ii
Cyril
A lb
erg
a
Ro
y
A dler
Ric
har
d
A nder
so
n
Geor
ge
A ndr
ews
Henr
y
Ba
k
er
Stephen
Ba
lzac
Y
ur
ij
Bar
ansk
y
Da
vid
R.
Ba
rto
n
Ger
ald
Baumga
rtner
Gil b
er
R.
Roy
RoyR.
yro0(b)-20c(er)]Tj 32.56 0 Tk (a)Tj 76.72 0 (Mumga)Tj 5.04 0 Tn (k)Tj29.68 0 TuelGerGersoykyGer
Da
vidR.Day
C
o n
t en
t s
1
Ax i
om
F
ea tures
1
1.1
In
tro d uctio
n
t o
Axio
m
iv
CO
NTENTS
3.2
. 4
Sym
b
ols,
V
a
ria
bles,
Assig
nm eb9.31000(4)]TD 18.24 [cla 0 Td 9q 0.12 0 0 0.12 0 0 cm /R7 gs 0 G 0 g q 8.33333 0 0 8.33333 0 0 cm BT /R81 0.12 Tf 1 0 0 -1 160.68 736.08 Tm (iv)Tj /R257 0.12 Tf 287.16 0 Td (CO)Tj 14q 0.12 0 0 0.12 0 0 cm /R7 gs 0 G 0 g q 8.33333 0 0 8.33333 0 0 cm BT /R81 0.12 t04[000(4)]TD 18.24 [cla 0 Td 9q 0.12 0 0 0v
vi
CO
NTENTS
7
I nput
Fi
les
an d
Output
St
yles
22
1
7.1
Inp ut
Files
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2
21
7.2
The
.ax
iom.inp ut
File
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2
22
7.3
Common
F
ea
t ur
es
of
Using
Outp ut
F
o
rmats
.
.
.
.
.
.
.
.
.
.
.
.
2
23
7.4
Monos
p a
ce
Tw
o-
D imensio
nal
Ma
t hema
t ica
l
F
or
mat
.
.
.
.
.
.
.
2
24
7.5
T
eX
F
oTd (of)Tj 11.4 0 T0 Td (23)Tj -318.84 12 Td (7.4)Tj 22.92 0 Td (Monos)Tj 28.56 0 Td [(p)-1000(a)]TJ 10.56 0 Td (ce)Tj 12.12 0 Td (Tw)Tj 14.16 0 Td (o-)Tj 8.28 0 Td [(D)-1000(imensio)]TJ 40.32 0 Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(t)-1000(hema)]TJ 27.12 0 Td [(t)-1000(ic0t(0j 14.04 0 Td (ce)Tj 12.12 0 Td (Tw)Tj 14.16 0 Td (o-)Tj 8.28 0 Td [(D)-1000(imensio)]TJ 40.32 0 Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.12 0 Td (Tw)Tj 14.16 0 Td (o-)Tj 8.28 0 Td [(D)-1000(imensio)]TJ 40.32 0 Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.12 0 Td (Tw)Tj 14.16 0 Td (o-)Tj 8.28 0 Td [(D)-1000(imensio)]TJ 40.32 0 Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.l)Tj 16.683 d (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(t)-1000(hema)]TJ 27.12 0 Td [(t)-1000(ic0t(0j 14.04 0SM0(ic03 27.12 0 TSc24 0 (.)8 0 Td (.i18.84 1pj 7.68al)7.12 0 T8.64 0 Td (2)Tj 4.92 0 Td (23)Tj -(mat)T (23)Tjula7.8 0 T57.12 0 T8.64 0 Td (2)Tj 424 0 Td (F)Tj 5[(m5.64 0 Td (or).)Tj 7.68 0t)Tj 1692 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.12 0 Td (Tw)Tj 14.16 0 Td (o-)Tj 8.28 0 Td [(D)-1000(imensio)]TJ 40.32 0 Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.l)Tj 16.683 d (nal)Tj 16.68 0 Td (Ma)T Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.l)Tj 16.683 d (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(t)-1000(hema)6TJ 27.12 0 Td [(t)-1070(ic0t(0j 14.04 Fsio)]TTj 16.68 OR8 0 Td 1000(ic0tTRAN8 0 32Ma)Tj 14.00 Td (Ma)Tj 14.04 0 Td [(t)-1000(hema)]TJ 27.12 0 Td [(t7T57.12 0 T[(ce)Tj 12.l)Tj 16.683 d (nal)Tj 16.68 0 Td (Ma)T Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.l)Tj 16.683 d (nal)Tj 16.68 0 Td (Ma)T Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.l)Tj 16.683 d (nal)Tj 16.68 0 Td (Ma)T Td (nal)Tj 16.68 0 Td (Ma)Tj 14.04 0 Td [(ce)Tj 12.lnal
Ma
CO
NTENTS
vii
New
F
o rew
o rd
O
n
Octob
er
1
,
20
01
Axio
m
w
as
withdra
wn
f r
om
th e
ma
rk
et
a
nd
ended
life
a
s
a
commer
cial
pro
duct.
C
hapte r
1
Axi
om
F
eat ures
1.1
In
tro
du
t ion
to
Axiom
W
elco
m e
to
t he
w
or
ld
o
f
A x
i o
m.
W
e
ca
ll
Axiom
a
2
CHAPTE
R
1.
A XIO
M
FEA
TUR E
S
whic
h
w
ould
g
1
.1.
IN TR
ODU CT
ION
TO
AX IO
M
3
liter
ally
d o
zens
of
kinds
of
n
u m
b
er
s
to
co
mp ute
wit h.
Th e
se
r
ang
e
fro
m
v
ar
-
io
us
kind s
o
f
in
00inr
4
CHAPTE
R
1.
A XIO
M
FEA
TUR E
S
i
nve
rs
e(%
)
1
x
+i
0
1
2
x
+2
i
1
2
Ty
pe
:
Un
io
n(M
at
rix
F
ra
ti
on
Po
ly
nom
ia
l
Com
pl
ex
In
te
ger
,.
..)
1.1.4
Hyp
er
Do
Figure
1.1
:
Hyp
er
do
c
o
p
e
n ing
men
u
Hyp
erDo
c
pres
en
ts
y
o
u
wind o
ws
o
1
.1.
IN TR
ODU CT
ION
TO
AX IO
M
5
k
1
.1.
IN TR
ODU CT
ION
TO
AX IO
M
7
d
ra
w(5
*b
es
sel
J(
0,s
qr
t(
x**
2+
y**
2)
),
x=
-2
0..
20
,
y
=-
20
..2
0)
F ig
ure
1.2
:
J
0
(
p
8
CHAPTE
R
1.
A XIO
M
FEA
TUR E
S
1
;
3
x ;
1
5
1
.1.
IN TR
ODU CT
ION
TO
AX IO
M
9
Ty
pe:
Ex
pre
ss
ion
I
nt
ege
r
No
t e
the
use
of
\%"
h er
e.
This
m e
ans
the
v
a
lue
of
t he
la
st
ex
p r
ess
ion
w
e
c
omput ed.
In
t his
case
it
is
the
lo
ng
expres
sion
a
b
o
v
e.
1.1.8
P
a tt
ern
Mat
hi8yTj 106P8yTj a 4.32 0 T(9)TjTj 10.08 0 Td (the)Tje
1
0
CHAPTE
R
1.
A XIO
M
FEA
TUR E
S
Using
i
nput
les
and
the
) read
co
m ma
nd ,
y
ou
ca
n
c
rea
t e
y
our
o
I2y
ou)ourourr84 0 TTj 20.4 0 ud (the)Tj 18.72 0 Td (o)Tjs12 07.2 0 Td (r84 0 TTj 20.4 (elev14.886)]TJ 12.72an000(XIO]TJ 12.72t1C2 96 Td (our)To 18.72 01Td (o)Tj 4.68 0 Td (I7Tj4rea)Tj a4.68 0 Td (Ipplications,4.68530.12 Tf 2 Td (our)Then Td (y2.58 0 Td (selectiv14.8310 Td (ou)Te000(e)]TJ 12.7[(l (our)Ty 18.71)T0 Td [(TUa4.68 0 Td (I[ppd (the)Ty Td (y2.]TJ 12.72t00(rea-31 04 0r84 0 TTj 20.4 0 ud (the)Tj 18.72 0 Td (o)Tjs12 07.3Td (o)Tj 4.68 0 Td (ITd (y)T Td (Ineed.(read)34517 0.12 Tf4 0 Td320.1226.28 1.94.68 10.12 Tf 27Pj 42.84 0 lo)Tjol000(XIO412 Tf 27ymor84 0 0M)Tj 12.48 pd (the)hi14.88 0 TJ 21.6 0 000(XIO412 Tf 27AlTd (y)T Td (Igori12 0 2. Td (ou)Tthm12 0 384 0 lo)Tjsg)Tj /R217 0.12 Tf180M)Tj 2. Tdf 27All14.886)56 Tcompd 2ur)Tonen Td (43. Td (ou) Td (our)Ts 18.71)T12 Tf 27o1C1)Tj4rea)Tj t00(rea7T12 Tf 27Axiom12 03204rea)Tj a4.68 0 Td (Ilgey)Tj 4.92 a4.688Tj4rea)Tj CHAPTE)Tj 42.84 0 lo)Tj 12 T8CHAPTE)Tj 42.84 0 lo)Tjej 42.8.12 Tf 27wr1C1oury401Td (o)Tjin1C1rea7T12 Tf 27Axiom12 03204reaououruag0 Td (M)Tj 12.4jej 429(c)Tj 4.32 0 Td (rea)Tj lled 0 Td (nput)Tj /R8108.12 Tf 27Spades
1
2
C
hapte r
2
T
en
F
undamen
tal
Ideas
Axioeas
1
4
CHA P
TER
2.
TE
NNAMENTj 1037.0 Td (N)ALj 10.7.04 Td (N)IDEASj /R25345.12 Tf 13-312.72 27.96d (2.)T12 Tj 4.97.70 Td (TE)j 4.9
15an /R7 gs 0Myth e
1
8
CHA P
TER
2.
TE
N
FUN D
AMENT
AL
IDEAS
Ty
pe
:
Ma
tri
x
Pol
yn
om
ial
F
ra
ti
on
In
te
ger
the
in
t er
preter
1
9
Axio
m's
use
o
f
a
bstra
ct
da
tat
yp
es
clea
rly
separ
ates
the
exp
or
ts
of
a
domain
(wha
t
o
p
er
ations
a
re
de ned)
fro
j 10.44 a-1TJ 1t.88 0 15 (domain)Timpleme1.52 4d (6at)Tj 12.430.4 0 Td (the)Tj 1(h88 0 Td (ations)Tw8 0 Td (j 10.44 8.24 0 Td [(yp)-2000ob)-5TJ 1ject.88 0 35d (Tj 4.92 0 Td (re)Tj 13.08 0 27.5.28(wha)Tj8 0 T3 (a)Tj 4.9epr.72 0 T (ct)Tj 12e1.52 9 (the)Tj 18ed2 0 Td 68Tj 4.92 0 Td (re)Tj 13nd8 0 Td (re)Tj 132 0 Td [(p)-3000(er)]TJ 1488 0 10(ct)Tj 12.2 0 T8 (j 10.44[64 -1TJ 1.4 8 0 11 (o)Tj 4.9n24 0 Td (of)Tj 12a.08 0 T6(ct)Tj 12)Tj 39.6..52 4d (j 10.44 User4 0 Td 68Tj 4.924 0 6 (the)Tj 1.48 0 T0.8Tj 4.92 0 T7.8Tj 4.9j -311.52 3d (re)Tj 13c6 0 Td (domain)Tn 0 T8 tat)Tj 12h 0 Td 1re
2
0
CHA P
TER
2.
