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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "# Maple Annoyances -
- VSU Talk -- SFB 25 Feb 00" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
128 "# Quote from computer designer Danny Hills \"What people mean by \+
the word _technology_ is the stuff that doesn't really work yet\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "# 1. Which symbol" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "L:=[Pi,pi,e^2,exp(2)];evalf(
L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7&%#PiG%#piG*$%\"eG\"\"#-
%$expG6#F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$\"+aEfTJ!\"*%#piG*$%
\"eG\"\"#$\"+*4c!*Q(F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "#
 2. Which order?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=2;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"#" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 4 "a+a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#7S%(animateG%*animate3dG%-changecoordsG%,complex
plotG%.complexplot3dG%*conformalG%,contourplotG%.contourplot3dG%*coord
plotG%,coordplot3dG%-cylinderplotG%,densityplotG%(displayG%*display3dG
%*fieldplotG%,fieldplot3dG%)gradplotG%+gradplot3dG%-implicitplotG%/imp
licitplot3dG%(inequalG%-listcontplotG%/listcontplot3dG%0listdensityplo
tG%)listplotG%+listplot3dG%+loglogplotG%(logplotG%+matrixplotG%(odeplo
tG%'paretoG%*pointplotG%,pointplot3dG%*polarplotG%,polygonplotG%.polyg
onplot3dG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG%+setoptio
nsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+sphereplotG%)surfd
ataG%)textplotG%+textplot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "fieldplot([sin(x),cos(x)],x=0..2*Pi,y=0..2*Pi);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*fieldplotG6%7$-%$sinG6#%\"xG-%$cosG
F)/F*;\"\"!,$%#PiG\"\"#/%\"yGF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "# 3. Mixing assignment and subs" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "restart:F:=a*x^2+b*x+c;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"FG,(*&%\"aG\"\"\"%\"xG\"\"#F(*&%\"bGF(F)F(F(%\"cGF(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(x=3,F);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,(%\"aG\"\"*%\"bG\"\"$%\"cG\"\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x:=5:F;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(%\"aG\"#D%\"bG\"\"&%\"cG\"\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "subs(x=3,F);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,(%\"aG\"#D%\"bG\"\"$%\"cG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "# What happened?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "subs(5=3,F);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"
aG\"#D%\"bG\"\"$%\"cG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
69 "# 4. Confusing usual function notation with Maple function definit
ion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "restart:f(x):=x^2;g:
=x->x^2;h:=proc(x) x^2; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"f
G6#%\"xG*$F'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6#%\"xG6\"
6$%)operatorG%&arrowGF(*$9$\"\"#F(F(6\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"hGR6#%\"xG6\"F(F(*$9$\"\"#F(F(6\"" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 51 "f(x);f(1);f(t);evalf(f(10));#Clearly not a functio
n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"fG6#%\"xG" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%\"fG6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
\"fG6#%\"tG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"fG6#\"#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "g(x);g(1);g(t);evalf(g(10));
#Function examples" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$%\"xG\"\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*$%\"tG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$+\"\"\"!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "h(x);h(1);h(t);evalf(h(10))
