Logging to /Users/s/tmp/pari-10.05
(15:44) gp > M=[1,2,3;8,9,4;7,6,5]

[1 2 3]

[8 9 4]

[7 6 5]

(15:44) gp > matdet(M)
-48
(15:44) gp > 7*21-15*19
-138
(15:46) gp > factor(%)

[-1 1]

[ 2 1]

[ 3 1]

[23 1]

(15:46) gp > M=[1,2,3;8,9,4;7,6,5]

[1 2 3]

[8 9 4]

[7 6 5]

(15:48) gp > #M
3

(15:48) gp > condensar(N)=matrix(#N-1,#N-1,a,b,matdet([N[a,b],N[a,b+1];N[a+1,b],N[a+1,b+1]]))
(N)->matrix(#N-1,#N-1,a,b,matdet([N[a,b],N[a,b+1];N[a+1,b],N[a+1,b+1]]))

(15:49) gp > condensar(M)

[ -7 -19]

[-15  21]

(15:49) gp > condensar(%)

[-432]

(15:50) gp > factor(432)

[2 4]

[3 3]

(15:50) gp > -432/9
-48
(15:50) gp > matdet(M)
-48
(15:51) gp > 144*3
432
(15:51) gp > 7*7
49
(15:51) gp > 5*19
95
(15:52) gp > 49+95
144
(15:52) gp > 144*3
432
(15:52) gp > ?condensar
condensar =
  (N)->matrix(#N-1,#N-1,a,b,matdet([N[a,b],N[a,b+1];N[a+1,b],N[a+1,b+1]]))

(15:52) gp > ?component
component(x,n): the n'th component of the internal representation of x. For 
vectors or matrices, it is simpler to use x[]. For list objects such as nf, bnf, 
bnr or ell, it is much easier to use member functions starting with ".".

(15:53) gp > ??component
component(x,n):

   Extracts the n-th-component of x.  This is to be understood as follows: every
PARI  type  has  one  or  two  initial code words.   The components are counted,
starting at 1, after these code words.   In particular if x is a vector, this is
indeed  the n-th-component of x,  if x is a matrix,  the n-th column,  if x is a
polynomial, the n-th coefficient (i.e. of degree n-1), and for power series, the
n-th significant coefficient.

   For  polynomials  and power series,  one should rather use polcoeff,  and for
vectors  and matrices,  the [] operator.   Namely,  if x is a vector,  then x[n]
represents  the  n-th component of x.   If x is a matrix,  x[m,n] represents the
coefficient  of row m and column n of the matrix,  x[m,] represents the m-th row
of x, and x[,n] represents the n-th column of x.

   Using  of  this  function requires detailed knowledge of the structure of the
different  PARI types,  and thus it should almost never be used directly.   Some
useful exceptions:

       ? x = 3 + O(3^5);
       ? component(x, 2)
/*-- (type RETURN to continue) --*/
       %2 = 81   \\ p^(p-adic accuracy)
       ? component(x, 1)
       %3 = 3    \\ p
       ? q = Qfb(1,2,3);
       ? component(q, 1)
       %5 = 1

   The library syntax is GEN compo(GEN x, long n).

(15:53) gp > ?extract
extract is aliased to:

vecextract(x,y,{z}): extraction of the components of the matrix or vector x 
according to y and z. If z is omitted, y represents columns, otherwise y 
corresponds to rows and z to columns. y and z can be vectors (of indices), 
strings (indicating ranges as in "1..10") or masks (integers whose binary 
representation indicates the indices to extract, from left to right 1, 2, 4, 8, 
etc.).

