PARA 273 "> " 0 "" {MPLTEXT 1 0 23 "w(x+y); w(x*y); w(x^3);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%\"+G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"
*G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G" }}}{EXCHG {PARA 274 "> " 
0 "" {MPLTEXT 1 0 5 "w(w);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'symbol
G" }}}{EXCHG {PARA 275 "" 0 "" {TEXT 266 63 "Besides whattype, there a
re two more commands that handle types" }}}{EXCHG {PARA 276 "> " 0 "" 
{MPLTEXT 1 0 33 "type(a,integer); type(b,integer);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%%trueG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" 
}}}{EXCHG {PARA 277 "> " 0 "" {MPLTEXT 1 0 39 "hastype(a,integer); has
type(b,integer);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 278 "" 0 "" {TEXT 
267 74 "The hastype(expr,t) returns true if expr has a subexpression o
f the type t" }}}{EXCHG {PARA 279 "> " 0 "" {MPLTEXT 1 0 15 "pol:=(x+x
*y)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG*$),&%\"xG\"\"\"*&F(F
)%\"yGF)F)\"\"#F)" }}}{EXCHG {PARA 280 "> " 0 "" {MPLTEXT 1 0 7 "w(pol
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G" }}}{EXCHG {PARA 281 "> " 
0 "" {MPLTEXT 1 0 14 "type(pol,`*`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#%&falseG" }}}{EXCHG {PARA 282 "> " 0 "" {MPLTEXT 1 0 17 "hastype(pol
,`*`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 
283 "> " 0 "" {MPLTEXT 1 0 14 "type(pol,`+`);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 284 "> " 0 "" {MPLTEXT 1 0 
17 "hastype(pol,`+`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "pol:=expand((x+x*y)^2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,(*$)%\"xG\"\"#\"\"\"F**(F)F*F'
F*%\"yGF*F**&F'F*)F,F)F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
7 "w(pol);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"+G" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "type(pol,`*`);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "
hastype(pol,`^`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}}
{SECT 1 {PARA 285 "" 0 "" {TEXT -1 54 " Access parts of a Maple expres
sion (op, nops, indets)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "  " }
{TEXT 300 42 "Tree structure of an expression in Maple. " }}{PARA 0 "
" 0 "" {TEXT 304 53 " Internal representation of mathematical expressi
ons." }{TEXT -1 0 "" }}}{EXCHG {PARA 286 "> " 0 "" {MPLTEXT 1 0 7 "a:=
x+y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG,&%\"xG\"\"\"%\"yGF'" }}
}{EXCHG {PARA 287 "> " 0 "" {MPLTEXT 1 0 8 "nops(a);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 288 "> " 0 "" {MPLTEXT 1 0 8 
"op(1,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 
289 "> " 0 "" {MPLTEXT 1 0 8 "op(2,a);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%\"yG" }}}{EXCHG {PARA 290 "> " 0 "" {MPLTEXT 1 0 11 "b:=sqrt(a)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG*$,&%\"xG\"\"\"%\"yGF(#F(\"
\"#" }}}{EXCHG {PARA 291 "> " 0 "" {MPLTEXT 1 0 8 "nops(b);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 292 "> " 0 "" 
{MPLTEXT 1 0 8 "op(1,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"
\"\"%\"yGF%" }}}{EXCHG {PARA 293 "> " 0 "" {MPLTEXT 1 0 8 "op(2,b);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}}{EXCHG {PARA 294 "> \+
" 0 "" {MPLTEXT 1 0 5 "w(b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"wG
6#*$,&%\"xG\"\"\"%\"yGF)#F)\"\"#" }}}{EXCHG {PARA 295 "> " 0 "" 
{MPLTEXT 1 0 14 "nops(op(2,b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"#" }}}{EXCHG {PARA 296 "> " 0 "" {MPLTEXT 1 0 29 "op(1,op(2,b)); op(
2,op(2,b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 524 "" 0 "" {TEXT -1 37 " B
ecause fractions are quite common, " }}{PARA 525 "" 0 "" {TEXT -1 38 "
 there are two special commands to get" }}{PARA 526 "" 0 "" {TEXT -1 
35 " the numerator and the denominator." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "numer(1/2); denom(1/2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG 
{PARA 297 "" 0 "" {TEXT -1 2 "  " }{TEXT 268 42 "There is a more compa
ct way to  write this" }}}{EXCHG {PARA 298 "> " 0 "" {MPLTEXT 1 0 25 "
op([2,1],b); op([2,2],b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 299 "> " 0 "" 
{MPLTEXT 1 0 8 "op(0,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"^G" }}}
{EXCHG {PARA 300 "> " 0 "" {MPLTEXT 1 0 19 "op(1..3,[5,6,7,8]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"'\"\"(" }}}{EXCHG {PARA 301 "
> " 0 "" {MPLTEXT 1 0 6 "op(b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&%
\"xG\"\"\"%\"yGF%#F%\"\"#" }}}{EXCHG {PARA 302 "> " 0 "" {MPLTEXT 1 0 
14 "indets(x+y^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$%\"xG%\"yG" }}
}{EXCHG {PARA 303 "> " 0 "" {MPLTEXT 1 0 21 "a:=x+z^3:  indets(a);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$%\"xG%\"zG" }}}{EXCHG {PARA 304 "> \+
" 0 "" {MPLTEXT 1 0 31 "indets(sqrt(x)); nops(sqrt(x));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<$%\"xG*$F$#\"\"\"\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 305 "> " 0 "" {MPLTEXT 1 0 24 "i
ndets(sqrt(x)+y^(1/3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&%\"xG%\"y
G*$F$#\"\"\"\"\"#*$)F%#F(\"\"$F(" }}}{EXCHG {PARA 306 "> " 0 "" 
{MPLTEXT 1 0 36 "indets(exp(x+y));  indets(log(x+y));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#<%%\"xG%\"yG-%$expG6#,&F$\"\"\"F%F*" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<%%\"xG%\"yG-%#lnG6#,&F$\"\"\"F%F*" }}}}{SECT 1 
{PARA 307 "" 0 "" {TEXT -1 26 " Sequences, Lists and Sets" }}{EXCHG 
{PARA 308 "" 0 "" {TEXT -1 1 " " }{TEXT 258 69 "A sequence is defined \+
as a succession of elements separated by commas" }}}{EXCHG {PARA 309 "
> " 0 "" {MPLTEXT 1 0 7 "1,2,3; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"
\"\"\"\"#\"\"$" }}}{EXCHG {PARA 310 "> " 0 "" {MPLTEXT 1 0 12 "whattyp
e(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(exprseqG" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT 259 42 "We can create fairly complicated sequences" 
}}}{EXCHG {PARA 311 "> " 0 "" {MPLTEXT 1 0 15 "seq(i,i=1..10);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"
\")\"\"*\"#5" }}}{EXCHG {PARA 312 "> " 0 "" {MPLTEXT 1 0 17 "seq(i^2,i
=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"\"\"\"%\"\"*\"#;\"#D\"
#O\"#\\\"#k\"#\")\"$+\"" }}}{EXCHG {PARA 313 "> " 0 "" {MPLTEXT 1 0 
18 "seq(x^i-1,i=1..7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6),&%\"xG\"\"