;#Function examples" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$%\"xG\"\"#" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*$%\"tG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$+\"\"\"!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "# but plot works!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot(f(x),x=-2..2,title=`I s
hould not work`);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6$7S7$$!\"
#\"\"!$\"\"%F*7$$!1LLL$Q6G\">!#:$\"1!e4#)QZ)eOF07$$!1nm;M!\\p$=F0$\"1
\\e7a<QuLF07$$!1LLL))Qj^<F0$\"1_xvy7AoIF07$$!1LLL=Kvl;F0$\"1dyQ%yLZx#F
07$$!1nm;C2G!e\"F0$\"1DF<nrG(\\#F07$$!1LL$3yO5]\"F0$\"1'\\9uT6JD#F07$$
!1++]nU)*=9F0$\"17DT^j^8?F07$$!1LL$3WDTL\"F0$\"1O(y=p!*)z<F07$$!1++]d(
Q&\\7F0$\"1WY\\1rMh:F07$$!1nmmc4`i6F0$\"1:$3_Ay9N\"F07$$!1LLLQW*e3\"F0
$\"1lK?Jn;z6F07$$!1,+++()>'***!#;$\"1r\"))\\%))R#***Fbo7$$!1++++0\"*H
\"*Fbo$\"1D5!QdEbL)Fbo7$$!1++++83&H)Fbo$\"1p4Oxt$3)oFbo7$$!1LLL3k(p`(F
bo$\"1Bt(zL,1o&Fbo7$$!1nmmmj^NmFbo$\"1@,BXx+.WFbo7$$!1ommm9'=(eFbo$\"1
$[s$3d(yW$Fbo7$$!1,++v#\\N)\\Fbo$\"1.`jPjd$[#Fbo7$$!1pmmmCC(>%Fbo$\"15
!*RKWoh<Fbo7$$!1*****\\FRXL$Fbo$\"1_<l<_\">6\"Fbo7$$!1+++D=/8DFbo$\"1H
$*>9#z`J'!#<7$$!1mmm;a*el\"Fbo$\"1sw$4j*)>u#Fbr7$$!1pmm;Wn(o)Fbr$\"1a/
+x'ova(!#=7$$!1qLLL$eV(>F]s$\"1CHSG34)*Q!#@7$$\"1Mmm;f`@')Fbr$\"1xsBc
\")3LuF]s7$$\"1)****\\nZ)H;Fbo$\"1**GqVMScEFbr7$$\"1lmm;$y*eCFbo$\"1Bo
$=Oul/'Fbr7$$\"1*******R^bJ$Fbo$\"1&>/'3\")G*4\"Fbo7$$\"1'*****\\5a`TF
bo$\"12NSD.>D<Fbo7$$\"1(****\\7RV'\\Fbo$\"1u0![HmWY#Fbo7$$\"1'*****\\@
fkeFbo$\"1eTe3TMRMFbo7$$\"1JLLL&4Nn'Fbo$\"1&3\\\"\\Hd`WFbo7$$\"1******
*\\,s`(Fbo$\"1C-;X1%4o&Fbo7$$\"1lmm\"zM)>$)Fbo$\"15F1'4l>#pFbo7$$\"1**
*****pfa<*Fbo$\"13Cjqg!*=%)Fbo7$$\"1HLLeg`!)**Fbo$\"1z\"p6+56'**Fbo7$$
\"1++]#G2A3\"F0$\"1MgH-E<r6F07$$\"1LLL$)G[k6F0$\"18jd&Q?gN\"F07$$\"1++
]7yh]7F0$\"1&GUH\"\\/k:F07$$\"1nmm')fdL8F0$\"1uR@7\\Uy<F07$$\"1nmm,FT=
9F0$\"1K$\\Af%*=,#F07$$\"1LL$e#pa-:F0$\"1+7LkskdAF07$$\"1+++Sv&)z:F0$
\"1^[pY)\\f\\#F07$$\"1LLLGUYo;F0$\"1XzA\")Gx$y#F07$$\"1nmm1^rZ<F0$\"1y
32%43X0$F07$$\"1++]sI@K=F0$\"1\"*)RIu/qN$F07$$\"1++]2%)38>F0$\"1')3\"
\\D2*fOF07$$\"\"#F*F+-%'COLOURG6&%$RGBG$\"#5!\"\"F*F*-%+AXESLABELSG6$%
\"xG%!G-%&TITLEG6#%2I~should~not~workG-%%VIEWG6$;F(Fhz%(DEFAULTG" 2 
391 171 171 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10030 
10061 10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 269 331 
0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(f(t),t=-
2..2,title=`I don't work`);" }}{PARA 8 "" 1 "" {TEXT -1 26 "Plotting e
rror, empty plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "# What \+
is happening here? f(x):=x^2 did create an \"empty\" proc with \"saved
 value\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "eval(f);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#R6\"F$6#%)rememberGE\\s\"%\"xG*$F(\"\"
#.-9!6#9\"F$F$6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "op(4,e
val(f));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7#/%\"xG*$F(\"
\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eval(g);op(4,eval(g)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"xG6\"6$%)operatorG%&arrowG
F&*$9$\"\"#F&F&6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eval(
h);op(4,eval(g));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"xG6\"F&F&*$
9$\"\"#F&F&6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "# Other p
laces Maple uses \"option remember\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "# A. well known values" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "op(4,eval(exp));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-
%&TABLEG6#7%/*&%\"IG\"\"\"%#PiGF*!\"\"/\"\"!F*/,$%)infinityGF,F." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "op(4,eval(sin));" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#71/,$%#PiG#\"\"$\"\"),$*$,&\"\"#
\"\"\"*$F0#F1F0F1F3F3/%\"IG*&F5F1-%%sinhG6#F1F1/,$F)#F1F,,$*$,&F0F1F2!
