AXIOM SESSIONscale=2.5]
N := NonNegativeInteger
(1) NonNegativeInteger
Type: Domain
Time: 0 sec
Z := Integer
(2) Integer
Type: Domain
Time: 0 sec
UZ := UnivariatePolynomial(x,Z)
(3) UnivariatePolynomial(x,Integer)
Type: Domain
Time: 0 sec
u: UZ := (3*x-1)**2 * (2*x + 8)
3 2
(4) 18x + 60x - 46x + 8
Type: UnivariatePolynomial(x,Integer)
Time: 0.01 (OT) = 0.01 sec
v: UZ := (1 - 6*x + 9*x**2)**2
4 3 2
(5) 81x - 108x + 54x - 12x + 1
Type: UnivariatePolynomial(x,Integer)
Time: 0.01 (OT) = 0.01 sec
u**2 + u*v
7 6 5 4 3 2
(6) 1458x + 3240x - 7074x + 10584x - 9282x + 4120x - 878x + 72
Type: UnivariatePolynomial(x,Integer)
Time: 0.01 (OT) = 0.01 sec
leadingCoefficient u
(7) 18
Type: PositiveInteger
Time: 0 sec
degree u
(8) 3
Type: PositiveInteger
Time: 0 sec
reductum u
2
(9) 60x - 46x + 8
Type: UnivariatePolynomial(x,Integer)
Time: 0 sec
gcd(u,v)
2
(10) 9x - 6x + 1
Type: UnivariatePolynomial(x,Integer)
Time: 0 sec
factor(u)
2
(11) 2(x + 4)(3x - 1)
Type: Factored UnivariatePolynomial(x,Integer)
Time: 0 sec
factor(v)
4
(12) (3x - 1)
Type: Factored UnivariatePolynomial(x,Integer)
Time: 0 sec
PZ := Polynomial Z
(13) Polynomial Integer
Type: Domain
Time: 0 sec
pz: PZ := (4*x**3+2*y**2+1)*(12*x**5-x**3*y+12)
3 3 5 2 6 3 8 5 3
(14) - 2x y + (24x + 24)y + (- 4x - x )y + 48x + 12x + 48x + 12
Type: Polynomial Integer
Time: 0.01 (IN) = 0.01 sec
factor(pz)
3 5 2 3
(15) - (x y - 12x - 12)(2y + 4x + 1)
Type: Factored Polynomial Integer
Time: 0.04 (EV) = 0.04 sec
Q := Fraction Integer
(16) Fraction Integer
Type: Domain
Time: 0 sec
PQ := Polynomial Q
(17) Polynomial Fraction Integer
Type: Domain
Time: 0 sec
pq: PQ := (4*x**3+(2/3)*x**2+1)*(12*x**5-(1/2)*x**3+12)
8 7 6 35 5 95 3 2
(18) 48x + 8x - 2x + -- x + -- x + 8x + 12
3 2
Type: Polynomial Fraction Integer
Time: 0.03 (IN) + 0.01 (OT) = 0.04 sec
factor(pq)
3 1 2 1 5 1 3
(19) 48(x + - x + -)(x - -- x + 1)
6 4 24
Type: Factored Polynomial Fraction Integer
Time: 0.03 (EV) + 0.01 (OT) = 0.04 sec
AXIOM SESSIONscale=2.5]
P := UnivariatePolynomial(x,Fraction Integer)
(1) UnivariatePolynomial(x,Fraction Integer)
Type: Domain
Time: 0 sec
euclideanGcd(a,b) ==
l := [a];
a:=unitCanonical a
b:=unitCanonical b
while not zero? b repeat
l := cons(b,l)
(a,b):= (b,a rem b)
b:=unitCanonical b
reverse l
Type: Void
Time: 0 sec
p1: P := x^8 + x^6 -3*x^4 -3*x^3 +8*x^2 +2*x -5
8 6 4 3 2
(3) x + x - 3x - 3x + 8x + 2x - 5
Type: UnivariatePolynomial(x,Fraction Integer)
Time: 0.01 (OT) = 0.01 sec
q1: P := 3*x^6 + 5*x^4 - 4*x^2 -9*x +21
6 4 2
(4) 3x + 5x - 4x - 9x + 21
Type: UnivariatePolynomial(x,Fraction Integer)