(15:53) gp > extract(M,[1,2],[1,2])

[1 2]

[8 9]

(15:54) gp > M

[1 2 3]

[8 9 4]

[7 6 5]

(15:54) gp > condensar(N)=matrix(#N-1,#N-1,a,b,matdet(extract(M,[a,a+1],[b,b+1])))
(N)->matrix(#N-1,#N-1,a,b,matdet(extract(M,[a,a+1],[b,b+1])))
(15:55) gp > condensar(M)

[ -7 -19]

[-15  21]

(15:55) gp > [m11,m12,m13;m21,m22,m23;m31,m32,m33]

[m11 m12 m13]

[m21 m22 m23]

[m31 m32 m33]

(15:56) gp > condensar(%)

[ -7 -19]

[-15  21]

(15:56) gp > condensar(N)=matrix(#N-1,#N-1,a,b,matdet(extract(N,[a,a+1],[b,b+1])))
(N)->matrix(#N-1,#N-1,a,b,matdet(extract(N,[a,a+1],[b,b+1])))
(15:57) gp > [m11,m12,m13;m21,m22,m23;m31,m32,m33]

[m11 m12 m13]

[m21 m22 m23]

[m31 m32 m33]

(15:57) gp > condensar(%)

[m22*m11 - m21*m12 m23*m12 - m22*m13]

[m32*m21 - m31*m22 m33*m22 - m32*m23]

(15:57) gp > condensar(%)

[(m33*m22^2 - m32*m23*m22)*m11 + ((-m33*m22*m21 + m31*m23*m22)*m12 + (m32*m22*m21 - m31*m22^2)*m13)]

(15:57) gp > %[1]
  ***   at top-level: %[1]
  ***                  ^---
  ***   incorrect type in _[_] OCcompo1 [not a vector] (t_MAT).
  ***   Break loop: type 'break' to go back to GP prompt
break> break

(15:57) gp > %[1,1]
(m33*m22^2 - m32*m23*m22)*m11 + ((-m33*m22*m21 + m31*m23*m22)*m12 + (m32*m22*m21 - m31*m22^2)*m13)
(15:57) gp > %/m22
(m33*m22 - m32*m23)*m11 + ((-m33*m21 + m31*m23)*m12 + (m32*m21 - m31*m22)*m13)
(15:57) gp > [a,b,c,d;e,f,g,h;i,j,k,l;m,n,o,p]

[a b c d]

[e f g h]

[i j k l]

[m n o p]

(15:58) gp > condensar(%)

[f*a - e*b g*b - f*c h*c - g*d]

[j*e - i*f k*f - j*g l*g - k*h]

[n*i - m*j o*j - n*k p*k - o*l]

(15:58) gp > M=[a,b,c,d;e,f,g,h;i,j,k,l;m,n,o,p]

[a b c d]

[e f g h]

[i j k l]

[m n o p]

(15:58) gp > M2=condensar(M)

[f*a - e*b g*b - f*c h*c - g*d]

[j*e - i*f k*f - j*g l*g - k*h]

[n*i - m*j o*j - n*k p*k - o*l]

(15:58) gp > M3=condensar(M2)

[(k*f^2 - j*g*f)*a + ((-k*f*e + i*g*f)*b + (j*f*e - i*f^2)*c) (l*g^2 - k*h*g)*b + ((-l*g*f + j*h*g)*c + (k*g*f - j*g^2)*d)]

[(o*j^2 - n*k*j)*e + ((-o*j*i + m*k*j)*f + (n*j*i - m*j^2)*g) (p*k^2 - o*l*k)*f + ((-p*k*j + n*l*k)*g + (o*k*j - n*k^2)*h)]

(15:59) gp > N3=matrix(#M3,#M3,a,b,M3[a,b]/M[a+1,b+1])

[(k*f - j*g)*a + ((-k*e + i*g)*b + (j*e - i*f)*c) (l*g - k*h)*b + ((-l*f + j*h)*c + (k*f - j*g)*d)]

[(o*j - n*k)*e + ((-o*i + m*k)*f + (n*i - m*j)*g) (p*k - o*l)*f + ((-p*j + n*l)*g + (o*j - n*k)*h)]

(15:59) gp > condensar(%)