TE
N
FUN D
AMENT
AL
IDEAS
C
hapte r
3
Starting
Axi
om
W
elco
m e
t o
th e
A x
i o
m
en
vir
onmen
t
for
in
t e
rac
t ivvir
2
2
CHAPTE
R
3.
ST
A R
TING
AXIOM
If
y
ou
a
re
running
Axiom
under
th e
X
W indo
w
System,
there
ma
y
b
e
t
w
o
windo
ws:
t he
c
onso
le
wind o
w
(as
j ust
descr
ib
ed)
a
n d
the
Hyp
e
rDo
c
main
men
u.
Hyp
erDo
c
is
a
m
u ltiple-windo
w
h
yp
ertext
sys
t em
that
lets
y
o
u
view
A x
iom
do
cumen
tatio
n
a
nd
examples
o
n-line,
execute
A x
iom
expre
ssions
,
a
nd
g
ener
ate
g
ra
p hics
.
If
y
o
u
ar
e
in
a
g
ra
2
4
CHAPTE
R
3.
ST
A R
TING
AXIOM
1
+
2
-
3
/
4
*
3
**
2
-
1
1
9
4
T
yp
e:
F
ra
ti
on
In
te
ger
The
a
b
o
v
e
ex
p r
essio
n
is
equiv
alen
t
to
th is
.
(
(1
+
2)
-
((3
/
4
)
*
(
3
*
*
2)
))
-
1
1
9
4
T
yp
e:
F
ra
ti
on
In
te
ger
If
a
n
expr
essio
n
co
n
t a
ins
s
ub
expr
essio
ns
enclo
sed
i n
par
en
theses,
t he
3
.2.
TH E
AXIOM
L
A NGUA
G E
2
5
99
99
99
99
99
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
This
is
the
la
st
r
esult .
%
%(
-1)
99
99
99
99
99
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
This
is
the
r
esult
fro
m
step
n
um
b
er
1.
%
%(
1)
10
00
00
00
000
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
3.2.3
Some
T
yp
es
E
v
e
rything
i n
Axiom
ha
s
a
t
y
p
e.
The
t
yp
e
determines
what
op
era
t io
ns
y
ou
can
p
er
f o
rm
o
n
a
n
ob
ject
a
nd
ho
w
the
ob
j e[
2
6
CHAPTE
R
3.
ST
A R
TING
AXIOM
x
**8
x
8
T
yp
e:
P
ol
yno
mi
al
In
te
ger
Here
a
nega
t iv
e
in
teg
er
exp
o
nen
t
pro d uce
s
a
fra
ct io
3
.2.
TH E
AXIOM
L
A NGUA
G E
2
7
This
giv
es
the
v
a
lue
z
+
3
=5
(a
2
8
CHAPTE
RA yp
ti als anrl=i(b)-2[(yp)-300038 Tm (2)Tjg736.08 Tm (2)Tjiv736.7..22 7e.14 0 3.5n.18.tog14 0 3..22 7ether 0 de5..22 7with 0 de3 A.71.1a736.08 Tm (2)Tj79.04 0 n.9 0as92 0((CHAPTE)Tj[(92 0[(tg)-3007..22 7nme.14 0e3 5n.9 0t.92 0n.9 0The14 0e0.76]TJ 19. 4.92 0 de la.22 7- 0 d-340.32 8)TT2 739.04 0HAPTE)Tj ation 0 de5.5n.18. 736.083n.9 0a.14 0 3. Tm (2)Tja736.08 Tm (2)Tjssis79.04210HAPTE
3
.2.
TH E
AXIOM
L
A NGUA
G E
2
9
T
ype
:
F
loa
t
Use
3
0
CHAPTE
R
3.
ST
A R
TING
AXIOM
3.2.6
Ca l
l
i
ng
F
un
ti
ons
As
w
e
sa
w
ear
lier,
when
y
ou
w
an
t
to
add
or
subtra
ct
t
w
o
v
alues,
y
ou
pla
ce
the
ar
it hmetic
op
era
t o
r
\
+"tt
3
.2.
TH E
AXIOM
L
A NGUA
G E
3
1
An
o
p
e
ra
t io
ns
that
r
eturns
a
B
oo
lea
n
v
a
lue
(that
is,
t
rue
o
r
fal
se
)
3
.3.
U SING
AXIOM
AS
A
P
OCK
ET
CA L
CU LA
TO
R
3
3
r
4(3)Tj 4.9[(b)-2J 27elong 0 Td 8.4s7PAS
3
4
CHAPTE
R
3.
ST
A R
TING
AXIOM
3.3.2
T
yp
e
Con
v
3
6
CHAPTE
R
3.
ST
A R
TING
AXIOM
3.3.3
Us eful
F
un ti
ons
T
o
obtain
the
a
bsolute
v
alue
o
f
a
n
3
.3.
U SING
AXIOM
AS
A
P
OCK
ET
CA L
CU LA
TO
R
3
7
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
T
es
t s
on
v
alues
ca
n
b
e
done
using
v
a
rious
functions
whic
h
ar
e
gener
ally
mo
re
e
Æ cien
t
than
using
r
elationa
l
o
p
era
t o
rs
s
uc
h
as
=
pa
rticular
ly
if
the
v
a
lue
is
a
ma
t r
ix.
E
xamples
of
s12 Td (ma)Tj 13mue
of
thses
3
8
CHAPTE
R
3.
ST
A R
TING
AXIOM
Ty
pe
:
Bo
ol
ean
e
3
.4.
U SING
AXIOM
AS
A
SYMBO
LIC
CALCULA
TO
R
4
1
3.4.2
Com
p l
ex
Num
b
ers
F
o
r
man
y
scien
ti c
calc
u la
ti o
ns
r
eal
n
um
b
ers
ar
en' t
suÆcien
t
a
n d
s
u pp
or
t
f o
r
c
omplex
n
um
b
er
s
is
a
lso
re
quired.
Complex
n
um
b
ers
ar
e
ha
ndled
in
a
n
in
tuitiv
e
ma
nn e
r.
A xio
m
us
es
t he
%
i
macr
o
to
r
eprese
n
t
the
squar
%
4
2
CHAPTE
R
3.
ST
A R
TING
AXIOM
Ty
pe:
Com
pl
ex
In
te
ger
f
a t
or
(%)
i
3
.4.
U SING
AXIOM
AS
A
SYMBO
LIC
CALCULA
TO
R
4
4
CHAPTE
R
3.
ST
A R
TING
AXIOM
r
adi
x(
3/2
1,
5)
0:0
32
41
2
T
yp
e:
R
41
2
T
yp41T41
3
.4.
U SING
AXIOM
AS
A
SYMBO
LIC
CALCULA
TO
R
4
5
om
pa
tF
ra
ti
on
(%)
6
3
4
6
CHAPTE
R
3.
ST
A R
TING
AXIOM
3
3
.5.
GENERAL
P
OINTS
ABO
U T
A XIO
M
4
7
The
rst
e
xample
s
h o
uld
b
e
rea
d
a
s:
Le
t
x
be
of
ty
pe
P
rim
eF
iel
d(
7)
an
d
ass
ig
n
t
o
it
th
e
val
ue
5
No
t e
that
it
is
o
nl y
p
os
sible
t o
in
v
er
t
no
n -
zer
o
v
alues
if
the
ar
it hmetic
is
p
er
-
fo
rmed
mo
dulo
a
prime
n
u m
b
er
.
Th
u s
ar
it hmetic
mo
dulo
a
no
n -
prime
in
teg
er
is
p
os
sible
bu t
the
r
ecipro cal
op
er
ation
is
unde ned
a
sn
3
.5.
GENERAL
P
OINTS
ABO
U T
A XIO
M
4
9
3.5.4
Com
men
ts
3
.5.
GENERAL
P
OINTS
ABO
U T
A XIO
M
5
1
le.
T
o
g
et
A x
iom
t o
rea
d
t his
le,
y
ou
use
the
system
command
)
rea
d
m
y.
inp
ut
.
If
y
o
u
need
to
m a
k
e
c
h a
nges
to
y
our
appr
oa
c
h
or
de niti o
ns,
g
o
in
t o
y
our
f a
v
or
it e
edit o
r,
c
hang
e
m
y
.i
nput ,
t hen
)re
ad
m
y.i
np
ut
ag
ain.
O
th e
r
sys
t em
co
m ma
nd s
in clude:
)
hi
sto
ry
,
t o
d is
pl a
y
pr
evious
input
a
nd/o
r
o
utp ut
lines;
)d
isp
la
y,
to
displa
y
pro
p
e
rties
and
v
alues
of
w
or
kspa
ce
v
ar
iables;
a
nd
)w
ha
t.
Is
sue
)w
ha
t
to
ge
t
a
li s
t
o
f
Axio
m
o
b
jects
thar5N 8.0(e)]TJ 10.2 0 Td (0 Td [(li)- [(pl)-1000(a)]TJalues)Tj 24.48 0ye12.6 0 T5000(jecwbstriTd (e)42nd)Tj 18.9
5
2
CHAPTE
5
6
CHAPTE
R
3.
ST
A R
TING
AXIOM
AXIOMTp11.88 0yTCHAitTCHAteT
3
.6.
D
A
T
A
STR
UCTURES
IN
A XIOM
5
7
r
ev
ers
e(
[7
,2,
-1
,2℄
)
[2;
1;
2;
7
]
T
yp
e:
L
ist
I
nt
ege
r
s
or
t([
7,
2,
-1,
2℄
)
[
1
;
2;
2;
7
]
T
yp
e:
L
ist
I
nt
ege
r
r
em
ove
Du
pl
i a
te
s([
1,
5,
3,5
,1
,1,
2℄
)
[1;
5
;
3;
2
]
Ty
pe
:
Li
st
Po
si
tiv
eI
nt
ege
r
#
[7
,2,
-1
,2
℄
4
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
L
i s
t s
in
A xio
m
ar
e
m
ut a
ble
and
so
th e
i r
co
n
t e
n
t s
( the
elemen
5
8
CHAPTE
R
3.
ST
A R
TING
AXIOM
[9;
2
;
4;
7
;
1
;
5;
4
2]
Typ
e:
Lis
t
Pos
it
iv
eIn
te
ger
e
ndO
fu
:=
r
est
(u
,4
)
[1;
5
;
4
2]
Typ
e:
Lis
t
Pos
it
iv
eIn
te
ger
p
art
Of
u
:
=
res
t(
u,
2)
[4
;
7;
1
;
5
;
42
]
Typ
e:
Lis
t
Pos
it
iv
eIn
te
ger
s
etr
es
t!(
en
dOf
u,
pa
rtO
fu
);
u
9;
2
;
6
0
CHAPTE
R
3.
ST
6
2
CHAPTE
R
3.
ST
A R
TING
AXIOM
[9;
9
9;
20
;
7]
Typ
e:
Lis
t
Pos
it
iv
eIn
te
ger
In
th e
pr
evious
ex
ample
a
new
e6j 30.96 0 ad (9)T 10.68 0 y (ex)T210.44 0 of (In)21.12 0 constd (pr266 23.08 0 Tu[(th)-1c00(e) Tf 9.96 0 Td[(th)-1ing00(e))Tj210.44 0 ld (Lis)Tj 9.36 0 Td[(th)-1s00(e)]Tj 11.88 0 Td (e6j 42.84 0 a (Pos)2j 30.96 0 gd (9)Tj 4.92 0 Td (iv Tf 7.8 0 end (3.))T24.04 0 T (iv T 13.08 0 T [(th)-1is00(e)]6Tf 4.32 0 d (Lis)Tj 10.68 0 ad (9-338.76 1 0. 0 Tp)-2h)-1o00(e)]0.561.88 0 Td (e6j 42.84 0 erful (pr236 23.08 0 Tmetho)-2h)-1d00(e)36j 42.84 0 whic (3.))T561.88 0 h(Lis)T 15.48 0 gTd (iv)2j 15.72 0 T (Pos)2j249.36 0 Td[(th)-1h000(e)]TJ7.n9
3
.6.