\"F%!\"\",&*$)F$\"\"#F%F%F%F&,&*$)F$\"\"$F%F%F%F&,&*$)F$\"\"%F%F%F%F&,
&*$)F$\"\"&F%F%F%F&,&*$)F$\"\"'F%F%F%F&,&*$)F$\"\"(F%F%F%F&" }}}
{EXCHG {PARA 314 "" 0 "" {TEXT -1 1 " " }{TEXT 261 2 "A " }{TEXT 260 
4 "list" }{TEXT 262 55 " is defined as a sequence enclosed in (square)
 brackets" }}}{EXCHG {PARA 315 "> " 0 "" {MPLTEXT 1 0 11 "l:=[1,2,3];
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG7%\"\"\"\"\"#\"\"$" }}}
{EXCHG {PARA 316 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%%listG" }}}{EXCHG {PARA 317 "" 0 "" {TEXT -1 1 
" " }{TEXT 263 12 "You can use " }{TEXT 284 4 "seq " }{TEXT 285 19 "to
 define new lists" }}}{EXCHG {PARA 318 "> " 0 "" {MPLTEXT 1 0 28 "l:=[
seq(ifactor(i),i=1..6)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG7(\"
\"\"-%!G6#\"\"#-F(6#\"\"$*$)F'F*F&-F(6#\"\"&*&F'F&F+F&" }}}{EXCHG 
{PARA 319 "" 0 "" {TEXT -1 2 "  " }{TEXT 283 36 "To access the i-th el
ement of a list" }}}{EXCHG {PARA 320 "> " 0 "" {MPLTEXT 1 0 5 "l[4];" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)-%!G6#\"\"#F(\"\"\"" }}}{EXCHG 
{PARA 321 "" 0 "" {TEXT -1 1 " " }{TEXT 281 2 "A " }{TEXT 269 4 "set \+
" }{TEXT 282 51 "is defined as a sequence enclosed in (curly) braces" 
}}}{EXCHG {PARA 322 "> " 0 "" {MPLTEXT 1 0 11 "s:=\{1,2,3\};" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"sG<%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 
323 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%$setG" }}}{EXCHG {PARA 324 "" 0 "" {TEXT -1 1 " " }
{TEXT 280 57 "Sets cannot contain multiple elements as opposed to list
s" }}}{EXCHG {PARA 325 "> " 0 "" {MPLTEXT 1 0 13 "l:=[1,1,2,3];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG7&\"\"\"F&\"\"#\"\"$" }}}{EXCHG 
{PARA 326 "> " 0 "" {MPLTEXT 1 0 13 "s:=\{1,1,2,3\};" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"sG<%\"\"\"\"\"#\"\"$" }}}{SECT 0 {PARA 519 "" 0 
"" {TEXT -1 51 " Apply a function to every element of a list (map) " }
}{EXCHG {PARA 327 "> " 0 "" {MPLTEXT 1 0 13 "l1:=[1,9,64];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#l1G7%\"\"\"\"\"*\"#k" }}}{EXCHG {PARA 
328 "> " 0 "" {MPLTEXT 1 0 13 "map(sqrt,l1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%\"\"\"\"\"$\"\")" }}}{EXCHG {PARA 329 "> " 0 "" 
{MPLTEXT 1 0 14 "l2:=[-1,4,-6];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
l2G7%!\"\"\"\"%!\"'" }}}{EXCHG {PARA 330 "> " 0 "" {MPLTEXT 1 0 12 "ma
p(abs,l2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"\"\"%\"\"'" }}}
{EXCHG {PARA 331 "> " 0 "" {MPLTEXT 1 0 17 "l3:=[10/3,2,3/7];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#l3G7%#\"#5\"\"$\"\"##F(\"\"(" }}}
{EXCHG {PARA 332 "> " 0 "" {MPLTEXT 1 0 14 "map(evalf,l3);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7%$\"+LLLLL!\"*$\"\"#\"\"!$\"+'G9dG%!#5" }}}
{EXCHG {PARA 333 "> " 0 "" {MPLTEXT 1 0 18 "map(evalf[15],l3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"0LLLLLLL$!#9$\"\"#\"\"!$\"0H9dG9d
G%!#:" }}}{EXCHG {PARA 334 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->x mod 3;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arr
owGF(-%$modG6$9$\"\"$F(F(F(" }}}{EXCHG {PARA 335 "> " 0 "" {MPLTEXT 1 
0 17 "map(f,[1,10,12]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"\"F$
\"\"!" }}}{EXCHG {PARA 336 "> " 0 "" {MPLTEXT 1 0 24 "map(x->x^2+1,[1,
10,12]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"#\"$,\"\"$X\"" }}}
{EXCHG {PARA 337 "> " 0 "" {MPLTEXT 1 0 26 "map(x->x^3-1,[x,y+1,z+2]);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,&*$)%\"xG\"\"$\"\"\"F)F)!\"\",&
*$),&%\"yGF)F)F)F(F)F)F)F*,&*$),&%\"zGF)\"\"#F)F(F)F)F)F*" }}}{EXCHG 
{PARA 338 "> " 0 "" {MPLTEXT 1 0 14 "map(factor,%);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#7%*&,&%\"xG\"\"\"F'!\"\"F',(*$)F&\"\"#F'F'F&F'F'F'F'*
&%\"yGF',(*$)F.F,F'F'*&\"\"$F'F.F'F'F3F'F'*&,&%\"zGF'F'F'F',(*$)F6F,F'
F'*&\"\"&F'F6F'F'\"\"(F'F'" }}}{EXCHG {PARA 339 "" 0 "" {TEXT -1 33 "W
hen the function has arguments, " }}{PARA 527 "" 0 "" {TEXT -1 26 "  t
hese appear at the end." }}}{EXCHG {PARA 340 "> " 0 "" {MPLTEXT 1 0 
41 "l:=[1+x^2+x^2*y+x-x^2*y^3,x^3-x^3*y+x^2];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"lG7$,,\"\"\"F'*$)%\"xG\"\"#F'F'*&F)F'%\"yGF'F'F*F'*
&F)F')F-\"\"$F'!\"\",(*$)F*F0F'F'*&F4F'F-F'F1F(F'" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 17 "map(collect,l,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$,(\"\"\"F%*&,(F%F%%\"yGF%*$)F(\"\"$F%!\"\"F%)%\"xG\"
\"#F%F%F.F%,&*&,&F%F%F(F,F%)F.F+F%F%*$F-F%F%" }}}}{SECT 0 {PARA 520 "
" 0 "" {TEXT -1 46 " Operations on sets (union, intersect, member)" }}
{EXCHG {PARA 341 "> " 0 "" {MPLTEXT 1 0 31 "s1 := \{1,2,3\};   s2 := \+
\{1,4,5\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s1G<%\"\"\"\"\"#\"\"$
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s2G<%\"\"\"\"\"%\"\"&" }}}
{EXCHG {PARA 342 "> " 0 "" {MPLTEXT 1 0 12 "s1 union s2;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<'\"\"\"\"\"#\"\"$\"\"%\"\"&" }}}{EXCHG {PARA 
343 "> " 0 "" {MPLTEXT 1 0 16 "s1 intersect s2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<#\"\"\"" }}}{EXCHG {PARA 344 "> " 0 "" {MPLTEXT 1 0 
27 "member(2,s1); member(2,s2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%t
rueG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 345 
"> " 0 "" {MPLTEXT 1 0 12 "s1 minus s2;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#<$\"\"#\"\"$" }}}{EXCHG {PARA 346 "> " 0 "" {MPLTEXT 1 0 12 "s2 \+
minus s1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$\"\"%\"\"&" }}}{EXCHG 
{PARA 347 "> " 0 "" {MPLTEXT 1 0 13 "s1 minus \{1\};" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#<$\"\"#\"\"$" }}}{EXCHG {PARA 348 "> " 0 "" 
{MPLTEXT 1 0 13 "s2 union \{6\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&
\"\"\"\"\"%\"\"&\"\"'" }}}}{SECT 0 {PARA 521 "" 0 "" {TEXT -1 21 " Ope
rations on lists " }}{EXCHG {PARA 350 "" 0 "" {TEXT -1 25 " Add an ele
ment to a list" }}}{EXCHG {PARA 351 "> " 0 "" {MPLTEXT 1 0 12 "m1:=[1,
2,3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#m1G7%\"\"\"\"\"#\"\"$" }}}
{EXCHG {PARA 352 "> " 0 "" {MPLTEXT 1 0 15 "m1:=[op(m1),4];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#m1G7&\"\"\"\"\"#\"\"$\"\"%" }}}{EXCHG 
{PARA 353 "> " 0 "" {MPLTEXT 1 0 17 "m1:=[5,op(m1),6];" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#m1G7(\"\"&\"\"\"\"\"#\"\"$\"\"%\"\"'" }}}
{EXCHG {PARA 354 "> " 0 "" {MPLTEXT 1 0 38 "m1:=[op(1..3,m1),100,op(4.