[((p*k^2 - o*l*k)*f^2 + (((-2*p*k + o*l)*j + n*l*k)*g + (o*k*j - n*k^2)*h)*f + ((p*j^2 - n*l*j)*g^2 + (-o*j^2 + n*k*j)*h*g))*a + ((((-p*k^2 + o*l*k)*f + (p*k - o*l)*j*g)*e + (((p*k*i - m*l*k)*g + (-o*k*i + m*k^2)*h)*f + ((-p*j*i + m*l*j)*g^2 + (o*j*i - m*k*j)*h*g)))*b + ((((p*k*j - n*l*k)*f + (-p*j^2 + n*l*j)*g)*e + ((-p*k*i + m*l*k)*f^2 + ((p*j*i - m*l*j)*g + (n*k*i - m*k*j)*h)*f + (-n*j*i + m*j^2)*h*g))*c + (((-o*k*j + n*k^2)*f + (o*j^2 - n*k*j)*g)*e + ((o*k*i - m*k^2)*f^2 + ((-o*j - n*k)*i + 2*m*k*j)*g*f + (n*j*i - m*j^2)*g^2))*d))]

(15:59) gp > M4=%

[((p*k^2 - o*l*k)*f^2 + (((-2*p*k + o*l)*j + n*l*k)*g + (o*k*j - n*k^2)*h)*f + ((p*j^2 - n*l*j)*g^2 + (-o*j^2 + n*k*j)*h*g))*a + ((((-p*k^2 + o*l*k)*f + (p*k - o*l)*j*g)*e + (((p*k*i - m*l*k)*g + (-o*k*i + m*k^2)*h)*f + ((-p*j*i + m*l*j)*g^2 + (o*j*i - m*k*j)*h*g)))*b + ((((p*k*j - n*l*k)*f + (-p*j^2 + n*l*j)*g)*e + ((-p*k*i + m*l*k)*f^2 + ((p*j*i - m*l*j)*g + (n*k*i - m*k*j)*h)*f + (-n*j*i + m*j^2)*h*g))*c + (((-o*k*j + n*k^2)*f + (o*j^2 - n*k*j)*g)*e + ((o*k*i - m*k^2)*f^2 + ((-o*j - n*k)*i + 2*m*k*j)*g*f + (n*j*i - m*j^2)*g^2))*d))]

(16:00) gp > F=M4[1,1]
((p*k^2 - o*l*k)*f^2 + (((-2*p*k + o*l)*j + n*l*k)*g + (o*k*j - n*k^2)*h)*f + ((p*j^2 - n*l*j)*g^2 + (-o*j^2 + n*k*j)*h*g))*a + ((((-p*k^2 + o*l*k)*f + (p*k - o*l)*j*g)*e + (((p*k*i - m*l*k)*g + (-o*k*i + m*k^2)*h)*f + ((-p*j*i + m*l*j)*g^2 + (o*j*i - m*k*j)*h*g)))*b + ((((p*k*j - n*l*k)*f + (-p*j^2 + n*l*j)*g)*e + ((-p*k*i + m*l*k)*f^2 + ((p*j*i - m*l*j)*g + (n*k*i - m*k*j)*h)*f + (-n*j*i + m*j^2)*h*g))*c + (((-o*k*j + n*k^2)*f + (o*j^2 - n*k*j)*g)*e + ((o*k*i - m*k^2)*f^2 + ((-o*j - n*k)*i + 2*m*k*j)*g*f + (n*j*i - m*j^2)*g^2))*d))

(16:00) gp > F/M2[2,2]
((p*k - o*l)*f + ((-p*j + n*l)*g + (o*j - n*k)*h))*a + (((-p*k + o*l)*e + ((p*i - m*l)*g + (-o*i + m*k)*h))*b + (((p*j - n*l)*e + ((-p*i + m*l)*f + (n*i - m*j)*h))*c + ((-o*j + n*k)*e + ((o*i - m*k)*f + (-n*i + m*j)*g))*d))