\"\"F3F3/,$F)#F1\"\"%,$F2F3/\"\"!FG/,$F)#\"\"&\"#7,$*&\"\"'F3,&F1F1*$F
+F3#F1F+F1FC/,$F)#F1FK,$*&F0F3,&FKF1*$FKF3F@F3FC/,$F)#F1FL,$*&FOF3,&F1
F1FQ#F@F+F1FC/,$F)F3F1/,$F)#F1\"#5,&FYFC#F@FDF1/F)FG/,$F)#F0FK,$*&F0F3
,&FKF1FYF1F3FC/,$F)#F+F`o,&FYFCFCF1/,$F)#F1FOF3/,$F)FR,$FQF3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "# B. Recursive defined funct
ions (they can remember for speed)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "R:=proc(x) R(x-1) + 1; end;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"RGR6#%\"xG6\"F(F(,&-F$6#,&9$\"\"\"!\"\"F.F.F.F.F(F(
6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "R(0):=37;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"RG6#\"\"!\"#P" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 5 "R(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#U" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "# 5. Confusing exp(x) with \+
exp^x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "# This seems fairl
y common beginner's error." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
42 "plot(exp^x,x=-1..1,title=`I should fail`);" }}{PARA 13 "" 1 "" 
{INLPLOT "6&-%'CURVESG6$7_o7$$!\"\"\"\"!$\"18y&okFS])!#M7$$!1nmm;p0k&*
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\"1:9otIi\"\\\"!#J7$$!1mmm\"4m(G$)F1$\"1%)oUb#\\W!*)F@7$$!1ML$3i.9!zF1
$\"1#yUvK&oq_!#I7$$!1nm;/R=0vF1$\"1#z@^mL1u#!#H7$$!1++]P8#\\4(F1$\"1#p
[!eM\"3^\"!#G7$$!1nm;/siqmF1$\"16\"f0\"**HH))FW7$$!1++](y$pZiF1$\"1EJV
8LxI^!#F7$$!1LLL$yaE\"eF1$\"1t9$*RlbNJ!#E7$$!1nmm\">s%HaF1$\"1!Ru%z%HV
a\"!#D7$$!1+++]$*4)*\\F1$\"1)y809Y\\H*Fho7$$!1+++]_&\\c%F1$\"16)R!)Q'y
Nc!#C7$$!1+++]1aZTF1$\"19-%HQ^1?$!#B7$$!1nm;/#)[oPF1$\"1s`Wf8`\\:!#A7$
$!1MLL$=exJ$F1$\"1oubZ$\\3,\"!#@7$$!1MLLL2$f$HF1$\"1$[>7\\e1&\\Feq7$$!
1++]PYx\"\\#F1$\"1=h^6'fC9$!#?7$$!1MLLL7i)4#F1$\"1:#y%>3H8;!#>7$$!1++]
P'psm\"F1$\"1'4FYX\\\"4(*Ffr7$$!1++]74_c7F1$\"1];jG^9j`!#=7$$!1JLL$3x%
z#)!#<$\"1M2#emj0>$Fes7$$!1MLL3s$QM%Fes$\"13LY+uyS;F17$$!1^omm;zr)*Ffr
$\"1)pg0Iqvf*F17$$\"1<LLezw5VFes$\"1#ebO5\\8,'!#:7$$\"1!****\\PQ#\\\")
Fes$\"1h1>]j\"*oH!#97$$\"1KLLe\"*[H7F1$\"1%3>ktAim\"!#87$$\"1*******pv
xl\"F1$\"19nGh=j+**Fcu7$$\"1)****\\_qn2#F1$\"1a,7tc\")fc!#77$$\"1)***
\\i&p@[#F1$\"1Q1(e(*\\v0$!#67$$\"1)****\\2'HKHF1$\"1**\\Y&4:'*)>!#57$$