.nops(m1))];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#m1G7(\"\"&\"\"\"\"
\"#\"$+\"\"\"%\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 
305 37 "This technique is not efficient when " }}{PARA 528 "" 0 "" 
{TEXT -1 33 "   we are dealing with big lists." }}}{EXCHG {PARA 355 "
" 0 "" {TEXT -1 30 " Delete an element from a list" }}}{EXCHG {PARA 
356 "> " 0 "" {MPLTEXT 1 0 23 "m2:= subsop(2=NULL,m1);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#m2G7'\"\"&\"\"#\"$+\"\"\"%\"\"'" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 306 51 "Note that the initial li
st has been left unaltered." }}{PARA 529 "" 0 "" {TEXT -1 60 " m2 is a
 simply copy of m1, with the second element removed." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 3 "m1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(
\"\"&\"\"\"\"\"#\"$+\"\"\"%\"\"'" }}}{EXCHG {PARA 357 "" 0 "" {TEXT 
-1 28 " Modify an element of a list" }}}{EXCHG {PARA 358 "> " 0 "" 
{MPLTEXT 1 0 10 "m1[2]:=20;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#m1G
6#\"\"#\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "m1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7(\"\"&\"#?\"\"#\"$+\"\"\"%\"\"'" }}}{EXCHG 
{PARA 359 "> " 0 "" {MPLTEXT 1 0 16 "subsop(2=25,m1);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#7(\"\"&\"#D\"\"#\"$+\"\"\"%\"\"'" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 3 "m1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(
\"\"&\"#?\"\"#\"$+\"\"\"%\"\"'" }}}}}{SECT 0 {PARA 361 "" 0 "" {TEXT 
-1 30 " Sums and Products (sum, prod)" }}{EXCHG {PARA 362 "> " 0 "" 
{MPLTEXT 1 0 17 "sum(i,i=1..10^6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"-++]++]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "add(i,i=1..10^
6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"-++]++]" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 2 "  " }{TEXT 307 53 "sum looks for a closed form and \+
then substitutes the " }}{PARA 530 "" 0 "" {TEXT -1 45 " numerical val
ues of the bounds of summations" }}}{EXCHG {PARA 531 "" 0 "" {TEXT -1 
61 "  add performs a loop from the lower bound to the upper bound" }}}
{EXCHG {PARA 363 "> " 0 "" {MPLTEXT 1 0 28 "sum(i^2,i=1..1000000000000
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"E+++++]LLLLL$QLLLLL$" }}}
{EXCHG {PARA 364 "> " 0 "" {MPLTEXT 1 0 14 "sum(i,i=1..n);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"#!\"\",&%\"nG\"\"\"F)F)F%F)*&F%F&F(F
)F&#F)F%F&" }}}{EXCHG {PARA 365 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#!\"\"%\"nG\"\"\",&F'F(F(F
(F(F(" }}}{EXCHG {PARA 366 "> " 0 "" {MPLTEXT 1 0 24 "factor(sum(i^3,i
=1..n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"%!\"\"%\"nG\"\"#,&
F'\"\"\"F*F*F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "factor(
sum(i^3,i=a..b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"%!\"\",(%
\"aG\"\"\"F)F&%\"bGF&F),&F(F)F*F)F),**$)F(\"\"#F)F)F(F&*$)F*F/F)F)F*F)
F)F&" }}}{EXCHG {PARA 367 "> " 0 "" {MPLTEXT 1 0 26 "product(i,i=1..10
);   10!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(+)GO" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"(+)GO" }}}{EXCHG {PARA 368 "" 0 "" {TEXT -1 2 "  \+
" }{TEXT 278 38 "Infinite sums and products are handled" }}}{EXCHG 
{PARA 369 "> " 0 "" {MPLTEXT 1 0 29 "sum('1/i^2','i=1..infinity');" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"'!\"\"%#PiG\"\"#\"\"\"" }}}
{EXCHG {PARA 370 "> " 0 "" {MPLTEXT 1 0 29 "sum('1/k!', 'k'=0..infinit
y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#\"\"\"" }}}{EXCHG 
{PARA 371 "> " 0 "" {MPLTEXT 1 0 37 "product('1-z^2/n^2','n=1..infinit
y');" }}{PARA 6 "" 1 "" {TEXT -1 68 "product:   \"Cannot show that 1-z
^2/n^2 has no zeros on [1,infinity]\"" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#*(%\"zG!\"\"%#PiGF%-%$sinG6#*&F&\"\"\"F$F+F+" }}}{EXCHG {PARA 372 "
" 0 "" {TEXT -1 1 " " }{TEXT 279 50 "Sometimes the results are not imm
ediately readable" }}}{EXCHG {PARA 373 "> " 0 "" {MPLTEXT 1 0 26 "prod
uct('1/i^2','i=1..n');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$*$
)-%&GAMMAG6#,&%\"nGF$F$F$\"\"#F$!\"\"" }}}{EXCHG {PARA 374 "> " 0 "" 
{MPLTEXT 1 0 57 "i:='i':k:='k':\nsum(combinat[binomial](i+k-1,k-1),i=0
..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"nG\"\"\"F&F&F&%\"kG!\"
\"-%)binomialG6$,&F%F&F'F&,&F'F&F&F(F&" }}}{EXCHG {PARA 375 "> " 0 "" 
{MPLTEXT 1 0 40 "sum('(2*z)/(z^2-n^2)','n=1..infinity'); " }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,&-%$PsiG6#,&\"\"\"F(%\"zG!\"\"F(-F%6#,&F)F(F(F
(F*" }}}{EXCHG {PARA 376 "" 0 "" {TEXT -1 1 " " }{TEXT 272 47 "use sin
gle quotes to avoid premature evaluation" }}}{EXCHG {PARA 377 "> " 0 "
" {MPLTEXT 1 0 5 "i:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"#
" }}}{EXCHG {PARA 378 "> " 0 "" {MPLTEXT 1 0 17 "sum(i,i=1..1000);" }}
{PARA 8 "" 1 "" {TEXT -1 99 "Error, (in sum) summation variable previo
usly assigned, second argument evaluates to 2 = 1 .. 1000\n" }}}
{EXCHG {PARA 379 "> " 0 "" {MPLTEXT 1 0 21 "sum('i','i'=1..1000);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"'+0]" }}}{EXCHG {PARA 257 "" 0 "" 
{TEXT -1 43 "in the following sum we access the command " }{TEXT 275 
8 "binomial" }{TEXT -1 9 " from the" }}{PARA 258 "" 0 "" {TEXT -1 8 "p
ackage " }{TEXT 273 9 "combinat " }{TEXT -1 31 "in the long form, avoi
ding the " }{TEXT 274 14 "with(combinat)" }}}{EXCHG {PARA 380 "> " 0 "
" {MPLTEXT 1 0 45 "n:='n'; \nsum(combinat[binomial](n,k),k=0..n);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nGF$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#)\"\"#%\"nG" }}}{EXCHG {PARA 381 "" 0 "" {TEXT -1 1 " " }{TEXT 
276 56 "the sum is actually equal to  (1+1)^n (binomial theorem)" }}}
{EXCHG {PARA 382 "" 0 "" {TEXT -1 2 "  " }{TEXT 277 36 "we can have ne
sted sums and products" }}}{EXCHG {PARA 383 "> " 0 "" {MPLTEXT 1 0 42 
"factor(sum(sum('i*j','i=1..n'),'j=1..n'));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*(\"\"%!\"\"%\"nG\"\"#,&F'\"\"\"F*F*F(F*" }}}{EXCHG 
{PARA 384 "> " 0 "" {MPLTEXT 1 0 23 "i:='i': j:='j': n:='2':" }}}
{EXCHG {PARA 385 "> " 0 "" {MPLTEXT 1 0 46 "sum(sum(n!/(i!*j!*(n-i-j)!