D
A
T
A
STR
UCTURES
IN
A XIOM
6
3
3.6.2
Segmen
ted
Li
sts
A
se
gmen
ted
list
is
one
in
whic
h
so
me
of
the
elemen
ts
ar
e
ra
nges
of
v
alues.
The
e
x pand
fun c
t io
n
con
v
er
t s
lists
o
f
th is
t
yp
e
in
to
or
dinary
lists:
[
1.
.10
℄
[1::10
]
Ty
pe:
Lis
t
3
.6.
D
A
T
A
STR
UCTURES
IN
A XIOM
6
5
T
o
crea
te
t he
s
eries
the
windo
w
is
p la
ced
at
the
star
0
3
.6.
D
A
T
A
STR
UCTURES
IN
A XIOM
6
7
y
:
=
xy36 0 0 Td (:)Tj 5.16 0pe Td (26)Tj 10.56 On Td (:)Tj 5.16 0eDi Td (5)Tj 6.36 0me Td (:)Tj 5.16 0nsi Td (5)Tj 6.36 0on Td (:)Tj 5.16 0alA Td (5)Tj 6.36 0rr Td (:)Tj 5.16 0ay Td (5)Tj 6.36 0Po Td (:)Tj 5.16 0si Td (:)Tj 5.16 0tiv Td (5)Tj 6.36 0eI Td (:)Tj 5.16 0nt Td (:)Tj 5.16 0ege Td (5)Tj 6.36 0r Td 96 Td4 32.44 0 Td =
5
6
8
CHAPTE
R
3.
ST
A R
TING
AXIOM
s
wap
!(
b,2
,3
);
b
[2;
4
;
3;
5
;
6]
T
yp
e:
O
ne
Dim
en
sio
na
lA
rra
y
Pos
it
iv
eIn
te
ger
opy
In
to!
(a
,b,
3)
[4;
4
;
2
lArr73r3;
4
2
;
4
;
2
5
;
6]
T
yp
e:
O
ne
Dim
en
sio
na
lA
rra
y
3.30 Td (a 0.12 Tf 4.44 0 T124.25.72 0 Td (In)Tj 10.44 0 Td (to!)Tj 15.72 0 Td ((a)Tj 10.44 0 Td (,b,)Tj 15.72 0 Td (3))Tj /R81 0.12 Tf 51 28.56 Td ([4)Tj /R24 0.12 Tf 7.8 0 Td (;)Tj /R81 0.12 Tf 4.44 0 Td (4)Tj /R24 0.12 Tf 4.92 0 Td (;)Tj /R81 0.12 Tf 4.44 0 Td (2)Tj /R24 0.12 Tf )Tj 10.44 0 Td (lA)Tj 10.44 0 Td (rr73r3;)Tj /R84 0.12 Tf 4.92 0 Td (;)Tj /R81 0.12 Tf 4.44 0 Td (4)Tj /R26 0.12 Tf 4.92 0 Td (;)Tj /R81 0.12 Tf 4.44 0 Td (2)Tj /R24 0.12 Tf 4.92 0 Td (;)Tj /R81 0.12 Tf 4.44 0 Td (4)Tj /R24 0.12 Tf 4.92 0 Td (;)Tj /R81 0.12 Tf 4.44 0 Td (2)Tj /R24 0.12 Tf 5.04 0 Td 87.6 /R8880.12 Tf 4.44 0 Td (5)Tj /R24 0.12 Tf 4.92 0 Td (;)Tj /R81 0.12 Tf 4.44 0 Td (6℄)Tj /R83 0.12 Tf -64.08 23.76 Td (T)Tj 5.16 0 Td (yp)Tj 10.44 0 Td (e:)Tj 21 0 Td (O)Tj 5.16 0 Td (ne)Tj 10.44 0 Td (Dim)Tj 15.72 0 Td (en)Tj 10.44 0 Td (sio)Tj 15.72 0 Td (na)Tj 10.44 0 Td (lA)Tj 10.44 0 Td (rra)Tj 15.72 0 Td (y)Tj 10.44 0 Td (Po4 0 (yv81 0.12 Tf 4.44e tj 10.44 0 Td (rrorj /R83 0.12 Tf -3([1j 10.44 0 Td (rr/24 0 Td (ger)Tj -31/.96 36.24 Td ( )T,4 0 Td (ger)Tj -1/.96 3d (ger)Tj -14 0.12 Td (te)Tj 10 5.16 03625.04 0 Td3881 019 (geTj 1 0.12 Tf 4.44 0 T68 737r3;)Tj -1 0.1ET Q q 4-4 2630.9 3452.9 BI /IM true /W 1 /H 1 /BPC 1 ID EI Q3 Td (t40481 0.m/R24 0.12 Tf 7.8 0 TPos)T-60 m /R81 0.12 Tf 4.44 0 T5.6)T-607;)Tj -1 0.1ET Q q 4-4 27APT9 3452.9 BI /IM true /W 1 /H 1 /BPC 1 ID EI Q327.6 40481 0.m/R4 0.12 Tf )Tj 10.4Po4 0-60 m /R81 0.12 Tf 4.44 0 T812 T-607;)Tj -1 0.1ET Q q m B-4 28 0 T 3452.9 BI /IM true /W 1 /H 1 /BPC 1 ID EI Q339.30 40481 0.m/R1 0.1d (;)Tj /R845.16 03625.04 0 TdPos)T-208880.12 0.12 Tf 5.04 0 Td 3 48 73.12 Tf 4.44 0 Td (5)Tj /R24 0.12 Tf 4.92 0 Td (;)Tj /V81 0.12 Tf 4.44e 44 0 Td (eIn)Tj 15r 0 Td (;)Tj /F81 0.12 Tf 4.44ra j 10.44 0 Td (rrai44 0 Td (eIn)Tj oTj 10.44 0 Td (rr0.44 0 Td (eIn)Tj 1)Tj 15.72 0 Td (y)Tj 10.44 0 Td (3.30 Td ("81 0.12 Tf 4.44Helj 10.44 0 Td (rrlo4 0 Td (ger)Tj -34 0 Td 5 Tf 4.44W72 0 Td (it)Tj 1rj /R83 0.12 Tf -ld"81 07781 0.72 0 Td ("H /R24 0.12 Tf 4.9lj /R83 0.12 Tf -lo4 0 Td (ger)Tj -34 0 Td 5 Tf 4.44W72 0 Td (it)Tj 1rj /R83 0.12 Tf -ld"81 083 (;)/R8880.12 Tf 4.44 0 Td (5)Tj /R24 0.12 Tf 4.92 0 Td (;)Tj /Sf 4.44 0 Td (5)trj /R83 0.12 Tf -ing 10.44 0 Td (Pos)Tj 15bf 4.44 0 Td (5)itTj 10.44 0 Td (si 0 m Td (ger)Tj -3trj /R844 0 Td (siu)Tj 15.72 0 Td (y0 5.1688.25.72 0 Td ("1.96 3d (ger)Tj -11.96 3d (ger)Tj -111j 10.44 0 Td (rr11.96 3d (ger)Tj -"81 0938 73/R81 0.12 Tf 4.44 0 Td (5)Tj /R24 0.12 Tf 4.92 0 Td (;)Tj /Bf 4.44 0 Td (5)itTj 1044 0 Td 2681 0.12 )Tj 5. 4.92 0 Tdyv81 0d (;)Tj /R[4e tjTj /R2o7 0.12781 0f 4.44r5.1683.)TTd (5)isTj 5. 4 0 Td (5)similar5.16(3.8(eIn)Tj 15Tj 5.3r3;)Tj /R8j 10.9.30 it)Tj 181 0d (;)Tj /R[4njTj /R2e-7 0.123r3;)Tj /R[(d.12Tj /R2e7 0.1d (;)Tj [4njTj /R2s7 0.198 736.08 Tionalj /R250.12 Tf 4.ar5.1683.92 0 TdyTj 10.8.6)Td (Dim)Tj 1964.08 23.76x j 10. Tf 179.04 eptj 10.8.30 it)Tj thaj 10. T.)TTd (5)t 10.8..12 Tf -if /R24 02 Td (5)itTj 1015 Td (5) o 10.9.30 it)Tj[(mp)-3 /R2o7 0.129)Tj f 4.44 0Tj 10.442(eIn)Tj 1s 10.44353.92. 4.92)Tj[(b)-20/R2elong 0.131!eIn.8(eIn)Tj ing 10.16 Tf 1 0 0 th0Tj 1022 Tf 1 0 0 a81 0d (;)Tj /R[4rithmetjTj /R2i 0.143.;
3
.6.
D
A
T
A
STR
UCTURES
IN
A XIOM
6
9
3.6.5
Flexi
bl
e
Ar
ra
ys
Flexible
ar
ra
ys
ar
e
desig
ned
to
pr
o
v
id e
th e
eÆciency
o
f
one-
d imensio
nal
a
rr
a
ys
while
r
ri-T39(pr)Tj 9.3the 0 Td [1r
7
0
CHAPTE
R
3.
ST
A R
TING
AXIOM
T
ype
:
F
lex
ib
leA
rr
ay
In
te
ger
d
ele
te
!(f
,5
)
[4
;
3;
4
2;
8;
2
;
28
]
T
ype
:
F
lex
ib
leA
rr
ay
In
te
ger
g
:=f
(3
..5
)
[42
;
8;
2]
T
ype
:
F
lex
ib
leA
rr
ay
In
te
ger
g
.2:
=7
;
f
[4
;
3;
4
2;
8;
2
;
28
]
T
ype
:
F
lex
ib
leA
rr
ay
In
te
ger
i
7
2
CHAPTE
R
3.
ST
A R
TING
AXIOMTING
3
.7.
FU NCTIO
N S,
CHO
ICES,
AND
LOO
PS
7
3
:=a
+
b
)
2:8
28
42
71
24
7
4
61
90
09
76
T
ype
:
F
loa
t
No
t e
tha
t
inden
tatio
n
i s
ext rem
el
y
imp
or
t a
n
t.
If
the
exa
mple
ab
o
v
7nTu.12 Tf 9. .
7
4
CHAPTE
R
3.
ST
A R
TING
AXIOM
Er
ro
r
A:
Mi
ss
in
g
m
at
e.
Li
ne
2:
a:
=3.
0
Li
ne
3:
b:
=1.
0
Li
ne
4:
:
=a
+
b
Li
ne
5:
Li
ne
6:
)
...
..
..
..A
Er
ro
r
A:
(f
ro
m
A
u
p
to
A)
I
gno
re
d.
Er
ro
r
A:
Im
pr
op
er
sy
nta
x.
Er
ro
r
A:
sy
nt
ax
er
ro
r
a
t
to
p
l
ev
el
Er
ro
r
A:
Po
ss
ib
ly
mi
ssi
ng
a
)
5
e
rro
r(
s)
pa
rs
ing
a
similar
er
ro
r
will
b
e
r
aise
d .
F ina
lly
,
the
\
) "
m
3
.7.