\"1lmmmZvOLF1$\"1UikzTjq5!\"*7$$\"1+++]2goPF1$\"1)G6%fpeckF`w7$$\"1KL$
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F1$\"1_KdioClP!\"#7$$\"1*******p(G**yF1$\"1$[Ok*fl!)=F)7$$\"1mmmT6KU$)
F1$\"1c%z+=%>)=\"F*7$$\"1++]P$[/a)F1$\"1JA2=Wj4FF*7$$\"1LLLLbdQ()F1$\"
1wp$odC#zhF*7$$\"1+]i!*z>W))F1$\"1#[2o()Q&*e*F*7$$\"1nm\"zW?)\\*)F1$\"
1)eA!y0?)[\"\"\"\"7$$\"1L$3_!HWb!*F1$\"1P:pQ&Q&4BFh\\l7$$\"1++]i`1h\"*
F1$\"11H)Q&H<%e$Fh\\l7$$\"1++++PDj$*F1$\"1r:,$ynGJ)Fh\\l7$$\"1++]P?Wl&
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'*F1$\"1b$pg!4!*HIF]^l7$$\"1+vVt7SG(*F1$\"11x7)et#)z$F]^l7$$\"1++v=5s#
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)*F1$\"1jlA\\T+pfF]^l7$$\"1](=nj+U')*F1$\"1]$*=dN9$o'F]^l7$$\"1+]P40O
\"*)*F1$\"1oiKJNs#[(F]^l7$$\"1^7.#Q?&=**F1$\"1[.$>HmzP)F]^l7$$\"1+voa-
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PMF,%G(**F1$\"1mRNP!f-0\"\"\"$7$$\"1v=nj+U')**F1$\"1`F(yo686\"Fjal7$$F
h\\lF*$\"1qY[#R8f<\"Fjal-%'COLOURG6&%$RGBG$\"#5F)F*F*-%&TITLEG6#%.I~sh
ould~failG-%+AXESLABELSG6$%\"xG%!G-%%VIEWG6$;F(Fabl%(DEFAULTG" 2 274 
143 143 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10030 10061 
10056 10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 416 647 0 0 0 
0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot(e^x,x=-1..1,ti
tle=`I'm empty`);" }}{PARA 8 "" 1 "" {TEXT -1 26 "Plotting error, empt
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$$!1MLL3s$QM%Fds$\"13LY+uyS;F07$$!1^omm;zr)*Fer$\"1)pg0Iqvf*F07$$\"1<L
Lezw5VFds$\"1#ebO5\\8,'!#:7$$\"1!****\\PQ#\\\")Fds$\"1h1>]j\"*oH!#97$$
\"1KLLe\"*[H7F0$\"1%3>ktAim\"!#87$$\"1*******pvxl\"F0$\"19nGh=j+**Fbu7
$$\"1)****\\_qn2#F0$\"1a,7tc\")fc!#77$$\"1)***\\i&p@[#F0$\"1Q1(e(*\\v0
$!#67$$\"1)****\\2'HKHF0$\"1**\\Y&4:'*)>!#57$$\"1lmmmZvOLF0$\"1UikzTjq
5!\"*7$$\"1+++]2goPF0$\"1)G6%fpeckF_w7$$\"1KL$eR<*fTF0$\"1'Gm*GrZ*G$!
\")7$$\"1+++])Hxe%F0$\"1f%RC*Gu]>!\"(7$$\"1lm;H!o-*\\F0$\"1f-4u<OT5!\"
'7$$\"1****\\7k.6aF0$\"1)ze(eN;(*fFfx7$$\"1mmm;WTAeF0$\"1D[>w:S@L!\"&7
$$\"1****\\i!*3`iF0$\"1'HjiKsK*>!\"%7$$\"1MLLL*zym'F0$\"1?:4v'>(>6!\"$
7$$\"1LLL3N1#4(F0$\"1OF$R&3rSlF]z7$$\"1mm;HYt7vF0$\"1_KdioClP!\"#7$$\"
1*******p(G**yF0$\"1$[Ok*fl!)=F(7$$\"1mmmT6KU$)F0$\"1c%z+=%>)=\"F)7$$
\"1++]P$[/a)F0$\"1JA2=Wj4FF)7$$\"1LLLLbdQ()F0$\"1wp$odC#zhF)7$$\"1+]i!