),i=0..n),j=0..n-i);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"$)G\"\"
\",&\"\"&F&*&\"\"(#F&\"\"#^#F&F&F&!\"\",&F(F.F)F&F.F." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalc(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"*" }}}{EXCHG {PARA 386 "" 0 "" {TEXT -1 69 "the sum
 is actually equal to  (1+1+1)^2 = 9, by the trinomial theorem" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 308 46 "now let us try to
 verify  that (1+1+1)^3 = 27:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 23 "i:='i': j:='j': n:='3':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 46 "sum(sum(n!/(i!*j!*(n-i-j)!),i=0..n),j=0..n-i);" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#*.,&*D\"\"#\"\"\",&%\"iGF'F&!\"\"F'F)F*,&F)F'\"\"$F*
F',&\"\"%F*F)F'F',&*&,&*&,&-%*factorialG6#F-F'*&#F'\"\"'F'-F56#,&F'F*F
)F'F'F'F'-F56#F(F'F'*&F4F'F:F'F'F'-F56#F+F'F'*&#F'F&F'*(F=F'F4F'F:F'F'
F'F',&F)F'#\"\"&F&F*F'F<F',(*$)F)F&F'F'*&FCF'F)F'F'\"\")F'F',&F&F'F)F'
F*,&F)F'F'F'F*-F56#,&F.F'F)F*F*F=F*F@F*F4F*F:F*-%*hypergeomG6%7$F&,&F'
F*F)F*7#,$F)F*F*F'F'*4,**(,4*$)F)FLF'F'*$)F)\"\"(F'F**&#\"\"*F.F'*$)F)
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^pF'*&F&F'FJF'F**&#\"#FF.F'F)F'F'#F'F.F'F'FNF'F(F'F)F'F+F'F-F'F/F'F<F'
-%$PsiG6#,&#FGF&F'*&F&F*F)F'F*F'F**6FMF'FepF'FNF'F(F'F)F'F+F'F-F'F/F'F
<F'-F\\q6#,&F&F'*&F&F*F)F'F*F'F'*&#FipF.F'*4FJF'F=F'F@F'F4F'F:F'FMF'FN
F',(FIF'*&F,F'F)F'F*FLF'F'FOF'F'F*F'FMF*FNF*F)!\"#FOF*F=F*F@F*F4F*F:F*
F'F',,FGF**&^#F*F'\"#BFCF'*&F&F'F)F'F**(F)F'F_rFC^#F'F'F'FIF'F*,,FGF**
&F_rFCFbrF'F'*&F&F'F)F'F**(F^rF'F)F'F_rFCF'FIF'F*,&FGF*FdrF'F*,&FGF'Fd
rF'F*,(\"%_6F'*&\"$#>F'F)F'F**&F\\sF'FJF'F'F'" }}}{EXCHG {PARA 533 "" 
0 "" {TEXT -1 41 " (more interesting things happen for n=4)" }}}
{EXCHG {PARA 532 "" 0 "" {TEXT -1 50 " to actually do this sum we brea
k it in two pieces" }}}{EXCHG {PARA 387 "> " 0 "" {MPLTEXT 1 0 23 "i:=
'i': j:='j': n:='3':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sum
(n!/(i!*j!*(n-i-j)!),j=0..n-i);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*
*\"#[\"\"\"-%*factorialG6#%\"iG!\"\"-F(6#,&\"\"$F&F*F+F+)\"\"#F*F+F&" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "sum(%,i=0..n);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"#F" }}}{EXCHG {PARA 534 "" 0 "" {TEXT -1 
54 " now we know how to do the general sum (1+1+1)^n = 3^n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "i:='i': j:='j': n:='n':" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sum(n!/(i!*j!*(n-i-j)!),j=0..n-i);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**-%*factorialG6#%\"nG\"\"\"-F%6#%
\"iG!\"\"-F%6#,&F'F(F+F,F,)\"\"#,&F'F,F+F(F," }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "simplify(sum(%,i=0..n));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#)\"\"$%\"nG" }}}}{SECT 0 {PARA 388 "" 0 "" {TEXT -1 22 
" Conversions (convert)" }}{EXCHG {PARA 389 "> " 0 "" {MPLTEXT 1 0 21 
"convert([1,2,3],set);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"\"\"\"
#\"\"$" }}}{EXCHG {PARA 390 "> " 0 "" {MPLTEXT 1 0 24 "convert(\{1,2,3
,4\},list);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"\"\"\"#\"\"$\"\"%
" }}}{EXCHG {PARA 391 "> " 0 "" {MPLTEXT 1 0 23 "convert([1,1,2,3],set
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"\"\"\"#\"\"$" }}}{EXCHG 
{PARA 392 "> " 0 "" {MPLTEXT 1 0 19 "l:=seq(i^3,i=1..5);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"lG6'\"\"\"\"\")\"#F\"#k\"$D\"" }}}{EXCHG 
{PARA 393 "> " 0 "" {MPLTEXT 1 0 17 "convert([l],`+`);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"$D#" }}}{EXCHG {PARA 394 "> " 0 "" {MPLTEXT 1 0 
17 "convert([l],`*`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(+!G<" }}}
{EXCHG {PARA 395 "> " 0 "" {MPLTEXT 1 0 19 "series(tan(x),x,9);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#+-%\"xG\"\"\"F%#F%\"\"$F'#\"\"#\"#:\"
\"&#\"#<\"$:$\"\"(-%\"OG6#F%\"\"*" }}}{EXCHG {PARA 396 "> " 0 "" 
{MPLTEXT 1 0 5 "w(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"wG6#+-%\"
xG\"\"\"F(#F(\"\"$F*#\"\"#\"#:\"\"&#\"#<\"$:$\"\"(-%\"OG6#F(\"\"*" }}}
{EXCHG {PARA 397 "> " 0 "" {MPLTEXT 1 0 20 "convert(%%,polynom);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,*%\"xG\"\"\"*&#F%\"\"$F%*$)F$F(F%F%F%
*&#\"\"#\"#:F%*$)F$\"\"&F%F%F%*&#\"#<\"$:$F%*$)F$\"\"(F%F%F%" }}}
{EXCHG {PARA 398 "> " 0 "" {MPLTEXT 1 0 5 "w(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%\"wG6#,*%\"xG\"\"\"*&#F(\"\"$F(*$)F'F+F(F(F(*&#\"\"#
\"#:F(*$)F'\"\"&F(F(F(*&#\"#<\"$:$F(*$)F'\"\"(F(F(F(" }}}{EXCHG {PARA 
399 "> " 0 "" {MPLTEXT 1 0 19 "convert(16341,hex);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%%3FD5G" }}}{EXCHG {PARA 400 "> " 0 "" {MPLTEXT 1 0 
22 "convert(16341,binary);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"/,,,66
66" }}}{EXCHG {PARA 401 "> " 0 "" {MPLTEXT 1 0 21 "convert(16341,octal
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&Dx$" }}}{EXCHG {PARA 402 "" 
0 "" {TEXT -1 1 " " }{TEXT 270 48 "For more general bases, use the fol
lowing syntax" }}}{EXCHG {PARA 403 "> " 0 "" {MPLTEXT 1 0 19 "convert(
13,base,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"\"\"\"#" }}}
{EXCHG {PARA 404 "> " 0 "" {MPLTEXT 1 0 20 "convert(15,base,15);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"!\"\"\"" }}}{EXCHG {PARA 405 "" 