FU NCTIO
N S,
CHO
ICES,
AND
LOO
PS
7
5
3
:0
T
ype
:
F
loa
t
b
:=
1.0
1
:0
T
ype
:
F
loa
t
:=
a
+
b
4
:0
T
ype
:
F
loa
t
s
qr
t(4
.0
+
)
2:8
28
42
71
24
7
4
61
90
09
76
T
ype
:
F
loa
t
whic
h
a
c
hiev
es
the
same
r
esult
and
is
eas
ier
to
under
st a
7
6
CHAPTE
RA
3
.7.
FU NCTIO
N S,
CHO
ICES,
AND
LOO
PS
7
7
with
s
ome
in
v
o
ca
t io
ns
o
f
t hes
e
fun c
t io
ns:
f
()
Com
pi
li
ng
fu
n t
io
n
f
w
it
h
t
yp
e
(
)
->
Li
st
In
te
ge
r
[
]
T
yp
e:
L
ist
I
nt
ege
r
g
(4
)
Com
pi
li
ng
fu
n t
io
n
g
w
it
h
t
yp
e
I
nt
eg
er
->
Li
st
I
nte
ge
r
[4
]
T
yp
e:
L
ist
I
nt
ege
r
h
(2
,9)
Com
pi
li
ng
fu
n t
io
n
h
w
it
h
t
yp
e
(
7
8
CHAPTE
R
3.
ST
A R
TING
AXIOM
p
:
I
nte
ge
r
-
>
In
teg
er
T
yp
e:
V
oid
p
x
==
(a
8
0
CHAPTE
R
3.
ST
A R
TING
AXIOM
i
:=1
r
epe
at
if
i
>
4
the
n
br
eak
ou
tp
ut(
i)
i:
=i
+1
the
)read
yields:
i
:=1
1
Ty
pe:
Pos
it
iv
eIn
te
ger
r
epe
at
if
i
>
4
the
n
br
eak
ou
tp
ut(
i)
i:
=i
+1
1
2
3
4
T
yp
e:
V
oid
It
w
as
m e
n
t io
3
.7.
FU NCTIO
N S,
CHO
ICES,
AND
LOO
PS
8
1
0
Ty
pe:
No
nNe
ga
tiv
eI
nt
ege
r
r
ep
eat
i
:=
i
+
1
i
f
i
>
6
th
en
br
ea
k
8
2
CHAPTE
R
3.
8
4
CHAPTE
R
3.
ST
A R
TING
AXIOM
T
ypd (T)Tj.4 0 Td e:G
3
.7.
FU NCTIO
N S,
CHO
ICES,
AND
LOO
PS
8
5
4
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
r
:
=
1
1
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
w
hi
le
r
<=
la
st
row
r
ep
eat
:=
1
-
-
I
nd
ex
of
f
irs
t
ol
um
n
w
hil
e
<=
la
st
ol
r
epe
at
if
e
lt
(m,
r,
)
<
0
the
n
ou
tp
ut
[r
, ,
el
t(
m,r
,
)℄
r
:=
la
st
row
br
ea
k
-
-
3
.7.
FU NCTIO
N S,
CHO
ICES,
AND
LOO
PS
8
7
Typ
e:
3
.8.
N UMBE
RS
8
9
the
)read
yields:
f
or
a
in
1
..4
f
or
b
in
8.
.5
by
-
1
r
ep
ea
t
o
utp
ut
[
a,b
℄
[1,
8℄
[2,
7℄
[3,
6℄
[4,
5℄
Typ
e:
Voi
d
No
t e
t ha
t
wit ho
ut
the
\
b
y
-
1"
t he
segmen
t
8
..5Typ
9
0
CHAPTE
R
3.
ST
A R
TING
AXIOM
T
yp
e:
F
a t
or
ed
In
te
ger
In
teg
ers
ca
n
a
lso
b
e
di s
pla
y
ed
t o
ba
ses
o
t her
t ha
n
1
0.
This
is
an
in
teger
in
bas
e
1
1.
r
adi
x(
259
37
424
60
1,
11)
1
00
00
00
00
00
Ty
pe
:
Ra
dix
Ex
pa
nsi
on
11
Roma
n
n
umera
ls
a
r Tj 27.12 ma
n
n
umera
3
.8.
N UMBE
RS
9
1
Ty
pe
:
Si
ngl
eI
nt
ege
r
Ma
c
hine
double-pr
ecision
oa
tin g
-p
oin
t
n
um
b
ers
a
re
a
lso
a
v
aila
b le
for
n
umeric
a
nd
gr
aphica
l
applica
t io
ns.
1
23
.21
D
ou
ble
Fl
oat
12
3:2
10
00
000
00
00
01
Ty
pe:
Dou
bl
eF
loa
t
The
nor
mal
o
ating-
p
o
in
t
t
yp
e
in
A x
iom,
Fl
oa
t,
is
a
so
f t
w
ar
e
implemen
tation
o
f
o
ating-
p
o
in
t
n
u m
b
er
s
in
whic
h
the
exp
onen
t
and
the
m a
n
tissa
m a
y
ha
v
e
a
n
y
9
2
CHAPTE
R
3.
ST
A R
TING
AXIOM
d
igi
ts
(40
);
ex
p(
%p
i
*
s
qrt
1
63
.0)
2
62
53
74
1
2
64
07
68
74
3:9
99
99
99
99
9
992
50
07
25
9
76
Ty
pe
:
Fl
oat
Here
ar
e
co
mpl e
x
n
um
b
ers
with
ra
tional
n
um
b
er
s
3
.8.
N UMBE
RS
9
3
u
+
v
i
Typ
e:
C
om
ple
x
Po
lyn
om
ial
I
nt
ege
r
O
f
cour
se,
y
ou
can
do
co
m plex
ar
it hmetic
with
these
also
.
%
*
*
2
v
2
+
u
2
+
2
u
v
i
Typ
e:
C
om
ple
x
Po
lyn
om
ial
I
nt
ege
r
E
v
e
ry
r
ationa
l
n
u m
b
er
haor6 Tf 105 26.16 T8ehaor6 Tf 105
3
.8.
N UMBE
RS
9
5
Since
7
is
prime,
y
ou
can
in
v
er
t
nonzer
o
v
a
lues.
1
/x
3
T
yp
e:
P
rim
eF
ie
ld
7
Y
o
u
can
also
co
m pute
mo
dulo
an
i n
t eg
er
th a
t
is
n o
t
a
prime.
y
:
I
nt
eg
erM
od
6
:=
5
5
T
yp
e:
I
nte
ge
rM
od
6
All
o
f
th e
usual
ar
i thmetic
o
p
er
ations
ar
e
a
v
aila
bl e
.
y
**
3
5
T
yp
e:
I
nte
ge
rM
od
6
In
v
er
sion
is
noTd (eI(e:)Tj 21 0 (e:)Tj4b:)Tj 21Td (5)Tj /R81 0.12yp
Qd (5)Tj /RnfTodnoT1
9
6
CHAPTE
R
3.
ST
A R
TING
AXIOM
This
de nes
a
to
b
e
a
n
alg
ebra
i c
n
um
b
e
r,
that
is,
a
3
.9.
D
A
T
A
STR
UCTURES
9
7
2
/%
+1
0
a
4
a
3
+
2
a
2
a
+
1
b
3
+
a
4
a
3
+
2
a
2
a
+
1
b
2
+
a
4
a
3
+
2
a
2
a
+
1
b
+
a
4
a
3
+
2
a
2
a
+
3
1
A
0
a
4
a
3
+
2
a
2
a
+
1
b
3
+
a
4
a
3
+
2
a
2
a
+
1
b
2
+
a
4
a
3
+
2
a
2
a
+
1
b
+
a
4
a
3
+
2
a
2
a
+
1
1
A
Ty
pe:
Ex
pre
ss
ion
I
nt
ege
r
B
u t
w
e
need
t o
r
ationa
9
8
CHAPTE
R
3.
ST
A R
TING
AXIOM
u
:=
[
1,-
7,
11℄
3
.9.
D
A
T
A
STR
UCTURES
9
9
1;
7;
1
1;
9
T
yp
e:
L
ist
I
nt
ege
r
A
st
r
e
a m
is
a
structure
that
(p
o
t e
n
t ia
lly)
h a
s
a
n
in nite
n
um
b
er
of
disti nct
e
l e
m en
t s
.
Think
o
f
a
strea
m
as
an
\
in nite
list"
where
elemen
ts
a
re
co
mpu ted
s
uccessiv
ely
.
Cr
ea
t e
an
in nite
strea
m
of
f a
ct o
re
d
in
teger
s.
Only
a
certa
i n
n
um
b
1
00
CHAPTE
R
3.
ST
A R
TING
AXIOM
O
n e
-dim e
n s
ional
ar
ra
ys
a
re
also
m
u ta
ble:
y
ou
c
an
c
hang
e
their
cons
t ituen
t
elemen
ts
\in
pla
ce."
a
.3
:=
11
;
a
1
;
7
;
11
;
3
2
Ty
pe
:
On
eD
ime
ns
ion
al
Ar
ray
F
ra
ti
on
In
te
ger
Ho
w
ev
er,
one-
dim e
n s
ional
ar
ra
ys
a
re
not
exible
str
u c
t ur
es.
Y
o
u
canno
t
d e
-
str
u c
t iv
ely
on a t!
them
tog
et her
.
on
at
!(a
,o
neD
im
en
sio
na
lAr
ra
y
[1,
-2
℄)
T
he
re
ar
e
5
e
xp
ose
d
and
0
u
nex
po
sed
l
ibr
ar
y
ope
ra
tio
ns
n
ame
d
on
a
t!
hav
in
g0.12 Tf -308.28ysedOn
3
.9.
D
A
T
A
STR
UCTURES
10
1
A
exi blea rr
3
.9.
D
A
T
A
STR
UCTURES
10
3
Typ
e:
Mul
ti
set
I
nt
ege
r
A
t
a ble
i s
conceptually
a
set
of
\
k
ey{
v
alue"
p a
irs
and
is
a
gener
aliza
t io
n
of
a
m
u ltiset.
F
or
e
xamples
of
ta
b le
s,
s
1
04
CHAPTE
R
3.
ST
A R
TING
AXIOM
d
ani
el
:
R
e o
rd
(a
ge
:
In
te
ge
r,
sa
lar
y
:
3
.10
.
E
X P
AN DING
TO
H IGHER
D IME
N SIO
N S
10
5
3.10
Expa n
ding
to
Higher
Di mensions
T
o
g
et
higher
dim e
n s
ional
ag
gr
ega
t e
s,
y
3
.11
.
WRITING
Y O
UR
O
W N
FUNCTIONS
10
7
n
u m
b
er
s
a
s
co
eÆcien
ts.
Mor
eo
v
er,
t he
libr
ar
y
pro
vides
a
w
1
08
CHAPTE
R
3.
ST
A R
TING
AXIOM
This
f unction
is
less
3
.11
.
WRITING
Y O
UR
O
W N
FUNCTIONS
10
9
Ty
pe
:
Po
si
tiv
eI
nt
ege
r
The
libr
ar
y
v
er
sio
n
use
s
an
a
lgo
rithm
that
is
di eren
1
10
CHAPTE
R
3.
ST
A R
TING
AXIOM
Cr
eate
a
n
exa
mpl e
matrix
to
p
er
m
ut e.
m
:=
m
atr
ix
[
[4
*i
+
j
for
j
i
n
1
..
4℄
fo
r
i
i
n
0..
3℄
2
6
6
4
1
2
3
4
5
6
7
8
9
10
1
1
1
2
13
14
1
5
1
6
3
7
7
5
T
ype
:
Ma
tr
ix
In
te
ger
In
ter
c
hang
e
the
se
cond
a
nd
3
.11
.