(16:00) gp > Dodg=%
((p*k - o*l)*f + ((-p*j + n*l)*g + (o*j - n*k)*h))*a + (((-p*k + o*l)*e + ((p*i - m*l)*g + (-o*i + m*k)*h))*b + (((p*j - n*l)*e + ((-p*i + m*l)*f + (n*i - m*j)*h))*c + ((-o*j + n*k)*e + ((o*i - m*k)*f + (-n*i + m*j)*g))*d))

(16:00) gp > Dodg-matdet(M)
0

(16:01) gp > [x,y]
[x, y]
(16:02) gp > substvec(%,[x,y],[y,(1+x)/y])
[y, 1/y*x + 1/y]
(16:03) gp > substvec(%,[x,y],[y,(1+x)/y])
[1/y*x + 1/y, (y^2 + y)/(x + 1)]
(16:03) gp > f(v)=[v[2],(1+v[1])/v[2]]
(v)->[v[2],(1+v[1])/v[2]]
(16:03) gp > [x,y]
[x, y]
(16:03) gp > f(%)
[y, 1/y*x + 1/y]
(16:03) gp > f(%)
[1/y*x + 1/y, (y^2 + y)/(x + 1)]
(16:03) gp > f(v)=[v[2],(1+v[2])/v[1]]
(v)->[v[2],(1+v[2])/v[1]]
(16:04) gp > [x,y]
[x, y]
(16:04) gp > f(%)
[y, (y + 1)/x]
(16:04) gp > f(%)
[(y + 1)/x, (x + (y + 1))/(y*x)]
(16:04) gp > f(%)
[(x + (y + 1))/(y*x), 1/y*x + 1/y]
(16:04) gp > f(%)
[1/y*x + 1/y, x]
(16:04) gp > f(%)
[x, y]
(16:04) gp > substvec(%,[x,y],[y,(1+y)/x])
[y, (y + 1)/x]
(16:04) gp > substvec(%,[x,y],[y,(1+y)/x])
[(y + 1)/x, (x + (y + 1))/(y*x)]
(16:04) gp > substvec(%,[x,y],[y,(1+y)/x])
[(x + (y + 1))/(y*x), 1/y*x + 1/y]
(16:04) gp > substvec(%,[x,y],[y,(1+y)/x])
[1/y*x + 1/y, x]
(16:04) gp > substvec(%,[x,y],[y,(1+y)/x])
[x, y]
(16:04) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[y, (y^2 + 1)/x]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(y^2 + 1)/x, (x^2 + (y^4 + 2*y^2 + 1))/(y*x^2)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^2 + (y^4 + 2*y^2 + 1))/(y*x^2), (x^4 + (2*y^2 + 2)*x^2 + (y^6 + 3*y^4 + 3*y^2 + 1))/(y^2*x^3)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^4 + (2*y^2 + 2)*x^2 + (y^6 + 3*y^4 + 3*y^2 + 1))/(y^2*x^3), (x^6 + (2*y^2 + 3)*x^4 + (3*y^4 + 6*y^2 + 3)*x^2 + (y^8 + 4*y^6 + 6*y^4 + 4*y^2 + 1))/(y^3*x^4)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^6 + (2*y^2 + 3)*x^4 + (3*y^4 + 6*y^2 + 3)*x^2 + (y^8 + 4*y^6 + 6*y^4 + 4*y^2 + 1))/(y^3*x^4), (x^8 + (2*y^2 + 4)*x^6 + (3*y^4 + 9*y^2 + 6)*x^4 + (4*y^6 + 12*y^4 + 12*y^2 + 4)*x^2 + (y^10 + 5*y^8 + 10*y^6 + 10*y^4 + 5*y^2 + 1))/(y^4*x^5)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^8 + (2*y^2 + 4)*x^6 + (3*y^4 + 9*y^2 + 6)*x^4 + (4*y^6 + 12*y^4 + 12*y^2 + 4)*x^2 + (y^10 + 5*y^8 + 10*y^6 + 10*y^4 + 5*y^2 + 1))/(y^4*x^5), (x^10 + (2*y^2 + 5)*x^8 + (3*y^4 + 12*y^2 + 10)*x^6 + (4*y^6 + 18*y^4 + 24*y^2 + 10)*x^4 + (5*y^8 + 20*y^6 + 30*y^4 + 20*y^2 + 5)*x^2 + (y^12 + 6*y^10 + 15*y^8 + 20*y^6 + 15*y^4 + 6*y^2 + 1))/(y^5*x^6)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^10 + (2*y^2 + 5)*x^8 + (3*y^4 + 12*y^2 + 10)*x^6 + (4*y^6 + 18*y^4 + 24*y^2 + 10)*x^4 + (5*y^8 + 20*y^6 + 30*y^4 + 20*y^2 + 5)*x^2 + (y^12 + 6*y^10 + 15*y^8 + 20*y^6 + 15*y^4 + 6*y^2 + 1))/(y^5*x^6), (x^12 + (2*y^2 + 6)*x^10 + (3*y^4 + 15*y^2 + 15)*x^8 + (4*y^6 + 24*y^4 + 40*y^2 + 20)*x^6 + (5*y^8 + 30*y^6 + 60*y^4 + 50*y^2 + 15)*x^4 + (6*y^10 + 30*y^8 + 60*y^6 + 60*y^4 + 30*y^2 + 6)*x^2 + (y^14 + 7*y^12 + 21*y^10 + 35*y^8 + 35*y^6 + 21*y^4 + 7*y^2 + 1))/(y^6*x^7)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^12 + (2*y^2 + 6)*x^10 + (3*y^4 + 15*y^2 + 15)*x^8 + (4*y^6 + 24*y^4 + 40*y^2 + 20)*x^6 + (5*y^8 + 30*y^6 + 60*y^4 + 50*y^2 + 15)*x^4 + (6*y^10 + 30*y^8 + 60*y^6 + 60*y^4 + 30*y^2 + 6)*x^2 + (y^14 + 7*y^12 + 21*y^10 + 35*y^8 + 35*y^6 + 21*y^4 + 7*y^2 + 1))/(y^6*x^7), (x^14 + (2*y^2 + 7)*x^12 + (3*y^4 + 18*y^2 + 21)*x^10 + (4*y^6 + 30*y^4 + 60*y^2 + 35)*x^8 + (5*y^8 + 40*y^6 + 100*y^4 + 100*y^2 + 35)*x^6 + (6*y^10 + 45*y^8 + 120*y^6 + 150*y^4 + 90*y^2 + 21)*x^4 + (7*y^12 + 42*y^10 + 105*y^8 + 140*y^6 + 105*y^4 + 42*y^2 + 7)*x^2 + (y^16 + 8*y^14 + 28*y^12 + 56*y^10 + 70*y^8 + 56*y^6 + 28*y^4 + 8*y^2 + 1))/(y^7*x^8)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^14 + (2*y^2 + 7)*x^12 + (3*y^4 + 18*y^2 + 21)*x^10 + (4*y^6 + 30*y^4 + 60*y^2 + 35)*x^8 + (5*y^8 + 40*y^6 + 100*y^4 + 100*y^2 + 35)*x^6 + (6*y^10 + 45*y^8 + 120*y^6 + 150*y^4 + 90*y^2 + 21)*x^4 + (7*y^12 + 42*y^10 + 105*y^8 + 140*y^6 + 105*y^4 + 42*y^2 + 7)*x^2 + (y^16 + 8*y^14 + 28*y^12 + 56*y^10 + 70*y^8 + 56*y^6 + 28*y^4 + 8*y^2 + 1))/(y^7*x^8), (x^16 + (2*y^2 + 8)*x^14 + (3*y^4 + 21*y^2 + 28)*x^12 + (4*y^6 + 36*y^4 + 84*y^2 + 56)*x^10 + (5*y^8 + 50*y^6 + 150*y^4 + 175*y^2 + 70)*x^8 + (6*y^10 + 60*y^8 + 200*y^6 + 300*y^4 + 210*y^2 + 56)*x^6 + (7*y^12 + 63*y^10 + 210*y^8 + 350*y^6 + 315*y^4 + 147*y^2 + 28)*x^4 + (8*y^14 + 56*y^12 + 168*y^10 + 280*y^8 + 280*y^6 + 168*y^4 + 56*y^2 + 8)*x^2 + (y^18 + 9*y^16 + 36*y^14 + 84*y^12 + 126*y^10 + 126*y^8 + 84*y^6 + 36*y^4 + 9*y^2 + 1))/(y^8*x^9)]