0 "" {TEXT -1 1 " " }{TEXT 271 53 "Partial fraction decomposition of a
 rational function" }}}{EXCHG {PARA 406 "> " 0 "" {MPLTEXT 1 0 32 "r:=
(3*x+1)/(x^2-4*x+4);    w(r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"r
G*&,&*&\"\"$\"\"\"%\"xGF)F)F)F)F),(*$)F*\"\"#F)F)*&\"\"%F)F*F)!\"\"F0F
)F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"wG6#*&,&*&\"\"$\"\"\"%\"xGF
*F*F*F*F*,(*$)F+\"\"#F*F**&\"\"%F*F+F*!\"\"F1F*F2" }}}{EXCHG {PARA 
407 "> " 0 "" {MPLTEXT 1 0 21 "convert(r,parfrac,x);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,&*&\"\"(\"\"\",&%\"xGF&\"\"#!\"\"!\"#F&*&\"\"$F&F'F
*F&" }}}}{SECT 0 {PARA 409 "" 0 "" {TEXT -1 34 " Iterative constructs \+
(for, while)" }}{EXCHG {PARA 410 "> " 0 "" {MPLTEXT 1 0 29 "for i from
 1 to 4 do i^2; od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}}{EXCHG {PARA 411 
"> " 0 "" {MPLTEXT 1 0 6 "l:=[];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"lG7\"" }}}{EXCHG {PARA 412 "> " 0 "" {MPLTEXT 1 0 40 "for i from 1 t
o 4 do l:=[op(l),i^2]; od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG7#
\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG7$\"\"\"\"\"%" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG7%\"\"\"\"\"%\"\"*" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"lG7&\"\"\"\"\"%\"\"*\"#;" }}}{EXCHG {PARA 
413 "> " 0 "" {MPLTEXT 1 0 5 "i:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"iG\"\"\"" }}}{EXCHG {PARA 414 "> " 0 "" {MPLTEXT 1 0 28 "while i+
2 < 6 do i:=i+1: od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"#" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"iG\"\"%" }}}}{SECT 0 {PARA 416 "" 0 "" {TEXT -1 10 
" Functions" }}{EXCHG {PARA 417 "> " 0 "" {MPLTEXT 1 0 10 "f:=x->x+1;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&a
rrowGF(,&9$\"\"\"F.F.F(F(F(" }}}{EXCHG {PARA 418 "> " 0 "" {MPLTEXT 1 
0 5 "f(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 
419 "> " 0 "" {MPLTEXT 1 0 44 "type(f,'function');\ntype(cos(x),'funct
ion');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 420 "> " 0 "" {MPLTEXT 1 0 
12 "whattype(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'symbolG" }}}
{EXCHG {PARA 421 "" 0 "" {TEXT -1 3 "   " }{TEXT 286 14 "The operators
 " }{TEXT 287 1 "@" }{TEXT 288 5 " and " }{TEXT 289 2 "@@" }{TEXT 290 
30 " are used to compose functions" }}}{EXCHG {PARA 422 "> " 0 "" 
{MPLTEXT 1 0 9 "(f@f)(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}
}{EXCHG {PARA 423 "> " 0 "" {MPLTEXT 1 0 10 "(f@@5)(2);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 424 "> " 0 "" {MPLTEXT 1 
0 10 "g:=y->y+2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"yG6\"
6$%)operatorG%&arrowGF(,&9$\"\"\"\"\"#F.F(F(F(" }}}{EXCHG {PARA 425 ">
 " 0 "" {MPLTEXT 1 0 9 "(f@g)(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
&%\"xG\"\"\"\"\"$F%" }}}{EXCHG {PARA 426 "> " 0 "" {MPLTEXT 1 0 14 "((
f@g)@@3)(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"\"\"\"*F%" 
}}}{EXCHG {PARA 427 "> " 0 "" {MPLTEXT 1 0 24 "h:=(x,y,z)->x^2+y^2-z^2
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGf*6%%\"xG%\"yG%\"zG6\"6$%)o
peratorG%&arrowGF*,(*$)9$\"\"#\"\"\"F3*$)9%F2F3F3*$)9&F2F3!\"\"F*F*F*
" }}}{EXCHG {PARA 428 "> " 0 "" {MPLTEXT 1 0 9 "h(3,4,5);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 429 "" 0 "" {TEXT -1 1 "
 " }{TEXT 291 42 "Recursive functions (factorial, Fibonacci)" }}}
{EXCHG {PARA 430 "> " 0 "" {MPLTEXT 1 0 44 "fact:=n->if n = 0 then 1; \+
else n*f(n-1); fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%factGf*6#%\"n
G6\"6$%)operatorG%&arrowGF(@%/9$\"\"!\"\"\"*&F.F0-%\"fG6#,&F.F0F0!\"\"
F0F(F(F(" }}}{EXCHG {PARA 431 "> " 0 "" {MPLTEXT 1 0 17 "fact(3); fact
(7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#\\" }}}{EXCHG {PARA 432 "> " 0 "" {MPLTEXT 1 0 83 "f
ibo:=n->if n = 0 then 0 \n    elif n = 1 then 1 \n    else fibo(n-1)+f
ibo(n-2); \nfi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%fiboGf*6#%\"nG6
\"6$%)operatorG%&arrowGF(@'/9$\"\"!F//F.\"\"\"F1,&-F$6#,&F.F1F1!\"\"F1
-F$6#,&F.F1\"\"#F6F1F(F(F(" }}}{EXCHG {PARA 433 "> " 0 "" {MPLTEXT 1 
0 21 "seq(fibo(i),i=0..12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6/\"\"!\"
\"\"F$\"\"#\"\"$\"\"&\"\")\"#8\"#@\"#M\"#b\"#*)\"$W\"" }}}{EXCHG 
{PARA 434 "> " 0 "" {MPLTEXT 1 0 45 "phi := (1+sqrt(5))/2;  \nPhi := (
1-sqrt(5))/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phiG,&#\"\"\"\"\"#
F'*&F(!\"\"\"\"&F&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PhiG,&#\"\"
\"\"\"#F'*&F(!\"\"\"\"&F&F*" }}}{EXCHG {PARA 435 "> " 0 "" {MPLTEXT 1 
0 34 "fibo1:=n->(phi^n-Phi^n)/(sqrt(5));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&fibo1Gf*6#%\"nG6\"6$%)operatorG%&arrowGF(*&,&)%$phiG9$\"\"\")
%$PhiGF0!\"\"F1-%%sqrtG6#\"\"&F4F(F(F(" }}}{EXCHG {PARA 436 "> " 0 "" 
{MPLTEXT 1 0 11 "fibo1(100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"
\"&!\"\",&*$),&#\"\"\"\"\"#F,*&F-F&F%F+F,\"$+\"F,F,*$),&F+F,*&F-F&F%F+
F&F/F,F&F,F%F+F," }}}{EXCHG {PARA 437 "> " 0 "" {MPLTEXT 1 0 10 "expan
d(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"6v]\">Ez\"[[Aa$" }}}{EXCHG 
{PARA 438 "> " 0 "" {MPLTEXT 1 0 38 "seq(fibo(i)-expand(fibo1(i)),i=1.