WRITING
Y O
UR
O
W N
FUNCTIONS
11
1
1
:0
T
ype
:
F
loa
t
Her
e
w
e
de ne
o
u r
o
wn
(user
-de ned)
f unction.
os
inv
(y
)
==
o
s(1
/y
)
Typ
e:
Voi
d
P
a
ss
t his
f unction
a
s
an
a
rg
um en
t
t o
t.
t
(
osi
nv
,
5.2
05
8)
1:
3
3
.12
.
P
OL
YNOMIALS
11
3
m
:
MP
OL
Y(
[x,
y℄
,IN
T)
:
=
(
x*
*2-
x*
y**
3+
3*
y)*
*2
x
4
2
y
3
x
3
+
y
6
+
6
y
x
2
6
y
4
x
+
9
y
2
Ty
pe
:
Mu
lt
iva
ri
ate
Po
lyn
om
ia
l([
1
14
CHAPTE
R
3.
ST
A R
TING
3
.14
.
SE
R IE
S
11
5
l
im
it(
sq
rt
(y*
*2
)/y
,y
=
0)
[l ef
tH
andLi
mit
=
1
;
r
ig
htH
andL
imi
t
=
1]
Ty
pe:
Uni
on
(R
e o
rd
(le
ft
Ha
ndL
im
it:
Uni
on
(O
rde
re
dCo
mp
le
tio
n
Ex
pr
ess
io
n
Int
eg
er,
"f
ail
ed
")
,ri
gh
tHa
nd
Li
mit
:
U
nio
n(
Ord
er
ed
Com
pl
eti
on
E
xpr
es
sio
n
Int
eg
er
,"f
ai
led
")
),
...
)
AsTy6Td ())Tj /R81 0.9 15.72 0pprTd (s)Tj
1
16
CHAPTE
R
3.
ST
A R
TING
AXIOM
T
yp
e:
U
ni
var
ia
te
Pui
se
uxS
er
ies
Tnr
te
3
.14
.
SE
R IE
S
11
7
f
*
*
2
1
+
2
1
18
CHAPTE
R
3.
ST
A R
TING
AXIOM
E
v
a
luate
the
serie
s
a
t
the
v
3
.15
.
DERIV
A
TIVES
11
9
Y
o
u
ca
n
als
o
comput e
par
tial
d er
iv
ativ
es
b
y
sp
ecifying
t he
or
der
of
di ere
n
t ia
-
tio
n .
g
:
=
s
in
(x
**2
+ Td (n)Tj 5.28 -1000(0/R81 0.12 Tf 262.2 0 Td (11)Tj 9.96 0 Td (9)Tj -338.64 2 0 27(x)Tj2
1
20
CHAPTE
R
3.
ST
A R
TING
AXIOM
Y
ou
c
an
use
F,
x ,
and
y
in
expr
essio
ns.
a
:=
F
(x
z,
y
z,
z
**2
)
+
x
y
(z
+1)
x
(y
( z
+
1))
+
F
x
(z
0 Td (+)Tj 10.567[(; 0 4Td [yA)-10 0 cm BT /R81 12 Tf Tf 6.84 0 Td (()Tj /R24 0.12 Tf 3.96 0 Td (z)Tj /R815sio
0 Td (+)Tj 10.567[(; 0 4Td [zA)-10 0366
F
3
.16
.
INTEGRA
TION
12
1
0
B
B
B
B
2
z
2
+
2
z
1
22
CHAPTE
R
3.
ST
A R
TING
AXIOM
omp
le
xIn
te
gra
te
(1
/(x
**
2
+
a
),
x)
lo
g
x
p
a+a
p
a
log
x
p
a
a
p
a
2
p
a
T
yp
e:
E
xp
res
si
on
In
te
ger
The
f o
llo
wing
t
w
o
examples
illu s
t r
ate
t he
limit a
t io
ns
o
f
table-ba
sed
appro
ac
hes.
The
t
w
o
in
tegr
ands
ar
e
v
ery
similar
,
but
the
a
nsw
er
to
one
of
them
r
equires
the
a
d dition
of
t
w
o
new
alg
eb r
aic
n
um
b
ers.
This
o
ne
is
t he
e
asy
o
ne.
The
next
one
lo
o
ks
v
ery
s
i mila
r
but
the
a
nsw
er
is
m
uc
h
more
co
m plica
t ed.
i
nte
gr
ate
(x
**3
/
(
a+b
*x
)**
(1
/3
),x
)
12
0
b
3
x
3
13
5
a
b
2
x
2
+
1
62
a
2
b
x(3)Tj /R395 0.12 T 0 i72 Tf 6.72 3.72 T4 (b)Tj /R366 0.12 1
62
3
.16
.
INTEGRA
TION
12
3
c
onclusiv
e
ly
pr
o
v
es
that
an
in
tegr
al
canno
t
b
e
expres
sed
i n
terms
o
f
elemen
tar
y
functions.
When
A x
iom
returns
a
n
i n
t eg
ra
l
sign,
it
has
pr
o
v
ed
th a
t
no
answ
er
exists
a
s
an
e
l e
m en
t a
ry
f unction.
i
nt
egr
at
e(
log
(1
+
sq
rt
(a*
x
+
b
))
/
x,
x)
Z
x
log
p
b
+
%Q
a
+
1
%Q
d%Q
T
yp
e:
U
nio
n(
Exp
re
ss
ion
I
nte
ge
r,
...
)
Axio
m
can
ha
ndl e
complica
t ed
mixed
f unctions
m
u c
h
b
ey
o
n d
wh a
t
y
o
u
can
nd
in
1
24
CHAPTE
R
3.
ST
A R
TING
AXIOM
1.
If
x
=
tan
t
and
g
=
t a
n(t=3
)
then
the
follo
wing
a
lgebr
aic
r
elation
is
t r
3
.17
.
DIFF E
RENTIAL
E
QUA
TIONS
12
5
y
:
=
o
pe
ra
tor
'
y
y
Ty
pe
:
Ba
si
Op
er
ato
r
Her
e
w
e
so
lv
e
a
third
or
d e
r
eq
u a
tion
with
p
olyno
mial
co eÆ c
ien
ts.
d
eq
:=
x
**
3
*
D
(y
x,
x
,
3
)
+
x
**
2
*
D
(y
x,
x
,
2
)
-
2
*
x
*
D(
y
x
,
x
)
+
2
*
y
x
=
2
*
x
**
4
x
3
y
;;;
( x)
+
x
2
y
;;
( x)
2
x
y
;
( x)
+
2
y
(x)
=
2
x
4
T
ype
:
Eq
ua
tio
n
Ex
pre
ss
ion
I
nt
ege
r
s
ol
ve(
de
q,
y,
x
)
h
par
ti u
l
ar
=
x
5
10
x
3
+20
x
2
+4
15
x
;
b
asis
=
2
x
3
3
x
2
+
1
3
.18
.
SOL
U TIO
N
OF
E
QUA
1
28
CHAPTE
R
3.
ST
A R
TING
AXIOM
T
yp
e:
V
oid
Find
the
re
al
r
o
ots
of
S
(1
9)
with
r
ationa
l
ar
it hmetic,
co
rr
ect
to
wit hin
3
.18
.
SOL
U TIO
N
OF
E
QUA
TIONS
12
9
e
qn
s
:
=
[x
**2
-
y
+
z,
x**
2*
z
+
x
**4
-
b
*y,
y
**2
*
z
-
a
-
b*
x℄
*
C
hapte r
4
G
raphi s
Figure
4.1
:
1
32
CH AP
TER
4
.
GRAPHICS
13
3
Pl
otting
2D
gra phs
of
1
v
ariable
The
gener
al
fo
rmat
fo
r
dr
a
w
i ng
a
fu nctio
n
de ned
b
y
a
for
m
ula
f
(x )
is
:
d
raw
(f
(x
),
x
=
a
..
b,
o ptions)
wher
e
a
: :b
de nes
th e
r
ange
o
f
x ,
and
wher
e
1
34
CH AP
TER
4
.
GRAPHICS
Plo
t ti
ng
2D
para m
13
5
Pl
otting
2D
a l
gebrai
urv
es
The
g
enera
l
f o
rma
t
fo
r
dra
wing
a
non-
singular
so
lu tio
n
c
u r
v
e
giv
e
n
b
y
a
p
olyno
mial
o
f
th e
f o
rm
p( x;
y
)
=
0
is:
dr
aw
(p
(x,
y)
=
0,
x,
y
,
ran
ge
==
[
a.
.b,
..d
℄,
op t
i ons)
wher
e
th e
s
econd
a
n d
third
ar
gumen
ts
na
m e
the
rs
t
a
nd
s
econd
indep
e
n den
t
v
a
riables
of
p.
A
r
an
ge
option
is
a
lw
a
ys
g
iv
en
to
designa
te
a
b
ounding
r
ectang
u la
r
r
egio
n
of
the
plane
a
x
b
;
y
d.
Z
ero
or
mor
e
additi o
nal
o
pt io
ns
a
s
des
crib
ed
in
4
.0.1
on
pa
ge
13
6
m a
y
b
e
giv
en.
A
third
k
i nd
o
f
t
w
o-
dim e
n s
ional
g
ra
1
36
CH AP
TER
4
.
GRAPHICS
co
me
to
a
p
o
in
t
(cusp).
Algebr
aica
lly
13
7
adaptiv
e
T
h e
ad
apt
iv
e
o
pti o
n
turns
ada
p tiv
e
plotting
o
n
o
r
o
.
Ada
p tiv
e
plotting
us
es
a
n
1
38
CH AP
TER
4
.
GRAPHICS
13
9
Fig
u r
e
4
.6:
Tw
o-dimensio
nal
co
n
tro
l-panel.
14
1
Pi
k :
k :
1
42
CH AP
TER
4
.
GRAPHICS
ax e
sCol
orD e
f ault
([
o l
or (dar k
bl ue()) ])
sets
o
r
indica
t es
th e
def a
ult
colo
r
o
f
t he
axes
in
a
t
w
o-
dim e
n s
ional
gr
aph
viewp
o
rt.
li
pP
oi
n
ts
darda (ul)
(
[ o
1
44
CH AP
TER
4
.
GRAPHICS
regi
on
(
viewp
o rt,
int e
ge r(1) ,
str i
ng ("of f"))
d e
clar
es
whether
g
ra
ph
i nt
e
ger
is
or
is
no
t
to
b
e
displa
y
ed
wit h
a
b
o
undi ng
rectang
le.
rese
t
(vi
e wp
or
1
46
CH AP
TER
4
.
GRAPHICS
p
8
:
=
poi
nt
[.
5,
1℄
$(P
oi
nt
DF
LO
AT)
1
48
CH AP
TER
4
.
GRAPHICS
p
3
:=
pa
st
el
ye
ll
ow(
)
[ Hue:
1
1W
eigh
t:
1
:0]
fr
om8i48 20 TdasTj 4.6 te
1
5068 762571 0.12 Tf216.482 0 Td[(CH)-1000(AP)]TJ 284.92 0 Td TER068 24.792 0 Td 41
15
3
f
or
p
in
lp
r
epe
at
o
mp
on
ent
(g
,p,
po
in
tCo
lo
rDe
fa
ult
()
,l
ine
Co
lor
De
fa
ult
()
,
po
in
tSi
ze
De3f0sCdfafa
inin
lorp
lorplorin
ofa
m (in)Tj 15.72 0ak())Tj 10.44 0 TdViinine
on
inlorpoinDe3f0sCdDe
,3ze)
De
1
54
CH AP
TER
4
.
GRAPHICS
15
5
Pl
otting
3D
fun tio
ns
of
2
v
a riabl
es
The
gener
al
f o
rma
t
f o
r
dra
wing
a
surfac
e
de ned
a
1
56CH AP1t tipara metr ispac ec urv
15
7
Pl
otting
3D
pa ram
etri
surfa es
1
58
15
9
4.0.9
Three- Di
m
en si
ona l
Con
trol
-P
ane l
O
nce
y
oC7ron
1
60
CH AP
TER
4
.