(16:05) gp > substvec(%,[x,y],[y,(1+y^2)/x])
[(x^16 + (2*y^2 + 8)*x^14 + (3*y^4 + 21*y^2 + 28)*x^12 + (4*y^6 + 36*y^4 + 84*y^2 + 56)*x^10 + (5*y^8 + 50*y^6 + 150*y^4 + 175*y^2 + 70)*x^8 + (6*y^10 + 60*y^8 + 200*y^6 + 300*y^4 + 210*y^2 + 56)*x^6 + (7*y^12 + 63*y^10 + 210*y^8 + 350*y^6 + 315*y^4 + 147*y^2 + 28)*x^4 + (8*y^14 + 56*y^12 + 168*y^10 + 280*y^8 + 280*y^6 + 168*y^4 + 56*y^2 + 8)*x^2 + (y^18 + 9*y^16 + 36*y^14 + 84*y^12 + 126*y^10 + 126*y^8 + 84*y^6 + 36*y^4 + 9*y^2 + 1))/(y^8*x^9), (x^18 + (2*y^2 + 9)*x^16 + (3*y^4 + 24*y^2 + 36)*x^14 + (4*y^6 + 42*y^4 + 112*y^2 + 84)*x^12 + (5*y^8 + 60*y^6 + 210*y^4 + 280*y^2 + 126)*x^10 + (6*y^10 + 75*y^8 + 300*y^6 + 525*y^4 + 420*y^2 + 126)*x^8 + (7*y^12 + 84*y^10 + 350*y^8 + 700*y^6 + 735*y^4 + 392*y^2 + 84)*x^6 + (8*y^14 + 84*y^12 + 336*y^10 + 700*y^8 + 840*y^6 + 588*y^4 + 224*y^2 + 36)*x^4 + (9*y^16 + 72*y^14 + 252*y^12 + 504*y^10 + 630*y^8 + 504*y^6 + 252*y^4 + 72*y^2 + 9)*x^2 + (y^20 + 10*y^18 + 45*y^16 + 120*y^14 + 210*y^12 + 252*y^10 + 210*y^8 + 120*y^6 + 45*y^4 + 10*y^2 + 1))/(y^9*x^10)]
(16:05) gp > g(v,n=1)=[v[2],(1+v[2]^n)/v[1]]
(v,n=1)->[v[2],(1+v[2]^n)/v[1]]
(16:06) gp > [x,y]
[x, y]
(16:06) gp > g(%,2)
[y, (y^2 + 1)/x]
(16:06) gp > g(%,2)
[(y^2 + 1)/x, (x^2 + (y^4 + 2*y^2 + 1))/(y*x^2)]
(16:06) gp > [1,1]
[1, 1]
(16:06) gp > g(%,2)
[1, 2]
(16:06) gp > g(%,2)
[2, 5]
(16:06) gp > g(%,2)
[5, 13]
(16:06) gp > g(%,2)
[13, 34]
(16:06) gp > g(%,2)
[34, 89]
(16:06) gp > g(%,2)
[89, 233]
(16:06) gp > g(%,2)
[233, 610]
(16:06) gp > g(%,2)
[610, 1597]
(16:06) gp > g(%,2)
[1597, 4181]
(16:06) gp > g(%,2)
[4181, 10946]
(16:06) gp > 1/(1-t-t^2+O(t^20))
1 + t + 2*t^2 + 3*t^3 + 5*t^4 + 8*t^5 + 13*t^6 + 21*t^7 + 34*t^8 + 55*t^9 + 89*t^10 + 144*t^11 + 233*t^12 + 377*t^13 + 610*t^14 + 987*t^15 + 1597*t^16 + 2584*t^17 + 4181*t^18 + 6765*t^19 + O(t^20)
(16:07) gp > Vec(%)
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765]