Time: 0.01 (IN) + 0.01 (OT) = 0.02 sec
euclideanGcd(p1,q1)
(5)
8 6 4 3 2 6 5 4 4 2
[x + x - 3x - 3x + 8x + 2x - 5, x + - x - - x - 3x + 7,
3 3
4 1 2 3 2 25 49 6150
x - - x + -, x + -- x - --, x - ----, 1]
5 5 13 13 4663
Type: List UnivariatePolynomial(x,Fraction Integer)
Time: 0.01 (IN) + 0.01 (OT) = 0.02 sec
p2: P := x^30 + x^19 + 1
30 19
(6) x + x + 1
Type: UnivariatePolynomial(x,Fraction Integer)
Time: 0 sec
q2: P := x^29 - x^17 + 3
29 17
(7) x - x + 3
Type: UnivariatePolynomial(x,Fraction Integer)
Time: 0 sec
euclideanGcd(p2,q2)
(8)
30 19 29 17 19 18
[x + x + 1, x - x + 3, x + x - 3x + 1,
18 17 11 10 9 8 7 6 5 4 3 2
x + x - 3x + 4x - 4x + 4x - 4x + 4x - 4x + 4x - 4x + 4x
+
- 4x - 2
,
12 4 11 4 10 4 9 4 8 4 7 4 6 4 5 4 4 4 3
x - - x + - x - - x + - x - - x + - x - - x + - x - - x
3 3 3 3 3 3 3 3 3
+
4 2 1 1
- x - - x + -
3 3 3
,
11 8732 10 8732 9 8732 8 10919 7 5816 6 10433 5
x - ---- x + ---- x - ---- x + ----- x - ---- x + ----- x
6545 6545 6545 6545 6545 6545
+
676 4 9164 3 8588 2 1756 878
- --- x + ---- x - ---- x + ---- x + ----
595 6545 6545 1309 1309
,
10 9 19619 8 6553 7 15277 6 5 4 3 2
x - x - ----- x - ---- x - ----- x - 729x - 242x - 82x - 26x
16 4 16
+
59065 19555
- ----- x + -----
16 16
,
9 8 1 7 1 6 2 1
x + x + - x + - x + 3x - 2x + -,
3 3 3
8 78620 7 45799 6 34992 5 11616 4 4080 3 864 2
x + ----- x + ----- x + ----- x + ----- x + ----- x + ----- x
58777 58777 58777 58777 58777 58777
+
177403 58697
------ x - -----
58777 58777
,
7 170782 6 2173617 5 1746351 4 5658021 3 8599611 2
x + ------ x + ------- x - ------- x + ------- x - ------- x
923785 3695140 3695140 3695140 3695140
+
2278869 1232437
------- x - -------
739028 1847570
,
6 2515753 5 15269857 4 12227447 3 2492039 2 2531080
x - ------- x + -------- x - -------- x + ------- x - ------- x
142893 428679 428679 142893 428679
+
4446728
-------
428679
,
5 160644757 4 130375607 3 27115175 2 25927747 49124846
x - --------- x + --------- x - -------- x + -------- x - --------,
73785531 73785531 24595177 73785531 73785531
4 4553589485 3 1129145127 2 163361143 2886544997
x - ---------- x + ---------- x + --------- x + ----------,
7507014112 3753507056 234594191 7507014112
3 112557717874 2 270014099776 15748937137
x - ------------ x + ------------ x - ------------,
43571774195 130715322585 130715322585
2 619536582958 472414012299 19773994490288
x - ------------ x + -------------, x + --------------, 1]
633789802471 2535159209884 34258486832515
Type: List UnivariatePolynomial(x,Fraction Integer)
Time: 0.04 (OT) = 0.04 sec