GRAPHICS
ob
je
t:
The
ob
je t
button
indicates
that
the
ro
tation
is
to
o
ccur
with
res
p
ec
t
to
t he
cen
ter
o
f
v
o
l ume
o
f
t he
o
b
ject,
indep
enden
t
of
the
ax
es'
or
igin
p
os
it io
n.
S a l
e:
A
scaling
t r
ans
f o
rmatio
n
o ccurs
b
y
clic
king
t he
mo
use
1
62
CH AP
TER
4
.
GRAPHICS
BW
co
n
v
er
ts
a
co
lor
viewp
or
t
to
b la
c
k
and
whi te,
or
vic
e-v
e
rsa
.
When
this
b utton
is
selected
th e
con
tr
ol-pa
nel
and
viewp
or
t
switc
h
to
a
n
imm
ut a
ble
colo
rmap
co
mp
o
sed
o
f
a
ra
nge
o
f
gr
ey
sca
le
patterns
or
t iles
t ha
t
ar
e
used
wh e
rev
eTj 8.88 s is
neces
sar
y
.
Ligh
t
ta
k
esj 8.88 s
16
3
Vi
ew
V
ol
um
e
The
V i
ew
V
o
lum
e
but to
n
c
hang
es
the
co
n
1
16
5
s
etAda pti
v
e3D
(b
o
ol
e 0 Td e (o)Tj 4.39[Tj t6 0 Td rue)D16
16
7
vi
ewS ale
D e
f aul
t
([ o
a t
1
68
CH AP
TER68TER
C
1
70
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
-
3
3
Ty
pe
:
In
te
ger
Here
w
e
crea
te
a
r
ationa
l
n
um
b
er
bu t
i t
lo
oks
lik
e
the
las
t
res
ult .
5
.1.
TH E
BASIC
I
D E
A
17
1
An
y
doma
in
can
b
e
re
ned
t o
a
su
b
d omai n
b
y
a
mem
b
er
ship
p
re
di
at
e.
A
p
re
di
at
e
is
a
f unction
t ha
t ,
when
a
pp244 0 an
1
72
CHAPTE
R
5
.1.
TH E
BASIC
I
D E
A
17
3
1
74
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
P
oly
n o
mial
Squa
reMa
trix(7,Co
mp le
x
In
teg
er)
T
yp
e:
D
om
ain
Another
common
c
atego
ry
is
F
iel
d,
the
cla
ss
o
f
al24 0 4o elds68 0 29 0.12 Tf 5A6 0 Td (o)]TJ 10 eld0 Td (S36y)Tj 12.24 0 3 0.12 Tf 9a4 0 Td(ss)Tj 11Td (An 0.12 Tf 9ing 0 Td ((om)Tj 10with 0 T1 04S36yTd 88 Tf 9a4 0 40(O)]TJ 16.d 0 Td [ditiona-1000(6y)Tj 12l28 0 T7,Co)Tj 39o6 02Td [era-100004S1O)]TJ 16.t 0 Td [i[(n)-101Td (x)Tj 8ns68 0 d ((o)]TJ 10.84 0 Td (x)Tj 8or2 0 Td d (,)Tj 5example.28 041Td (x)Tj 8a4 0 7Td (o)Tj 4 eld0 Td (S36y)Tj 12ha6 0 Td (om)Tj 10s92 0 T9er)Tj 38.74 0 3 3,Co
M
5
.1.
TH E
BASIC
I
D E
A
17
5
1.
a
n a
me
(f o
r
e
xample,
R
in
g),
use
d
t o
1
76
CHAPTE
R
5.
U SING
5
.2.
W RITING
TYP
ES
AND
M O
DES
17
7
When
migh
t
y
5
.2.
W RITING
TYP
ES
AND
M O
DES
17
9
If
the
t
y
p
e
it se
lf
ha
s
pa
ren
t hese
s
a
ro
u nd
it
and
w
e
ar
e
no
t
in
t he
cas
e
o
f
the
r
st
exa
mpl e
ab
o
v
e,
t hen
t he
p a
ren
t hes
es
ca
n
usua
ll y
b
e
omitted.
(
2/
3)
Fr
a
tio
n(
Pol
yn
om
ial
I
nte
ge
r)
2
3
T
ype
:
Fr
a
tio
n
Po
lyn
om
ial
I
nt
ege
r
If
t he
t
yp
e
i s
use
d
in
a
d e
clar
ation
and
t he
ar
gumen
t
is
a
single-
w
or
d
t
y
p
e,
in
t eg
er
or
sym
b
o
l,
th e
n
t he
par
en
theses
can
usua
lly
b
e
o
mi tted.
(
d,
f,g
)
:
Co
mp
lex
P
ol
yno
mi
al
In
teg
er
Typ
e:
Voi
e:
1
80
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
?
(In
te
ger
),
Ma
tr
ix(
?
(P
ol
yno
mi
al
)),
Sq
ua
reM
at
ri
x(?
,
Int
eg
er
)
( it
re
-
quir
es
a
n
um e
ric
ar
gumen
t)
a
n d
Sq
ua
reM
at
rix
(?
,
?)
a
re
all
in
v
alid.Fhe 0 Td 26.5j -340.32 14 0 Td 9re
1
82
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
Y
ou
can
alw
a
ys
co
m
bine
a
decla
ra
ti o
n
with
an
a
ssig
nmen
t.
When
y
ou
do,
it
is
equiv
ale
n
t
t o
r
st
giv
i ng
a
declar
atio
n
statemen
t,
then
g
i v
in g
a
n
Scan (n76TJ 16.68 0 Td4ar)Tj 26:0 Td (sine)Tj 21I16 05 (st)Tj 1(nte0 Td (sine)Tj 21s (n)Tj 96TJ 16.68yV[T8f 1e)Tj 21I16 05 (yp)Tj 21s (n)Tj 9e:Tj 8.0n
5
.3.
D E
CLARA
TIO
N S
18
3
(
p,
q,r
)
:
Ma
tr
ix
Po
ly
nom
ia
l
?
Typ
e:
Voi
d
h(ia)Tj 10.44 0 Tdhis7.3.72 0 Td nis8.0.44 0 Td eg(?)Tj ..72 0 Td (tr)Tj138.62 0 Tdrea(?)Tj .3.72 0 Td (l)T6 0.12 0 Tdan (d)T1910.44 0 Td maoir(ly)Tj218.48 0 Td p(N)-100a(E)]TJ 10.56 0 Tdrts.(3)Tj /R83 0.12 Tf2-3388 24 0.12 Td )
:l:
d5d3
1
84
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
i
x
+
1
7
y
+
4
i
T
yp
e:
M
atr
ix
Po
ly
no
mia
l
Com
pl
ex
In
te
ger
Note
the
di erence
b
et
w
een
this
a
nd
t he
n e
xt
example.
This
is
a
complex
ob
ject
with
p
olyno
m ia
l
r
eal
a
nd
imag
inary
par
ts.
f
:
C
OMP
LE
X
P
OL
Y
?
:
=
(x
+
7
5
.4.
RECO
R DS
18
5
Ty
pe
:
Re
or
d(
a:
I
nt
ege
r,
b:
S
tr
ing
)
T
o
acce
ss
a
co
mp
o
nen
a
5
.4.
RECO
R DS
18
7
Rec
ords
ma
y
b
e
nested
and
the
selec
t o
r
na
mes
ca
n
b
e
shar
ed
at
di eren
t
lev
els.
r
:
R
e
or
d(a
:
R
e
or
d(b
:
In
te
ger
,
:
I
nt
ege
r)
,
b:
I
nte
ge
r)
Typ
e:
Voi
d
The
reco
rd
d
5
.5.
U NIO
N S
18
9
It
is
p
os
sible
to
cre
ate
unio
n s
lik
e
Un
io
n(
Int
eg
er,
P
osi
ti
ve
Int
eg
er)
but
they
a
re
diÆ c
u lt
to
w
o
rk
with
b
e
cause
of
the
o
v
erla
p
in
the
bra
nc
h
t
1
90
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
1.
A xio
m
nor
mally
co
n
v
erts
a
r
esult
t o
the
tar
get
v
a
lu e
b
efo
re
pa
ssing
it
t o
t he
funct io
n.
If
w
e
left
the
decla
ra
t io
n
in fo
rmation
o
ut
o
f
t his
functi o
n
d e
nition
th e
n
the
s
a
yBr an
h
5
.5.
U NIO
N S
19
1
3
Ty
pe:
Un
ion
(I
1
92
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
5.5.2
Un i
ons
Wi
t
h
Sel
e
tors
Lik
e
r
ecor
ds,
y
ou
ca
n
wr
it e
1
94
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
1
;
7:2
;
3
2
;
x
2
;
"w
al
ly"
Typ
e:
Lis
t
Any
When
w
e
ask
for
th e
elemen
ts,
Axio
m
displa
ys
these
t
yp
e
s.
u
.1
1
Ty
pe:
Pos
it
iv
eIn
te
ger
Actually
,
th e
se
ob
jects
b
elong
to
A
ny
but
A x
iom
automa
t ica
lly
5
.7.
CONVERSION
19
5
B
y
default,
3
has
t he
t
yp
e
Po
si
tiv
eI
nt
ege
r.
3
1
96
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
x
3
i
4
y
2
z
+
1
2
3
i
7
y
4
x
60
9
i
5
Ty
pe:
Sq
uar
eM
atr
ix
(2
,Po
ly
nom
ia
l
F
ra
t
ion
C
omp
le
x
Int
eg
er)
In
ter
c
hang
e
the
P
oly
no
mia
l
and
the
F
ra
ti
on
lev
e
l s
.
m
2
:
=
m1
::
S
qu
ar
eMa
tr
ix(
2,
FR
AC
PO
LY
CO
MPL
EX
I
NT)
"
4
x
3
i
4
2
y
2
z
+1
2
3
i
y
4
7
x
7
60
9
i
5
#
Ty
pe:
Sq
uar
eM
atr
ix
(2
,Fr
a
tio
n
Pol
yn
om
ial
C
omp
le
x
Int
eg
er)
In
ter
c
hang
e
the
P
oly
no
mia
l
and
the
C
omp
le
x
le
v
els.
m
3
:
=
m2
::
S
qu
ar
eMa
tr
ix(
2,
FR
AC
CO
MPL
EX
PO
LY
I
NT)
"
4
x
3
i
4
2
y
2
z
+1
2
5
.7.
CONVERSION
19
7
c
atego
ry
19
9
F
ur
t her
m o
re
,
unl e
ss
y
o
u
a
re
a
ssig
n ing
an
in
t e
Tm-e.84 0 Tdtore
aaTm-).84 Td (GAIN)Tj /100012 06ug1(Tf 22.84 Td 3GAIN)Tj /59cm B24.
2
00
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
T
yp
e:
F
ra
ti
on
In
te
ger
It
mak
es
sense
t hen
tha
t
t his
is
a
list
o
f
2
02
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
Ty
pe
:
Fl
oat
P
erha
ps
w
e
a
5
.9.
P
A
CK
A
GE
CALLING
AND
T
A R
G E
T
TYP
ES
20
3
So
met imes
it
m a
k
es
sense,
a
s
in
this
expr
essio
n,
to
s
a
y
\c
ho
os
e
th e
op
era
tions
in
t his
expres
sion
so
t ha
t
t he
nal
r
esult
is
Flo
at.