(16:08) gp > [1,1]
[1, 1]
(16:08) gp > g(%,3)
[1, 2]
(16:08) gp > g(%,3)
[2, 9]
(16:08) gp > g(%,3)
[9, 365]
(16:08) gp > g(%,3)
[365, 5403014]
(16:08) gp > g(%,3)
[5403014, 432130991537958813]
(16:08) gp > g(%,3)
[432130991537958813, 14935169284101525874491673463268414536523593057]
(16:08) gp > g(%,3)
[14935169284101525874491673463268414536523593057, 7709301567111884917552482697377779958720974702081890294692569618782709587228523998549841753711433720909908231142293680138]
(16:08) gp > g(%,3)
[7709301567111884917552482697377779958720974702081890294692569618782709587228523998549841753711433720909908231142293680138, 30678558804624930034147518983886576131984287731428646793729131734971009607463088977063686819285457914061964438723180951618875342373102579206143383988098867574773466530609855189428388655512096141865165628736994949749324128574019159720823464396778723815816289810746085419640007051909449686839610063507440280012340958089]
(16:08) gp > [x,y]
[x, y]
(16:08) gp > g(%,3)
[y, (y^3 + 1)/x]
(16:08) gp > g(%,3)
[(y^3 + 1)/x, (x^3 + (y^9 + 3*y^6 + 3*y^3 + 1))/(y*x^3)]
(16:08) gp > g(%,3)
[(x^3 + (y^9 + 3*y^6 + 3*y^3 + 1))/(y*x^3), (x^9 + (3*y^6 + 6*y^3 + 3)*x^6 + (3*y^15 + 15*y^12 + 30*y^9 + 30*y^6 + 15*y^3 + 3)*x^3 + (y^24 + 8*y^21 + 28*y^18 + 56*y^15 + 70*y^12 + 56*y^9 + 28*y^6 + 8*y^3 + 1))/(y^3*x^8)]
(16:08) gp > g(%,3)
[(x^9 + (3*y^6 + 6*y^3 + 3)*x^6 + (3*y^15 + 15*y^12 + 30*y^9 + 30*y^6 + 15*y^3 + 3)*x^3 + (y^24 + 8*y^21 + 28*y^18 + 56*y^15 + 70*y^12 + 56*y^9 + 28*y^6 + 8*y^3 + 1))/(y^3*x^8), (x^24 + (6*y^6 + 15*y^3 + 8)*x^21 + (3*y^15 + 39*y^12 + 127*y^9 + 177*y^6 + 114*y^3 + 28)*x^18 + (30*y^21 + 236*y^18 + 786*y^15 + 1440*y^12 + 1570*y^9 + 1020*y^6 + 366*y^3 + 56)*x^15 + (15*y^30 + 205*y^27 + 1170*y^24 + 3780*y^21 + 7770*y^18 + 10710*y^15 + 10080*y^12 + 6420*y^9 + 2655*y^6 + 645*y^3 + 70)*x^12 + (3*y^39 + 92*y^36 + 870*y^33 + 4356*y^30 + 13805*y^27 + 30096*y^24 + 47124*y^21 + 54120*y^18 + 45837*y^15 + 28380*y^12 + 12518*y^9 + 3732*y^6 + 675*y^3 + 56)*x^9 + (28*y^45 + 420*y^42 + 2940*y^39 + 12740*y^36 + 38220*y^33 + 84084*y^30 + 140140*y^27 + 180180*y^24 + 180180*y^21 + 140140*y^18 + 