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
Marc Moreno Maza