.10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"!F#F#F#F#F#F#F#F#F#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "time(fibo(25));" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#$\"%qU!\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "time(expand(fibo1(500)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"%5\\!\"$" }}}}{SECT 0 {PARA 439 "" 0 "" {TEXT -1 11 
" Procedures" }}{EXCHG {PARA 440 "> " 0 "" {MPLTEXT 1 0 20 "f:=proc(x)
 x^2; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"F(F(*$
)9$\"\"#\"\"\"F(F(F(" }}}{EXCHG {PARA 441 "> " 0 "" {MPLTEXT 1 0 5 "f(
3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}}{EXCHG {PARA 442 "> \+
" 0 "" {MPLTEXT 1 0 89 "ff:=proc(n,g) \n   local aux,i;\n      aux:=[s
eq(i^2,i=1..n)]; \n      map(g,aux);\nend proc;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#ffGf*6$%\"nG%\"gG6$%$auxG%\"iG6\"F,C$>8$7#-%$seqG6$*
$)8%\"\"#\"\"\"/F6;F89$-%$mapG6$9%F/F,F,F," }}}{EXCHG {PARA 443 "> " 
0 "" {MPLTEXT 1 0 8 "ff(3,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"
\"\"\"#;\"#\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 294 
46 "The option remember updates the remember table" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 103 "fib := proc(n) option remember;\n    if n<
2 then n \n           else fib(n-1)+fib(n-2) end if; \nend proc;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$fibGf*6#%\"nG6\"6#%)rememberGF(@%29
$\"\"#F-,&-F$6#,&F-\"\"\"F3!\"\"F3-F$6#,&F-F3F.F4F3F(F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "st:=time():\nfib(100);\ntime()-st;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"6v]\">Ez\"[[Aa$" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"\"!F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " \+
" }{TEXT 295 28 "Accessing the remember table" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 16 "op(4,eval(fib));" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#-%&TABLEG6#7aq/\"#g\".?fv3![:/\"\"!F+/\"#h\".h>yIZ]#/\"\"\"F0/\"
#i\".\")y`RF0%/\"\"#F0/\"#j\".U)>.Zdl/\"\"$F5/\"\"%F:/\"#k\"/Bx&)4-h5/
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G@qb%\\%/\"#o\"/T\"[-YBF(/FG\"#@/\"#p\"0%*4YI!pw6/\"\"*\"#M/\"#q\"0N\"
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/\"#()\"3eAhQwj\"*)z'/\"#F\"'=k>/\"#G\"'6yJ/\"#))\"4J>5m$yx3+6/\"#H\"'
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#\"*\"44.`v.hY+m%/\"##*\"4HkMYZ!Q6Sv/\"#K\"(4$y@/\"#$*\"5Qn(=7:/;+A\"/
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[V6i$)/\"#Q\")p\")3R/\"#)*\"6\\gu1ZM_=IN\"/\"#R\")')fCj/\"#**\"6E!p^bM
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{MPLTEXT 1 0 16 "op(4,eval(cos));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%&TABLEG6#7-/\"\"!\"\"\"/,$*&\"\"'!\"\"%#PiGF)F),$*&\"\"#F.\"\"$#F)F2F
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&\"#7!\"\"%#PiG\"\"\"F,,&*&\"\"%F*\"\"'#F,\"\"#F,*&F/F*F2F1F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "op(4,eval(cos));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7./\"\"!\"\"\"/,$*&\"\"'!\"\"%#Pi
GF)F),$*&\"\"#F.\"\"$#F)F2F)/,$%\"xGF.-%$cosG6#F7/,$*&F2F.F/F)F)F(/F/F
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oshG6#F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "cos(Pi/12);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"%!\"\"\"\"'#\"\"\"\"\"#F)*&F%F
&F*F(F)" }}}}{SECT 0 {PARA 445 "" 0 "" {TEXT -1 18 " Matrices (linalg)
" }}{EXCHG {PARA 446 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
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20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRde
compG%*WronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%(augmentG%
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%*fibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG%(geneqns
G%*genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG%+htransp
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*issimilarG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacianG%*leastsq
rsG%)linsolveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%)
multiplyG%%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG%&pivotG%
*potentialG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG%'rowdimG%
)rowspaceG%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smithG%,stackm
atrixG%*submatrixG%*subvectorG%)sumbasisG%(swapcolG%(swaprowG%*sylvest
erG%)toeplitzG%&traceG%*transposeG%,vandermondeG%*vecpotentG%(vectdimG
%'vectorG%*wronskianG" }}}{EXCHG {PARA 448 "> " 0 "" {MPLTEXT 1 0 37 "
m:=matrix([[1,2,3],[2,3,1],[3,2,1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"mG-%'matrixG6#7%7%\"\"\"\"\"#\"\"$7%F+F,F*7%F,F+F*" }}}{EXCHG 
{PARA 450 "> " 0 "" {MPLTEXT 1 0 7 "det(m);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#!#7" }}}{EXCHG {PARA 452 "> " 0 "" {MPLTEXT 1 0 15 "im:
=inverse(m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#imG-%'matrixG6#7%7%
#!\"\"\"#7#F+\"\"$#\"\"(F,7%F*#\"\"#F.#!\"&F,7%#\"\"&F,F-#\"\"\"F," }}
}{EXCHG {PARA 454 "> " 0 "" {MPLTEXT 1 0 18 "id3:=evalm(m&*im);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$id3G-%'matrixG6#7%7%\"\"\"\"\"!F+7%
F+F*F+7%F+F+F*" }}}{EXCHG {PARA 456 "> " 0 "" {MPLTEXT 1 0 15 "eigenva
lues(m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"!\"#\"\"'" }}}
{EXCHG {PARA 458 "> " 0 "" {MPLTEXT 1 0 15 "map(evalf,[%]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7%$\"\"\"\"\"!$!\"#F&$\"\"'F&" }}}{EXCHG 
{PARA 460 "> " 0 "" {MPLTEXT 1 0 19 "charpoly(m,lambda);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,**$)%'lambdaG\"\"$\"\"\"F(*&\"\"&F()F&\"\"#F(!
\"\"*&\"\")F(F&F(F-\"#7F(" }}}{EXCHG {PARA 462 "> " 0 "" {MPLTEXT 1 0 
23 "eig:=[eigenvectors(m)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eigG
7%7%\"\"\"F'<#-%'vectorG6#7%F'#!\"$\"\"#F'7%\"\"'F'<#-F*6#7%F'F'F'7%!
\"#F'<#-F*6#7%#!#8\"#6#\"\"$F>F'" }}}{EXCHG {PARA 464 "> " 0 "" 
{MPLTEXT 1 0 15 "eiv:=eig[2][1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
$eivG\"\"'" }}}{EXCHG {PARA 466 "> " 0 "" {MPLTEXT 1 0 21 "eigm2:=op(e
ig[2][3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&eigm2G-%'vectorG6#7%
\"\"\"F)F)" }}}{EXCHG {PARA 468 "> " 0 "" {MPLTEXT 1 0 26 "evalm((m-ei
v*id3)&*eigm2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"\"!
F'F'" }}}{EXCHG {PARA 470 "> " 0 "" {MPLTEXT 1 0 13 "nullspace(m);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 472 "" 0 "" 
{TEXT -1 1 " " }{TEXT 256 20 "Gaussian Elimination" }}}{EXCHG {PARA 
473 "> " 0 "" {MPLTEXT 1 0 44 "m:=matrix([[1,2,3,-2],[2,3,1,4],[3,2,1,
7]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG-%'matrixG6#7%7&\"\"\"
\"\"#\"\"$!\"#7&F+F,F*\"\"%7&F,F+F*\"\"(" }}}{EXCHG {PARA 475 "> " 0 "
" {MPLTEXT 1 0 35 "m:=addrow(addrow(m,1,2,-2),1,3,-3);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"mG-%'matrixG6#7%7&\"\"\"\"\"#\"\"$!\"#7&\"\"!!