*z>W))F0$\"1#[2o()Q&*e*F)7$$\"1nm\"zW?)\\*)F0$\"1)eA!y0?)[\"\"\"\"7$$
\"1L$3_!HWb!*F0$\"1P:pQ&Q&4BFg\\l7$$\"1++]i`1h\"*F0$\"11H)Q&H<%e$Fg\\l
7$$\"1++++PDj$*F0$\"1r:,$ynGJ)Fg\\l7$$\"1++]P?Wl&*F0$\"1d\\8jb-G>\"\"#
7$$\"1+D\"Gyh(>'*F0$\"1jU;jj'pT#F\\^l7$$\"1+]7G:3u'*F0$\"1b$pg!4!*HIF
\\^l7$$\"1+vVt7SG(*F0$\"11x7)et#)z$F\\^l7$$\"1++v=5s#y*F0$\"12Vy)*H]hZ
F\\^l7$$\"1^iS\"*3))4)*F0$\"1Ym+,a<J`F\\^l7$$\"1+D1k2/P)*F0$\"1jlA\\T+
pfF\\^l7$$\"1](=nj+U')*F0$\"1]$*=dN9$o'F\\^l7$$\"1+]P40O\"*)*F0$\"1oiK
JNs#[(F\\^l7$$\"1^7.#Q?&=**F0$\"1[.$>HmzP)F\\^l7$$\"1+voa-oX**F0$\"1'Q
0!fqJ!Q*F\\^l7$$\"1Cc,\">g#f**F0$\"1.\">)[YgD**F\\^l7$$\"1\\PMF,%G(**F
0$\"1mRNP!f-0\"\"\"$7$$\"1v=nj+U')**F0$\"1`F(yo686\"Fial7$$Fg\\lF)$\"1
qY[#R8f<\"Fial" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalhf(ex
p^1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"1qY[#R8f<\"\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "s:=x->x;evalhf(s^1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sGR6#%\"xG6\"6$%)operatorG%&arrowG
F(9$F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"xG6\"6$%)operatorG
%&arrowGF&9$F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "# Th
is seems to be a Maple bug. The function plotted was exp(42*x) \"rough
ly\" in R4. But R5 things are different. Still wrong, but different." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalhf(exp^(-1));" }}
{PARA 8 "" 1 "" {TEXT -1 63 "Error, unable to evaluate built-in functi
on `readlib` in evalhf" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "e
valf(exp(-1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+7WzyO!#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalhf(exp^(-1));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"1VV(yRFS])!#M" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 35 "op(1,op(1,plot(exp^x,x=-1..1)))[1];" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#7$$!\"\"\"\"!$\"1VV(yRFS])!#M" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 20 "plot(exp^x,x=-1..1);" }}{PARA 13 "" 1 "" 
{INLPLOT "6%-%'CURVESG6$7_o7$$!\"\"\"\"!$\"1VV(yRFS])!#M7$$!1nmm;p0k&*
!#;$\"1Vi*3dJm@&!#L7$$!1LL$3<XZ=*F1$\"11+xUTDGD!#K7$$!1nmmT%p\"e()F1$
\"1uDVNIi\"\\\"!#J7$$!1mmm\"4m(G$)F1$\"14+HQ!\\W!*)F@7$$!1ML$3i.9!zF1$
\"1C4h0_oq_!#I7$$!1nm;/R=0vF1$\"1w$**[gL1u#!#H7$$!1++]P8#\\4(F1$\"1#)
\\mEM\"3^\"!#G7$$!1nm;/siqmF1$\"1,)=\"Q(*HH))FW7$$!1++](y$pZiF1$\"1q+e
>KxI^!#F7$$!1LLL$yaE\"eF1$\"19\"pl[cb8$!#E7$$!1nmm\">s%HaF1$\"1Y[#\\XH
Va\"!#D7$$!1+++]$*4)*\\F1$\"1-a\\/g%\\H*Fho7$$!1+++]_&\\c%F1$\"1*>:FJ'
yNc!#C7$$!1+++]1aZTF1$\"1jP2W8l+K!#B7$$!1nm;/#)[oPF1$\"1H'[BMJ&\\:!#A7
$$!1MLL$=exJ$F1$\"1[#QxL\\3,\"!#@7$$!1MLLL2$f$HF1$\"1(3k'[%e1&\\Feq7$$
!1++]PYx\"\\#F1$\"1G.f)efC9$!#?7$$!1MLLL7i)4#F1$\"1,bc43H8;!#>7$$!1++]
P'psm\"F1$\"1c?B2%\\\"4(*Ffr7$$!1++]74_c7F1$\"1&G,*3^9j`!#=7$$!1JLL$3x
%z#)!#<$\"1?l3eOc!>$Fes7$$!1MLL3s$QM%Fes$\"1_lP)R(yS;F17$$!1^omm;zr)*F
fr$\"1+LG+.d(f*F17$$\"1<LLezw5VFes$\"1BEC6\"\\8,'!#:7$$\"1!****\\PQ#\\
\")Fes$\"1sVFdj\"*oH!#97$$\"1KLLe\"*[H7F1$\"1XqTUFAm;!#87$$\"1*******p
vxl\"F1$\"1m7M4>j+**Fcu7$$\"1)****\\_qn2#F1$\"1tU`2d\")fc!#77$$\"1)***
