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Contents
CGBLisp User Guide and Manual
Marek Rychlik
Contents
The Gröbner Basis package
*grobner
-
debug*
*buchberger
-
merge
-
pairs*
*gebauer
-
moeller
-
merge
-
pairs*
*grobner
-
function*
select
-
grobner
-
algorithm
grobner
debug
-
cgb
spoly
grobner
-
primitive
-
part
grobner
-
content
normal
-
form
buchberger
grobner
-
op
buchberger
-
sort
-
pairs
mock
-
spoly
buchberger
-
merge
-
pairs
-
use
-
mock
-
spoly
buchberger
-
merge
-
pairs
-
smallest
-
lcm
buchberger
-
merge
-
pairs
-
use
-
smallest
-
degree
buchberger
-
merge
-
pairs
-
use
-
smallest
-
length
buchberger
-
merge
-
pairs
-
use
-
smallest
-
coefficient
-
length
buchberger
-
set
-
pair
-
heuristic
criterion
-
1
criterion
-
2
normalize
-
poly
normalize
-
basis
reduction
reduced
-
grobner
monom
-
depends
-
p
term
-
depends
-
p
poly
-
depends
-
p
ring
-
intersection
elimination
-
ideal
ideal
-
intersection
poly
-
contract
poly
-
lcm
grobner
-
gcd
grobner
-
equal
grobner
-
subsetp
grobner
-
member
ideal
-
equal
ideal
-
subsetp
ideal
-
member
ideal
-
saturation
-
1
add
-
variables
extend
-
polynomials
saturation
-
extension
polysaturation
-
extension
saturation
-
extension
-
1
ideal
-
polysaturation
-
1
ideal
-
saturation
ideal
-
polysaturation
buchberger
-
criterion
grobner
-
test
minimization
add
-
minimized
colon
-
ideal
colon
-
ideal
-
1
pseudo
-
divide
gebauer
-
moeller
update
gebauer
-
moeller
-
merge
-
pairs
-
use
-
mock
-
spoly
gebauer
-
moeller
-
merge
-
pairs
-
smallest
-
lcm
gebauer
-
moeller
-
merge
-
pairs
-
use
-
smallest
-
degree
gebauer
-
moeller
-
merge
-
pairs
-
use
-
smallest
-
length
gebauer
-
moeller
-
merge
-
pairs
-
use
-
smallest
-
coefficient
-
length
gebauer
-
moeller
-
set
-
pair
-
heuristic
spoly
-
sugar
spoly
-
with
-
sugar
normal
-
form
-
with
-
sugar
buchberger
-
with
-
sugar
buchberger
-
with
-
sugar
-
merge
-
pairs
buchberger
-
with
-
sugar
-
sort
-
pairs
criterion
-
1
-
with
-
sugar
criterion
-
2
-
with
-
sugar
gebauer
-
moeller
-
with
-
sugar
update
-
with
-
sugar
gebauer
-
moeller
-
with
-
sugar
-
merge
-
pairs
grobner
-
primitive
-
part
-
with
-
sugar
The String Interface to the Gröbner Basis package
string
-
normal
-
form
string
-
grobner
string
-
elimination
-
ideal
string
-
ideal
-
intersection
string
-
poly
-
lcm
string
-
ideal
-
saturation
-
1
string
-
ideal
-
polysaturation
-
1
string
-
ideal
-
saturation
string
-
ideal
-
polysaturation
string
-
colon
-
ideal
string
-
read
-
poly
poly
-
rational
-
to
-
integer
read
-
vars
The Comprehensive Gröbner basis package
*colored
-
poly
-
debug*
debug
-
cgb
make
-
colored
-
poly
make
-
colored
-
poly
-
list
color
-
poly
-
list
color
-
poly
colored
-
poly
-
to
-
poly
colored
-
poly
-
print
colored
-
poly
-
print
-
list
determine
determine
-
1
determine
-
white
-
term
cond
-
system
-
print
cond
-
print
add
-
pairs
cond
-
part
cond
-
hm
delete
-
green
-
polys
grobner
-
system
reorder
-
pairs
colored
-
criterion
-
1
colored
-
criterion
-
2
cond
-
normal
-
form
cond
-
spoly
cond
-
lm
cond
-
lc
colored
-
term
-
times
-
poly
colored
-
scalar
-
times
-
poly
colored
-
term*
color*
color+
color
-
colored
-
poly+
colored
-
poly
-
colored
-
term
-
uminus
colored
-
minus
-
poly
string
-
grobner
-
system
string
-
cond
string
-
cover
saturate
-
cover
saturate
-
cond
string
-
determine
tidy
-
grobner
-
system
tidy
-
pair
tidy
-
cond
colored
-
reduction
green
-
reduce
-
colored
-
poly
green
-
reduce
-
colored
-
list
cond
-
system
-
green
-
reduce
parse
-
to
-
colored
-
poly
-
list
red
-
reduction
The Coefficient Ring package
ring
*ring
-
of
-
integers*