\"\"!\"&\"\")7&F/!\"%!\")\"#8" }}}{EXCHG {PARA 477 "> " 0 "" {MPLTEXT 
1 0 20 "m:=addrow(m,2,3,-4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG
-%'matrixG6#7%7&\"\"\"\"\"#\"\"$!\"#7&\"\"!!\"\"!\"&\"\")7&F/F/\"#7!#>
" }}}{EXCHG {PARA 479 "> " 0 "" {MPLTEXT 1 0 23 "submatrix(m,1..2,1..3
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%\"\"\"\"\"#\"\"$
7%\"\"!!\"\"!\"&" }}}{EXCHG {PARA 481 "> " 0 "" {MPLTEXT 1 0 13 "minor
(m,1,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%\"\"!!\"&
\"\")7%F(\"#7!#>" }}}}{SECT 0 {PARA 484 "" 0 "" {TEXT -1 25 " Matrices
 (LinearAlgebra)" }}{EXCHG {PARA 485 "> " 0 "" {MPLTEXT 1 0 20 "with(L
inearAlgebra);" }}{PARA 7 "" 1 "" {TEXT -1 64 "Warning, the assigned n
ame GramSchmidt now has a global binding\n" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7[r%$AddG%(AdjointG%3BackwardSubstituteG%+BandMatrixG%&
BasisG%-BezoutMatrixG%/BidiagonalFormG%-BilinearFormG%5CharacteristicM
atrixG%9CharacteristicPolynomialG%'ColumnG%0ColumnDimensionG%0ColumnOp
erationG%,ColumnSpaceG%0CompanionMatrixG%0ConditionNumberG%/ConstantMa
trixG%/ConstantVectorG%2CreatePermutationG%-CrossProductG%-DeleteColum
nG%*DeleteRowG%,DeterminantG%/DiagonalMatrixG%*DimensionG%+DimensionsG
%+DotProductG%6EigenConditionNumbersG%,EigenvaluesG%-EigenvectorsG%&Eq
ualG%2ForwardSubstituteG%.FrobeniusFormG%4GaussianEliminationG%2Genera
teEquationsG%/GenerateMatrixG%2GetResultDataTypeG%/GetResultShapeG%5Gi
vensRotationMatrixG%,GramSchmidtG%-HankelMatrixG%,HermiteFormG%3Hermit
ianTransposeG%/HessenbergFormG%.HilbertMatrixG%2HouseholderMatrixG%/Id
entityMatrixG%2IntersectionBasisG%+IsDefiniteG%-IsOrthogonalG%*IsSimil
arG%*IsUnitaryG%2JordanBlockMatrixG%+JordanFormG%(LA_MainG%0LUDecompos
itionG%-LeastSquaresG%,LinearSolveG%$MapG%%Map2G%*MatrixAddG%.MatrixIn
verseG%5MatrixMatrixMultiplyG%+MatrixNormG%5MatrixScalarMultiplyG%5Mat
rixVectorMultiplyG%2MinimalPolynomialG%&MinorG%(ModularG%)MultiplyG%,N
oUserValueG%%NormG%*NormalizeG%*NullSpaceG%3OuterProductMatrixG%*Perma
nentG%&PivotG%*PopovFormG%0QRDecompositionG%-RandomMatrixG%-RandomVect
orG%%RankG%6ReducedRowEchelonFormG%$RowG%-RowDimensionG%-RowOperationG
%)RowSpaceG%-ScalarMatrixG%/ScalarMultiplyG%-ScalarVectorG%*SchurFormG
%/SingularValuesG%*SmithFormG%*SubMatrixG%*SubVectorG%)SumBasisG%0Sylv
esterMatrixG%/ToeplitzMatrixG%&TraceG%*TransposeG%0TridiagonalFormG%+U
nitVectorG%2VandermondeMatrixG%*VectorAddG%,VectorAngleG%5VectorMatrix
MultiplyG%+VectorNormG%5VectorScalarMultiplyG%+ZeroMatrixG%+ZeroVector
G%$ZipG" }}}{EXCHG {PARA 486 "> " 0 "" {MPLTEXT 1 0 43 "M:=Matrix(3,[[
1,2,3],[-1,-3,-5],[-5,7,9]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"M
G-%'RTABLEG6%\"*w<!\\:-%'MATRIXG6#7%7%\"\"\"\"\"#\"\"$7%!\"\"!\"$!\"&7
%F4\"\"(\"\"*%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "s
ort(CharacteristicPolynomial(M,lambda));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,**$)%'lambdaG\"\"$\"\"\"F(*&\"\"(F()F&\"\"#F(!\"\"*&\"#JF(F&F(F
(\"#5F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Eigenvalues(M);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*SC*e8-%'MATRIXG6#7%
7#,(*&\"\"'!\"\",&\"%))R\"\"\"*&\"#7F2\"'0$[\"#F2\"\"#F2#F2\"\"$F/*(\"
#))F2F9F/F0#F/F9F2#\"\"(F9F27#,**&F4F/F0F8F2*(\"#WF2F9F/F0F<F/F=F2*(^#
F6F2F9F6,&*&F.F/F0F8F/*(F;F2F9F/F0F<F/F2F27#,**&F4F/F0F8F2*(FCF2F9F/F0
F<F/F=F2*(^##F/F7F2F9F6FFF2F2&%'VectorG6#%'columnG" }}}{EXCHG {PARA 
487 "> " 0 "" {MPLTEXT 1 0 21 "f:= (i,j) -> x^i+y^j;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"fGf*6$%\"iG%\"jG6\"6$%)operatorG%&arrowGF),&)%\"
xG9$\"\"\")%\"yG9%F1F)F)F)" }}}{EXCHG {PARA 488 "> " 0 "" {MPLTEXT 1 
0 12 "Matrix(3,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*W
%)=O\"-%'MATRIXG6#7%7%,&%\"xG\"\"\"%\"yGF.,&F-F.*$)F/\"\"#F.F.,&F-F.*$
)F/\"\"$F.F.7%,&*$)F-F3F.F.F/F.,&F:F.F1F.,&F:F.F5F.7%,&*$)F-F7F.F.F/F.
,&F@F.F1F.,&F@F.F5F.%'MatrixG" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 
" " }{TEXT 293 40 "Differentiation, Integration (diff, int)" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "diff(x^n,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*()
%\"xG%\"nG\"\"\"F&F'F%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "diff(1/sqrt(x+1),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"\"
F%*&\"\"#F%),&%\"xGF%F%F%#\"\"$F'F%!\"\"F-" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "diff(x^x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)
%\"xGF%\"\"\",&-%#lnG6#F%F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "diff(exp(x*ln(x)),x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*&,&-%#lnG6#%\"xG\"\"\"F)F)F)-%$expG6#*&F(F)F%F)F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "int(x^n,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&)%\"xG,&%\"nG\"\"\"F(F(F(F&!\"\"" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 16 "int(sin(x)^5,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&#\"\"\"\"\"&F&*&)-%$sinG6#%\"xG\"\"%F&-%$cosGF,F&F&
!\"\"*&#F.\"#:F&*&)F*\"\"#F&F/F&F&F1*&#\"\")F4F&F/F&F1" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(exp(-x^2),x);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,$*&#\"\"\"\"\"#F&*&%#PiGF%-%$erfG6#%\"xGF&F&F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "int(sqrt(1-x^2),x=-1..1);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#!\"\"%#PiG\"\"\"F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int(1/(1+x^3),x=0..infinity)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"#\"\"\"\"\"*!\"\"%#PiGF&
\"\"$#F&F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int(1/(1+x^
6),x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"$!\"\"%#
PiG\"\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int(1/(1+x^7
),x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"(F
&-%%BetaG6$F%#\"\"'F'F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
29 "int(1/(1+x^n),x=0..infinity);" }}{PARA 6 "" 1 "" {TEXT -1 68 "Defi
nite integration: Can't determine if the integral is convergent." }}
{PARA 6 "" 1 "" {TEXT -1 30 "Need to know the sign of --> n" }}{PARA 
6 "" 1 "" {TEXT -1 57 "Will now try indefinite integration and then ta
ke limits." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"nG!\"\"%#PiG\"\"\"-
%$cscG6#*&F&F'F$F%F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "int
(cos(x)/(1+x^2),x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*
&#\"\"\"\"\"#F&*&%#PiGF&-%%sinhG6#F&F&F&!\"\"*&#F&F'F&*&-%%coshGF,F&F)