\\i&p@[#F1$\"1()44)**\\v0$!#67$$\"1)****\\2'HKHF1$\"1qja7^h*)>!#57$$\"
1lmmmZvOLF1$\"1]d5!>M12\"!\"*7$$\"1+++]2goPF1$\"1A@lIqeckF`w7$$\"1KL$e
R<*fTF1$\"1v0.prZ*G$!\")7$$\"1+++])Hxe%F1$\"1>?k=Hu]>!\"(7$$\"1lm;H!o-
*\\F1$\"1Q_I*yh8/\"!\"'7$$\"1****\\7k.6aF1$\"1J%pPljr*fFgx7$$\"1mmm;WT
AeF1$\"1!*[\"Gj,9K$!\"&7$$\"1****\\i!*3`iF1$\"1!4cFOsK*>!\"%7$$\"1MLLL
*zym'F1$\"1c6&pp>(>6!\"$7$$\"1LLL3N1#4(F1$\"1*QY(*)4rSlF^z7$$\"1mm;HYt
7vF1$\"1hORXpClP!\"#7$$\"1*******p(G**yF1$\"1m=$*Rgl!)=F)7$$\"1mmmT6KU
$)F1$\"1z454U>)=\"F*7$$\"1++]P$[/a)F1$\"1*eEe[M'4FF*7$$\"1LLLLbdQ()F1$
\"1LG$\\tC#zhF*7$$\"1+]i!*z>W))F1$\"1g>7D\"R&*e*F*7$$\"1nm\"zW?)\\*)F1
$\"1J(=qh+#)[\"\"\"\"7$$\"1L$3_!HWb!*F1$\"1mQ#**fQ&4BFh\\l7$$\"1++]i`1
h\"*F1$\"1Yx,]I<%e$Fh\\l7$$\"1++++PDj$*F1$\"1e1!4,oGJ)Fh\\l7$$\"1++]P?
Wl&*F1$\"1>78<c-G>\"\"#7$$\"1+D\"Gyh(>'*F1$\"1(=Q7VmpT#F]^l7$$\"1+]7G:
3u'*F1$\"1q%))=*4!*HIF]^l7$$\"1+vVt7SG(*F1$\"1MVJ'pt#)z$F]^l7$$\"1++v=
5s#y*F1$\"1kR;NJ]hZF]^l7$$\"1^iS\"*3))4)*F1$\"1wo7ab<J`F]^l7$$\"1+D1k2
/P)*F1$\"1Z49@V+pfF]^l7$$\"1](=nj+U')*F1$\"1NK?]P9$o'F]^l7$$\"1+]P40O
\"*)*F1$\"12w-[Ps#[(F]^l7$$\"1^7.#Q?&=**F1$\"1GVANl'zP)F]^l7$$\"1+voa-
oX**F1$\"1#H`@L<.Q*F]^l7$$\"1Cc,\">g#f**F1$\"1?+CQ\\gD**F]^l7$$\"1\\PM
F,%G(**F1$\"1]--o!f-0\"\"\"$7$$\"1v=nj+U')**F1$\"1&)eO?<J66Fjal7$$Fh\\
lF*$\"1;M\"pU8f<\"Fjal-%'COLOURG6&%$RGBG$\"#5F)F*F*-%+AXESLABELSG6$Q\"
x6\"%!G-%%VIEWG6$;F(Fabl%(DEFAULTG" 2 244 130 130 2 0 1 0 2 9 0 4 2 
1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 20530 0 
12020 0 0 0 0 0 0 0 1 1 0 0 0 286 157 0 0 0 0 0 0 }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 60 "# Solution? put e:=exp(1) in everyone's initi
alization file." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "# 6. Lis
ts vs Vectors" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linal
g);" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" 
}}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,Jor
danBlockG%)LUdecompG%)QRdecompG%*WronskianG%'addcolG%'addrowG%$adjG%(a
djointG%&angleG%(augmentG%(backsubG%%bandG%&basisG%'bezoutG%,blockmatr
ixG%(charmatG%)charpolyG%)choleskyG%$colG%'coldimG%)colspaceG%(colspan
G%*companionG%'concatG%%condG%)copyintoG%*crossprodG%%curlG%)definiteG
%(delcolsG%(delrowsG%$detG%%diagG%(divergeG%(dotprodG%*eigenvalsG%,eig
envaluesG%-eigenvectorsG%+eigenvectsG%,entermatrixG%&equalG%,exponenti
alG%'extendG%,ffgausselimG%*fibonacciG%+forwardsubG%*frobeniusG%*gauss
elimG%*gaussjordG%(geneqnsG%*genmatrixG%%gradG%)hadamardG%(hermiteG%(h
essianG%(hilbertG%+htransposeG%)ihermiteG%*indexfuncG%*innerprodG%)int
basisG%(inverseG%'ismithG%*issimilarG%'iszeroG%)jacobianG%'jordanG%'ke
rnelG%*laplacianG%*leastsqrsG%)linsolveG%'mataddG%'matrixG%&minorG%(mi
npolyG%'mulcolG%'mulrowG%)multiplyG%%normG%*normalizeG%*nullspaceG%'or
thogG%*permanentG%&pivotG%*potentialG%+randmatrixG%+randvectorG%%rankG
%(ratformG%$rowG%'rowdimG%)rowspaceG%(rowspanG%%rrefG%*scalarmulG%-sin
gularvalsG%&smithG%&stackG%*submatrixG%*subvectorG%)sumbasisG%(swapcol
G%(swaprowG%*sylvesterG%)toeplitzG%&traceG%*transposeG%,vandermondeG%*