(
2/
3)
Fl
oa
t
0:6
66
66
66
66
666
66
66
66
67
T
ype
:
F
loa
t
Her
e
w
e
used
\
2
04
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
This
sa
ys
th a
t
the
o
p
e
ra
t io
ns
s
hould
b
e
c
hos
en
so
that
t he
re
sult
is
a
Po
lyn
om
ial
o
b
j e
ct .
(
(x
+
y
*
%
i)*
*2
)
(Po
ly
nom
ia
l
Com
pl
ex
In
teg
i (eU.%m0(e) (re)Tj 8.2i 0 Td (s)Tj 3.8x0 Td (is)Tj y Td (ial)Tj /R81 7eU.pfyTd (+ Td (i (eU.%m0(e)9 Tf 0)10.4x 0 Tlud66eU.%m0(e)NG)℄T-d ( )10.42 Td (ia)℄TJ /R83 03d (s)TYP3327.96T 0 Td (%)Tj 5.1ype Td (teg)Tj 15.7: Td (teg)Tj 15.72 0 Td (Po)Tj 10.44 0 Td (ly)Tj 10.44 0 Td (ly)Tj 10.4m2 0 Td (Po)Tj 15.72 0 Td (l)Tj 10.44 0 Td (Com)Tj 15.72 0 Td (pl)Tj 10.44 0 Td (ex)Tj 15.72 0 Td (In)Tj 10.44 0 Td (In)Tj 10.4g2 0 Td(ial)Tj /R81 0.12 Tf %(Com)TW 0 Td (t7 Tf 0)10.4d 0 Td 3 (2)Tj 4.9y 0 Td 0)Tj 10.4 12 Td (o)Tj 4.(u0 Td (ra)Tj 8.88 0 Td [(hink)-100oul)Tj 10.4m2ghTd (Thi2)℄TJ 14.4 0 T0.12 Tf 7.3h 0 Td (ia)Tj 10.92 0 Td [(p0 Td [(bn)-100o4om)Tj 15.72f 0 T9 2)℄TJ 14.w 0 Td (s)Tj 3.8e 0 T0.a
5
.10
.
RE
S O
L
VING
TYPE
S
20
5
1
8
1
6
1
4
1
9
Ty
pe:
Mat
2
08
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
ate
go
rie
s
A
be
lia
nG
ro
up
A
BE
LGR
P
A
be
lia
nM
on
oid
A
BE
LMO
N
A
be
lia
nM
on
oid
Ri
ng
A
MR
A
be
lia
nS
em
iGr
ou
p
A
BE
LSG
A
gg
reg
at
e
A
GG
A
lg
ebr
a
A
LG
EBR
A
A
lg
ebr
ai
a
lly
Cl
ose
dF
ie
ld
A
CF
A
lg
ebr
ai
a
lly
Cl
ose
dF
un
ti
on
Spa
e
A
CF
S
A
r
Hyp
er
bo
li
Fu
n t
io
nC
ate
go
ry
A
HY
P
.
..
F
or
eac
h
co
nstructor
in
a
gr
oup,
the
f ull
name
a
n d
the
abbre
viation
is
g
i v
en.
Ther
e
a
re
other
gr
oups
in
e
x p
o
sed.
ls
p
but
init ia
lly
o
nly
the
constr
u c
t o
rs
in
exp
os
ure
g
ro
ups
\
basic"
\
categ
or
ies"
\na
glink"
and
\
anna
"
a
re
exp
osed.
As
an
in
t er
activ
e
user
o
f
Axiom,
y
o
u
do
5
.12
.
CO
MM AND S
F
OR
SNOO
PING
20
9
This
is
a
p
olyno
mi a
l.
x
+
x
2
x
Ty
pe:
Po
lyn
om
ial
I
nt
ege
r
E
xp
ose
Ou
tpu
tF
or
m.
)
se
t
e
xp
os
e
a
dd
o
ns
tr
u t
or
Ou
tp
utF
or
m
Out
pu
tF
orm
i
s
n
ow
e
xpl
i
itl
y
exp
os
ed
in
f
ram
e
G8
232
2
This
is
wha
t
w
e
get
when
O
ut
pu
tFo
rm
is
a
utomatica
l ly
a
v
ailable.
x
+
x
x
+
x
T
ype
:
Ou
tp
ut
For
m
Hide
O
ut
put
Fo
rm
so
w
e
don't
run
in
t o
pro
blems
with
a
n
y
la
ter
e
xamples!
)
se
t
e
xp
os
e
d
ro
p
on
st
ru
to
r
O
ut
put
Fo
rm
Out
pu
tF
orm
i
s
n
ow
e
xpl
i
itl
y
hid
de
n
in
fr
ame
G
82
322
Fina
l ly
,
exp
os
u r
e
is
d o
ne
on
a
f r
ame-
b
y-fra
me
ba
sis.
A
f r
a me
is
one
of
p
o
2
10
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
o
p
er
ations
.
T
h e
mos
t
p
o
5
.12
.
CO
MM AND S
F
OR
SNOO
PING
21
1
RM
ATC
AT
-
Re
ta
ngu
la
rM
atr
ix
Cat
eg
ory
&
RM
ATR
IX
Re
ta
ngu
la
rM
atr
ix
SM
ATC
AT
-
Squ
ar
eMa
tr
ix
Cat
eg
ory
&
SQ
MAT
RI
X
Squ
ar
eMa
tr
ix
Similar
ly
,
if
y
ou
wis
h
to
see
a
ll
p a
c
k
a
ges
w
h o
se
na
m e
s
con
t a
in
\g
aus
s"
,
en
ter
this.
)
wh
at
pa
k
age
g
aus
s
-
--
---
--
--
---
--
---
--
--
Pa
k
age
s
---
--
--
---
--
---
--
--
---
-
P
a
kag
es
w
ith
n
ame
s
ma
t h
in
g
p
at
ter
ns
:
g
au
ss
GA
USS
FA
C
Gau
ss
ian
Fa
t
ori
za
tio
nP
a k
ag
e
This
co
m ma
2
12
CHAPTE
R
5.
U SING
TYPE
S
AND
M O
D E
S
)
dis
pl
ay
op
era
ti
on
o
mp
lex
T
her
e
is
on
e
e
xp
os
ede
C
hapte r
6
U
si
ng
Hy
p
erDo
Fig
ure
6.1:
The
Hyp
er
D o c
r
o
ot
windo
w
pa
ge
Hyp
erDo
c
is
the
ga
t ew
a
y
to
Axio
m.
It's
b
oth
an
on-line
tut o
ria
l
a
nd
a
n
on-line
r
eference
ma
n
ual.
It
also
enables
y
ou
to
use
Axio
m
s
im ply
b
y
using
the
m o
use
a
nd
llin g
in
6
.3.
SCR
OLL
BARS
21
5
Do
wn
Arr o
w
Scro
ll
do
wn
one
line.
P
a g
e
Up
Scr
oll
up
o
ne
pag
e.
P
a g
e
ro
ll
S r
oll
do
wn
o
ne
pag
2
16
CHAPTE
R
6
.
USIN G
HYPE
RD O
C
The
inpu t
ar
ea
g
ro
ws
to
a
ccommo
date
as
m a
n
y
c
ha
ra
cters
a
s
y
o
u
t
yp
e.
Use
the
Ba
k s
pa e
k
ey
to
era
se
c
ha
ra
ct er
s
to
t he
left .
T
o
mo
dif y
wha
t
y
o
u
t
y
p
e,
u s
e
the
r
igh
t -
ar
ro
w
!
6
.7.
EXAMPLE
P
A
GE
S
21
7
The
glos
sar
y
ha
s
an
input
ar
ea
a
t
it s
b
o
tt o
m.
W
e
review
t he
v
a
rio
u s
kinds
o
f
s
ear
c
h
s
t r
ings
y
o
u
can
en 0 Td
2
18
CHAPTE
R
6
.
USIN G
HYPE
RD O
C
its
t ex
t !
Wh en
y
o
u
d o
,
the
example
lin e
is
co
p ie
d
in
to
a
new
in
tera
cti v
e
A x
iom
bu e
r
for
this
Hyp
erDo
c
page
.
Sometimes
one
exa
mple
line
ca
n no
t
b
e
run
b
efor
e
y
o
u
r
un
a
n
ea
rlier
one.
Don't
w
o
r0 Td [(U2F[(d)-1000(o)]T4 47.4 0 Tmaticalld (y)43 49.44 0 Td (sne.)Tj j 12 0 Tdllits)Tj 4.92 0 Td (the)T7j 8.16 0 Td c(un)Tj 20.28 0 Tesstera
C
hapte r
7
I
nput
Fil
es
and
Output
St
y
les
In
this
c
ha
p ter
7
.3.
COMMON
FE
A
TURE
S
OF
USING
OUTP
U T
F
ORMA
TS
22
3
2
24
CHA P
TER
7.
7
.5.
TEX
F
O
RMA
T
22
5
T
ur
n
T
E
X
output
on
a
ga
in.
)
se
t
o
ut
pu
t
t
ex
on
The
c
har
acters
u s
ed
f o
r
the
m a
trix
bra
c
k
ets
ab
o
v
e
a
re
ra
ther
ugly
.
Y
ou
g
et
this
c
har
acter
set
when
y
ou
iss
u e
)s
et
ou
tp
ut
h
ara
t
ers
p
la
in.
This
c
ha
ra
cter
s
et
should
b
e
used
wh e
n
y
o
u
ar
e
r
u nning
on
a
mac
hine
th a
t
do
es
n o
t
supp
o
rt
the
IBM
ex
t ended
ASCI
I
c
har
ac
t er
set.
If
y
o
u
ar
e
running
o
n
an
IBM
w
or
k-
s
t a
tion,
for
example,
i s
sue
)se
t
out
pu
t
ha
ra
te
rs
d
efa
ul
t
t o
get
b
et
2
26
CHA P
TER
7.
IN P
UT
FILES
A ND
OUTP
U T
STY LE
S
\
def
\
s h
{\
mat
ho
p{
\rm
s h
}\
no
lim
it
s}
\
def
\e
rf{
\m
ath
op
{\
rm
er
f}\
no
li
mit
s}
\
def
\z
ag#
1#
2{
{{
\h
fil
l
\le
ft
.
{#1
}
\ri
gh
t|
}
\
ov
er
{
\l
eft
|
{#2
}
\r
igh
t.
\h
fi
ll
}
}
}
7. 6
IBM
S ript
F
o rm
ula
F
o rmat
Axiom
can
pr
o
duce
IBM
Script
F
or
m
ula
F
o
rmat
o
7
.7.
F
OR
TRAN
F
ORMA
T
22
7
Since
so
me
v
er
sio
n s
of
F
OR
TRAN
ha
v
e
restr
ict io
ns
on
the
n
um
b
e
r
of
lines
p
er
sta
t emen
t ,
Axiom
brea
ks
long
expr
essio
ns
in
t o
s
egmen
ts
wit h
a
maxim
um
o
f
13
20
c
har
acter
s
(20
li nes
of
66
c
ha
ra
ct er
s)
p
e
r
seg
men
t.
If
y
ou
w
an
t
c
longj 4.92 0 Td 8n s6cwayTj 10.44 , Td (w)Tj 6.84 0 Td [(t)-1000(o)]ysegchara66haued (seg)th
2
28
7
.7.
F
OR
TRAN
F
ORMA
T
22
9
Ty
pe:
Po
lyn
om
ial
I
nt
ege
r
This
c
2
30
CHA P
TER
7.
IN P
UT
FILES
A ND
OUTP
U T
STY LE
S
R8=
SI
N(E
XP
C
hapte r
8
Axi
om
Sy
stem
Commands
This
c
ha
p ter
descr
ib
es
sys
t e
m
commands,
the
co
mmand-line
facilities
u s
ed
to
c
on
8
.2.