F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "convert(%,exp);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"\"\"\"#F&*&%#PiGF&,&*&#F&F'
F&-%$expG6#F&F&F&*&#F&F'F&*&F&F&F-!\"\"F&F3F&F&F3*&F,F&*&,&*&F,F&F-F&F
&*&F,F&F2F&F&F&F)F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "
simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"#F&*&%#
PiGF&-%$expG6#!\"\"F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "int(log(x)/(1+x)^3,x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6##!\"\"\"\"#" }}}}{SECT 0 {PARA 490 "" 0 "" {TEXT -1 26 " Number \+
Theory (numtheory)" }}{EXCHG {PARA 491 "> " 0 "" {MPLTEXT 1 0 16 "with
(numtheory);" }}{PARA 7 "" 1 "" {TEXT -1 69 "Warning, the protected na
me order has been redefined and unprotected\n" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7Q%&GIgcdG%)bigomegaG%&cfracG%)cfracpolG%+cyclotomicG%)
divisorsG%)factorEQG%*factorsetG%'fermatG%)imagunitG%&indexG%/integral
_basisG%)invcfracG%'invphiG%*issqrfreeG%'jacobiG%*kroneckerG%'lambdaG%
)legendreG%)mcombineG%)mersenneG%(migcdexG%*minkowskiG%(mipolysG%%mlog
G%'mobiusG%&mrootG%&msqrtG%)nearestpG%*nthconverG%)nthdenomG%)nthnumer
G%'nthpowG%&orderG%)pdexpandG%$phiG%#piG%*pprimrootG%)primrootG%(quadr
esG%+rootsunityG%*safeprimeG%&sigmaG%*sq2factorG%(sum2sqrG%$tauG%%thue
G" }}}{EXCHG {PARA 492 "> " 0 "" {MPLTEXT 1 0 19 "ifactor(2^(2^6)+1);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%!G6#\"/@2J@/Gn\"\"\"-F%6#\"'xT
FF(" }}}{EXCHG {PARA 493 "> " 0 "" {MPLTEXT 1 0 17 "divisors(111111);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<B\"\"\"\"\"$\"\"(\"#6\"#8\"#@\"#L
\"#P\"#R\"#x\"#\"*\"$6\"\"$V\"\"$J#\"$f#\"$t#\"$2%\"$H%\"$\"[\"$x(\"%,
5\"%@7\"%V9\"%\\G\"%.I\"%nL\"%\"H&\"%Z&)\"&,,\"\"&te\"\"&Pq$\"'666" }}
}{EXCHG {PARA 494 "> " 0 "" {MPLTEXT 1 0 11 "n:=2352356;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"nG\"(cBN#" }}}{EXCHG {PARA 495 "> " 0 "" 
{MPLTEXT 1 0 7 "phi(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(S'p6" }}
}{EXCHG {PARA 496 "> " 0 "" {MPLTEXT 1 0 31 "pr:=convert(factorset(n),
list);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#prG7%\"\"#\"$\">\"%zI" }}
}{EXCHG {PARA 497 "> " 0 "" {MPLTEXT 1 0 41 "n*product('(1-1/pr[i])','
i'=1..nops(pr));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(S'p6" }}}
{EXCHG {PARA 498 "> " 0 "" {MPLTEXT 1 0 16 "cyclotomic(3,x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(F&F(F(F(" }}}{EXCHG 
{PARA 499 "> " 0 "" {MPLTEXT 1 0 16 "cyclotomic(6,x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"F(F&!\"\"F(F(" }}}{EXCHG 
{PARA 500 "> " 0 "" {MPLTEXT 1 0 16 "cyclotomic(7,x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,0*$)%\"xG\"\"'\"\"\"F(*$)F&\"\"&F(F(*$)F&\"\"%F(F
(*$)F&\"\"$F(F(*$)F&\"\"#F(F(F&F(F(F(" }}}{EXCHG {PARA 501 "> " 0 "" 
{MPLTEXT 1 0 16 "cyclotomic(8,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
&*$)%\"xG\"\"%\"\"\"F(F(F(" }}}{EXCHG {PARA 502 "> " 0 "" {MPLTEXT 1 
0 18 "cyclotomic(100,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"xG
\"#S\"\"\"F(*$)F&\"#IF(!\"\"*$)F&\"#?F(F(*$)F&\"#5F(F,F(F(" }}}{EXCHG 
{PARA 503 "> " 0 "" {MPLTEXT 1 0 105 "for n from 1 to 500 do \n   if \+
\{coeffs(cyclotomic(n,x))\} minus \{1,-1\} <> \{\} \n      then lprint
(n); fi;\nod;" }}{PARA 6 "" 1 "" {TEXT -1 3 "105" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "165" }}{PARA 6 "" 1 "" {TEXT -1 3 "195" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "210" }}{PARA 6 "" 1 "" {TEXT -1 3 "255" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "273" }}{PARA 6 "" 1 "" {TEXT -1 3 "285" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "315" }}{PARA 6 "" 1 "" {TEXT -1 3 "330" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "345" }}{PARA 6 "" 1 "" {TEXT -1 3 "357" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "385" }}{PARA 6 "" 1 "" {TEXT -1 3 "390" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "420" }}{PARA 6 "" 1 "" {TEXT -1 3 "429" }}{PARA 6 "" 1 "" 
{TEXT -1 3 "455" }}{PARA 6 "" 1 "" {TEXT -1 3 "495" }}}{EXCHG {PARA 
504 "> " 0 "" {MPLTEXT 1 0 102 "s:=\{\};\nst:=time():\nfor n from 1 to
 2000 do \n   s:=s union \{coeffs(cyclotomic(n,x))\}: od:\ntime()-st;
\ns;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG<\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"&h,%!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<+!\"%!
\"$!\"#!\"\"\"\"\"\"\"#\"\"$\"\"%\"\"&" }}}{EXCHG {PARA 505 "" 0 "" 
{TEXT -1 1 " " }{TEXT 292 50 "Count the number of primes less than a g
iven limit" }}}{EXCHG {PARA 506 "> " 0 "" {MPLTEXT 1 0 8 "pi(100);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}}}{SECT 0 {PARA 507 "" 0 "" 
{TEXT -1 11 " resultants" }}{EXCHG {PARA 508 "> " 0 "" {MPLTEXT 1 0 
13 "p:=x^6+y^2-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,(*$)%\"xG
\"\"'\"\"\"F**$)%\"yG\"\"#F*F*F*!\"\"" }}}{EXCHG {PARA 509 "> " 0 "" 
{MPLTEXT 1 0 13 "q:=x^3+y^3-5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
qG,(*$)%\"xG\"\"$\"\"\"F**$)%\"yGF)F*F*\"\"&!\"\"" }}}{EXCHG {PARA 
510 "> " 0 "" {MPLTEXT 1 0 25 "factor(resultant(p,q,x));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#*$),*\"#C\"\"\"*$)%\"yG\"\"#F'F'*&\"#5F')F*\"\"$
F'!\"\"*$)F*\"\"'F'F'F/F'" }}}{EXCHG {PARA 511 "> " 0 "" {MPLTEXT 1 0 
19 "solve(\{p,q\},\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"y
G-%'RootOfG6#,*\"#C\"\"\"*$)%#_ZG\"\"#F+F+*&\"#5F+)F.\"\"$F+!\"\"*$)F.
\"\"'F+F+/%\"xG-F'6#,(*$F2F+F+\"\"&F4*$)F&F3F+F+" }}}{EXCHG {PARA 512 
"> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 
50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG 
{PARA 513 "> " 0 "" {MPLTEXT 1 0 22 "p:=x^2+y^2-1;q:=x-y-1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"pG,(*$)%\"xG\"\"#\"\"\"F**$)%\"yGF)F*F*F
*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,(%\"xG\"\"\"%\"yG!\"
\"F'F)" }}}{EXCHG {PARA 514 "> " 0 "" {MPLTEXT 1 0 35 "a:=implicitplot
(p,x=-1..1,y=-1..1):" }}}{EXCHG {PARA 515 "> " 0 "" {MPLTEXT 1 0 47 "b
:=implicitplot(q,x=-2..2,y=-2..1,color=green):" }}}{EXCHG {PARA 516 ">
 " 0 "" {MPLTEXT 1 0 15 "display(\{a,b\});" }}{PARA 13 "" 1 "" 
{GLPLOT2D 327 245 245 {PLOTDATA 2 "6%-%'CURVESG6cu7$7$$!3S+++++++#*!#=
$!3/**************QF*7$$!3&))**********\\K*F*$!33-++++++OF*7$F-7$$!3i)
*********\\(Q*F*$!3J.++++]7MF*7$7$$!3Anmmmmm\"f*F*$!3#>++++++!GF*F37$7
$$!37mmmmmm\"f*F*F<7$$!3*4AAAAAAs*F*$!3B!yxxxxxF#F*7$7$$!3Immmmmm\"z*F
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++++++D**F*$!3i,++++++7F*FN7$FT7$$!3I!444444***F*$!3+6\"444444%!#>7$7$
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