vecpotentG%(vectdimG%'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 32 "L:=[cos(t),sin(t)];V:=vector(L);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"LG7$-%$cosG6#%\"tG-%$sinGF(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"VG-%'VECTORG6#7$-%$cosG6#%\"tG-%$sinGF+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "diff(L,t);diff(V,t);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7$,$-%$sinG6#%\"tG!\"\"-%$cosGF'" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "diff(vector(L),t);map(diff,V,t);" }}{PARA 8 "" 1 "" {TEXT -1 52 "E
rror, please use map to differentiate tables/arrays" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%'VECTORG6#7$,$-%$sinG6#%\"tG!\"\"-%$cosGF*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "a:=curl([x*y*z,x*y*z,x*y*z],
[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'VECTORG6#7%,&*&%
\"xG\"\"\"%\"zGF,F,*&F+F,%\"yGF,!\"\",&F.F,*&F/F,F-F,F0,&F2F,F*F0" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "b:=curl(vector([x*y*z,x*y*z,
x*y*z]),[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'VECTORG6
#7%,&*&%\"xG\"\"\"%\"zGF,F,*&F+F,%\"yGF,!\"\",&F.F,*&F/F,F-F,F0,&F2F,F
*F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "whattype(eval(a));wh
attype(eval(b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&arrayG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%&arrayG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "# Appendix -- add-ons" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "# 7 answers that a calculus I student doesn't expect
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf((-8)^(1/3));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+++++5!\"*\"\"\"%\"IG$\"+330K<F&
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "# 8 More fun with vecto
rs." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 45 "a:=vector([1,0]):b:=vector([0,1]):evalm(a-b);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7$\"\"\"!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "evalm(a-a);evalm(vector([1,0])-vect
or([1,0]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "
norm(evalm(a-a),2);norm(evalm(vector([1,0])-vector([1,0])));" }}{PARA 
8 "" 1 "" {TEXT -1 45 "Error, (in norm) expecting a matrix or vector" 
}}{PARA 8 "" 1 "" {TEXT -1 45 "Error, (in norm) expecting a matrix or \+
vector" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "norm(matadd(a,a,1
,-1),2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 20 "#9 Maple can't count" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 25 "s1:=solve((x-5)^203=0,x):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 11 "nops([s1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "_MaxSols:=225;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)_MaxSolsG\"$D#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s1:=solve((x-5)^203=0,x):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "nops([s1]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"$.#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}}{MARK "74 0 0" 0 }{VIEWOPTS 1 1 0 2 1 1805 }