*field
-
of
-
rationals*
field
-
modulo
-
prime
*coefficient
-
ring*
The Division Package
divide
poly
-
exact
-
divide
The Dynamical Systems package
poly
-
scalar
-
composition
poly
-
composition
poly
-
dynamic
-
power
poly
-
scalar
-
evaluate
poly
-
evaluate
factorial
poly
-
scalar
-
diff
poly
-
diff
standard
-
vector
scalar
-
partial
partial
determinant
minor
drop
-
row
drop
-
column
drop
-
elt
matrix
-
scalar
-
times
-
matrix
monom
-
times
-
matrix
term
-
times
-
matrix
poly
-
list
-
scalar
-
times
-
poly
-
list
monom
-
times
-
poly
-
list
term
-
times
-
poly
-
list
characteristic
-
combination
characteristic
-
combination
-
poly
-
list
characteristic
-
matrix
characteristic
-
polynomial
identity
-
matrix
print
-
matrix
jacobi
-
matrix
jacobian
The Geometric Theorem Prover package
*prover
-
order*
csym
real
-
identical
-
points
identical
-
points
perpendicular
parallel
collinear
equidistant
euclidean
-
distance
midpoint
translate
-
statements
translate
-
assumptions
translate
-
conclusions
translate
-
theorem
prove
-
theorem
The Monomial Order Package
lex
>
total
-
degree
grlex
>
grevlex
>
revlex
>
invlex
>
elimination
-
order
elimination
-
order
-
1
The Polynomial Package
scalar
-
times
-
poly
term
-
times
-
poly
monom
-
times
-
poly
minus
-
poly
sort
-
poly
poly+
poly
-
poly*
poly
-
op
poly
-
expt
poly
-
mexpt
poly
-
constant
-
p
poly
-
extend
poly
-
extend
-
end
poly
-
zerop
lt
lm
lc
The Parser Package
parse
alist
-
form
alist
-
form
-
1
powers
parse
-
to
-
alist
parse
-
string
-
to
-
alist
parse
-
to
-
sorted
-
alist
parse
-
string
-
to
-
sorted
-
alist
sort
-
poly
-
1
sort
-
poly
poly
-
eval
-
1
poly
-
eval
monom
-
basis
convert
-
number
$poly+
$poly
-
$minus
-
poly
$poly*
$poly/
$poly
-
expt
Other packages
makelist
-
1
makelist
sum
list
-
of
list
-
of
-
1
union
-
of
union
-
of
-
1
set
-
of
set
-
of
-
1
select
monom/
monom*
nmonom*
monom
-
divides
-
p
monom
-
divisible
-
by
-
p
monom
-
rel
-
prime
monom
-
equal
monom
-
lcm
monom
-
gcd
poly
-
gcd
poly
-
pseudo
-
divide
poly
-
pseudo
-
remainder
mdeg
lcoeff
lrest
lpart
poly
-
primitive
-
part
poly
-
content
poly
-
with
-
sugar
-
poly
poly
-
with
-
sugar
-
sugar
poly
-
with
-
sugar
-
tail
(setf poly
-
with
-
sugar
-
poly)
(setf poly
-
with
-
sugar
-
sugar)
(setf poly
-
with
-
sugar
-
tail)
monom
-
sugar
coefficient
-
sugar
term
-
sugar
poly
-
add
-
sugar
scalar
-
times
-
poly
-
with
-
sugar
term
-
times
-
poly
-
with
-
sugar
monom
-
times
-
poly
-
with
-
sugar
minus
-
poly
-
with
-
sugar
poly
-
with
-
sugar+
poly
-
with
-
sugar
-
poly
-
with
-
sugar
-
op
poly
-
with
-
sugar
-
nreverse
poly
-
with
-
sugar
-
append
poly
-
with
-
sugar
-
zerop
poly
-
with
-
sugar
-
lm
poly
-
with
-
sugar
-
lc
poly
-
with
-
sugar
-
lt
poly
-
print
poly
-
print
-
1
poly
-
print
-
2
print
-
term
print
-
monom
num
denom
rat
-
simplify
-
2
rat
-
simplify
rat+
rat
-
rat*
rat/
scalar
-
times
-
rat
scalar
-
div
-
rat
rat
-
zerop
rat
-
uminus
rat
-
expt
rat
-
constant
rat
-
to
-
poly
ratpoly+
ratpoly
-
ratpoly
-
uminus
ratpoly*
scalar
-
times
-
ratpoly
rat
-
times
-
ratpoly
ratpoly
-
divide
ratpoly
-
remainder
ratpoly
-
gcd
ratpoly
-
diff
ratpoly
-
square
-
free
ratpoly
-
normalize
ratpoly
-
resultant
deg
lead
ratpoly
-
discriminant
ratpoly
-
print
poly
-
to
-
ratpoly
poly
-
to
-
poly1
poly1
-
to
-
ratpoly
ratpoly
-
to
-
poly1
poly1
-
to
-
poly
ratpoly
-
to
-
poly
poly
-
resultant
term*
term/
monom
-
times
-
term
term
-
divides
-
p
term
-
monom
term
-
coefficient
(setf term
-
monom)
(setf term
-
coefficient)
xgcd
All examples produced by the
all-examples
utility
About this document ...
Marek Rychlik
3/21/1998