) ABB
R E
VIA
TIO
N
23
5
8.2
)a b
brevi ati on
Use
r
Lev
e
l
R
equired:
compiler
2
36CH AP
8
.5.) CL
238
8
.7.
) CO
MPILE
23
9
)
l
ear
v
al
ue
al
l
)
l
ear
v
a
ll
This
re
t a
ins
wha
t e
v
er
decla
ra
t io
ns
the
ob
jects
h a
d.
T
o
r
emo
v
e
d e nitions
and
v
a
lues
for
the
sp
eci c
o
b
jects
x
,
y
a
nd
f,
i s
sue
)
l
ear
v
al
ue
x
y
f
)
l
ear
v
x
y
f
T
o
re
m o
v
e
th e
declar
2
40
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
) o
mp
ile
l eName.a
l
) o
mp
ile
di r
e
Des riptio(mp)51.20.44 0 Tn:ile
8
.38) CO
2
42
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
-
O
-
Fa
sy
-F
ao
-F
ls
p
-
la
xio
m
-M
no-
AX
L_W
_W
ill
Ob
so
let
e
-DA
xi
om
These
options
mean:
-O:
p
er
f o
rm
all
o
pt imiza
t io
ns,
-Fa
sy
:
gener
ate
a
.
asy
le,
-Fa
o:
g
enera
t e
a
.a
o
le,
-Fl
sp
:
gener
ate
a
.
8
.7.
) CO
MPILEMPILE
2
44
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
)
om
pi
le
ma
tri
x.
sp
ad
)
edi
t
)
om
pi
le
will
call
the
c
ompiler,
edit,
and
t hen
ca
l l
the
compiler
a
ga
in
o
n
the
le
m
a-
trix.s
pa d.
If
y
o
u
do
no
t
s
p
ecify
a
d ir
e
t
8
.8.
) DISPL
A
Y
24
5
8.8
)displa
y
Use
r
Lev
e
l
R
equired:
i n
t er
preter
Co
m
m
a nd
Syn
tax:
)d
is
pla
y
all
)d
is
pla
y
pro
pe
rti
es
)d
is
pla
y
pro
pe
rti
es
a
ll
)d
is
pla
y
pro
pe
rti
es
[tax:es
[
2
46
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
8
.10
.
)FIN
24
7
)
sy
ste
m
em
a s
/
et
/r
.
t p
ip
c
alls
e
ma
s
2
48
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
Some
fra
m es
a
re
crea
ted
b
y
the
Hyp
erDo
c
pro
gr
am
2
50
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
)
hel
p
le
ar
will
displa
y50)
8
.14
.
)HISTOR
Y
25
1
ha
s
b
een
is
sued.
Issuing
eit her
)
se
t
h
is
to
ry
of
f
)
hi
sto
ry
)
off
will
d is
con
tin
ue
t he
reco
rding
of
infor
m a
tion.
Whether
the
facilit
y
is
disa
b led
or
not,y
2
52
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
)
res
et
will
us
h
the
in
t er
nal
list
o
f
the
mo
st
r
ecen
t
w
o
rkspa
ce
calcula
t io
ns
so
t ha
t
t he
d a
ta
s
t r
uct ur
es
ma
y
b
e
g
ar
bag
e
co
llect e
d
b
y
the
underly
i ng
Common
Lisp
sy
stem.
Lik
e
)h
ist
or
y
)
h
ang
e,
t his
option
only
has
rea
l
e ect
w
h en
hi s
t o
ry
data
is
b
eing
sa
v
ed
in
a
le.
)
res
to
re
[sav e
d HistoryName
]
co
mp letely
clear
s
the
en
v
iro
n men
t
a
nd
re
store
s
i t
t o
a
s
a
v
ed
s
essio
n ,
if
p
o
ssible.
The
)s
av
e
option
8
.16
.
)LISP
25
3
)l
ib
rar
y
)no
ex
pos
e
Co
m
m
a nd
Des
ripti
on:
This
comma
n d
repla
ces
the
)lo
ad
sys
t em
command
tha
t
w
as
a
v
aila
b le
in
Axiom
r
elea
ses
2
54
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
Since
th is
co
mmand
is
only
useful
fo
r
ev
alua
t ing
s
in g
le
expre
ssions
,
t he
)
fin
co
mm a
nd
ma
y
8
.19
.
)QUIT
25
5
8.19
)qui t
Use
r
Lev
e
l
R
equired:
i n
t er
preter
Co
m
m
a nd
Syn
tax:
)q
ui
t
)s
et
qu
it
pr
ot
e t
ed
|
un
pr
ote
t
ed
Co
m
m
a nd
Des
ripti
on:
This
comma
n d
2
56
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
will
rea
d
the
c
on
ten
ts
of
t he
le
m
a trix.
input
in
t o
Axio
m.
T
h e
\
.i nput"
le
extensio
n
is
o
pti o
nal.
This
co
mmand
remem
b
er
s
the
previo
us
le
y
o
u
edited,
rea
d
or
compiled.
If
y
o
u
do
not
sp
ecify
a
le
na
me,
th e
prev
ious
le
will
b
e
rea
d.
The
)
if
the
re
option
c
hec
ks
t o
see
whet her
the
8
.22
2
58
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
)
sho
w
POL
Y
INT
)
op
era
ti
ons
)
sho
w
Pol
yn
omi
al
I
nte
ge
r
)
sho
w
Pol
yn
omi
al
I
nte
ge
r
)
op
er
ati
on
s
a
re
a
mong
th e
com
rm2 T
8
.25
.
)SYS TE
M
25
9
This
command
is
used
to
cr
ea
t e
shor
t
synon
yrrop9e624i
2
60
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
W
e
do
no
t
r
8
.26
.
)TRA
CE
26
1
8
.26
.
8
.28
.
)WH A
T
26
2
66
CH AP
TER
8
.
AXIOM
SYSTEM
COMMAN DS
)ap
ro
pos
p
att
ern1
[p
a t
tern2
.. .]
Com
m
and
Des riptio
n:
This
co
m ma
nd
is
used
8
.29
.
MAKE
FILE
26
7267
Bi
bliograph
y
[1]
Jenks
,
R.J.
and
S uto
r,
R .S.
\Axio
m
{
The
S c-1000u33i 0 Td [eS
I
n dex
Mult iplica
t io
n,
39
E
xp
onen
tiatio
n ,
39
+
Ad dition,
39
Nu mer
ical
N eg
atio
n ,
39
Sub tr
action,
39
=
D iv
ision,
3
9
<
less
t ha
n,
39
<
=
les
s
than
o
r
equal,
39
=
>
blo
c
k
exit,
7
8,
80
,
81
>
gr
eater
than,
3
9
>
=
g
rea
ter
tha
n
or
equa
l,
39
~
L
og
i c
al
Neg
ation,
3
9
)abb,
1
80
)abbr
eviation,
18
0,
2
44
)b
o ot,
2
36
,
25
4,
2
60
,
2
64
)cd,
2
36
,
25
3,
258
)clear
,
5
0,
2
388 Td (+)Tj 11.04 0 Td [4)cd,
INDEX
27
3
s
t a
rt-up
pr
o le,
2
22
n,
2
47
r
st,
5
5,
9
8
rst
,
97
r
stD eno
m,
46
r
stN umer
,
4
6
Flexible
A r
ra
ys
,
69
FlexibleAr
ra
y
,
6
7
ex
ib leAr
ra
y
,
1
01
Flo
at,
9
1,
1
69
,
2
01
o
ating
p
o
in
t,
91
fo
n
t ,
21
8
fo
r,
8
5
fo
r
b
y
,
88
fo
r
list,
8
5
fo
r
s
egmen
t,
8
5
F
OR
TRA N,
1
3
F
OR
TRA N
o
utp ut
for
mat,
2
26
a
rr
a
ys,
2
30
br
eak
i ng
in
to
m
ultiple
s
t a
t e
m en
t s
,
2
27
da
t a
t
yp
es,
22
8
in
t eg
ers
vs.
o
ats,
22
8
line
l e
n g
th,
22
7
o
pt imiza
t io
n
lev
el,
22
8
pr
ecisio
n ,
22
9
F
r
action,
18
,
17
4,
17
6,
191
,
2
01
,
2
04
fr
action
pa
rtial,
93
F
r
action(Complex(In
teg
er)),
17
4
F
r
action(In
tege
r),
1
74
fr
actionP
ar
t,
35
fr
ame,
2
09
,
24
7
ex
p
o
sure
and,
2
09
fr
ame
dr
op,
2
48
fr
ame
f1.88 Td (fr)Tj 6f1.88 Tdn6 0 Td (24)Tj 9.96 0 T (48)T73-88.56 12 Td (fr)Tj 6.84 0 Td (ame)Tj 21.12 0 Tla(in)Tj16.68 0 Td (st,)Tj 13.92 0 Td (24)Tj 9.96 0 T (48)T59-92.52 11.88 Td (fr)Tj 6.84 0 Td (ame)Tj 21.12 0 (n (da)Tj 10.44 0 Tdm[(l)-1000(e)]Tj 81.72 0 Ts (r,)Tj 10.08 0 Td (2)Tj 4.92 0 Td (48)Tj -66.12 12 Td (fr)Tj 6.84 0 Td (ame)Tj 21.12 0 (newame,)Tj 16 0 Td (24)Tj 9.96 0 T (48)Tj -13.08 12 Td (fr)Tj 6.84 0 Td (ame)Tj 21.12 0 (nex(mat,)T5 22.2 0 Td (2)Tj 4.92 0 Td (48)Tj -058.8 11.88 Tdun (action,)j -41.92 0 Td (1)Tj 4.92 0 T0 (27)Tj6-41.76 12 Tca(dr)Tj 9.36 0 Tld (gial,)Tj 9.96 0 Td (3)Tj 4.92 0 T0(30)Tj9 12.08 12 Tdiece-al,)Tj 6.84 0 Twis(ame)Tj 81.72 0 Tde ni(action,)j7j 8.04 0 Td (1)Tj 4.92 0 T0 (27)T1Tj 10.Tj 6. 0 TGalev)Tj 81.72 0 Tussiaametege
ra
74
,t,
o
1ar
,48
INDEX
27
5
a
daptiv
e,
14
1
a
xes
colo
r,
1
42
clip
p
o
in
t s
,
14
2
line
colo
r,
1
42
ma
x
p
oin
ts,
14
2
min
p
oin
ts,
14
2
p
oin
t
colo
r,
1
42
p
oin
t
size,
1
42
r
eset
v
i e
wp
o
rt,
1
42
s
creen
reso
lut io
n,
1
42
to
sca
le,
1
42
units
co
lor
,
1
42
v
i e
wp
o
rt
p
os
INDEX
27
7
P
o
stScript,
13
2,
14
1,
1
62
,
Wyszukiwarka
Podobne podstrony:
Axiom Volume 1Tutorial (2005)
2005 Volume 46 2 171 177
dr dobbs journal volume 30 issue 2 number 369 february 2005 een www!osiolek!com LJHWNJQZ7RJVY7VF3ROE
BS EN ISO 1133 2005 Plastics Determination of the melt mass flow rate (MFR) and the melt volume flow
AM1 2005 W1upg
Wytyczne ERC 2 2005
BYT 2005 Pomiar funkcjonalnosci oprogramowania
Wyklad3 2005
SWW epidem AIDS 2005
gemius 2005 zagrozenia
Świecie 14 05 2005
Walproiniany 2005
1 Podstawy diagnostyki w chorobach nerek 2005
N T 2005(fizjoterapia)
więcej podobnych podstron