84084*y^15 + 38220*y^12 + 12740*y^9 + 2940*y^6 + 420*y^3 + 28)*x^6 + (8*y^54 + 144*y^51 + 1224*y^48 + 6528*y^45 + 24480*y^42 + 68544*y^39 + 148512*y^36 + 254592*y^33 + 350064*y^30 + 388960*y^27 + 350064*y^24 + 254592*y^21 + 148512*y^18 + 68544*y^15 + 24480*y^12 + 6528*y^9 + 1224*y^6 + 144*y^3 + 8)*x^3 + (y^63 + 21*y^60 + 210*y^57 + 1330*y^54 + 5985*y^51 + 20349*y^48 + 54264*y^45 + 116280*y^42 + 203490*y^39 + 293930*y^36 + 352716*y^33 + 352716*y^30 + 293930*y^27 + 203490*y^24 + 116280*y^21 + 54264*y^18 + 20349*y^15 + 5985*y^12 + 1330*y^9 + 210*y^6 + 21*y^3 + 1))/(y^8*x^21)]
(16:08) gp > g(%,3)
[(x^24 + (6*y^6 + 15*y^3 + 8)*x^21 + (3*y^15 + 39*y^12 + 127*y^9 + 177*y^6 + 114*y^3 + 28)*x^18 + (30*y^21 + 236*y^18 + 786*y^15 + 1440*y^12 + 1570*y^9 + 1020*y^6 + 366*y^3 + 56)*x^15 + (15*y^30 + 205*y^27 + 1170*y^24 + 3780*y^21 + 7770*y^18 + 10710*y^15 + 10080*y^12 + 6420*y^9 + 2655*y^6 + 645*y^3 + 70)*x^12 + (3*y^39 + 92*y^36 + 870*y^33 + 4356*y^30 + 13805*y^27 + 30096*y^24 + 47124*y^21 + 54120*y^18 + 45837*y^15 + 28380*y^12 + 12518*y^9 + 3732*y^6 + 675*y^3 + 56)*x^9 + (28*y^45 + 420*y^42 + 2940*y^39 + 12740*y^36 + 38220*y^33 + 84084*y^30 + 140140*y^27 + 180180*y^24 + 180180*y^21 + 140140*y^18 + 84084*y^15 + 38220*y^12 + 12740*y^9 + 2940*y^6 + 420*y^3 + 28)*x^6 + (8*y^54 + 144*y^51 + 1224*y^48 + 6528*y^45 + 24480*y^42 + 68544*y^39 + 148512*y^36 + 254592*y^33 + 350064*y^30 + 388960*y^27 + 350064*y^24 + 254592*y^21 + 148512*y^18 + 68544*y^15 + 24480*y^12 + 6528*y^9 + 1224*y^6 + 144*y^3 + 8)*x^3 + (y^63 + 21*y^60 + 210*y^57 + 1330*y^54 + 5985*y^51 + 20349*y^48 + 54264*y^45 + 116280*y^42 + 203490*y^39 + 293930*y^36 + 352716*y^33 + 352716*y^30 + 293930*y^27 + 203490*y^24 + 116280*y^21 + 54264*y^18 + 20349*y^15 + 5985*y^12 + 1330*y^9 + 210*y^6 + 21*y^3 + 1))/(y^8*x^21), (x^63 + (15*y^6 + 39*y^3 + 21)*x^60 + (6*y^15 + 165*y^12 + 684*y^9 + 1122*y^6 + 804*y^3 + 210)*x^57 + (127*y^21 + 1697*y^18 + 7990*y^15 + 18938*y^12 + 25258*y^9 + 19268*y^6 + 7858*y^3 + 1330)*x^54 + (39*y^30 + 1596*y^27 + 16074*y^24 + 77496*y^21 + 218019*y^18 + 389400*y^15 + 456825*y^12 + 352080*y^9 + 172050*y^6 + 48420*y^3 + 5985)*x^51 + (3*y^39 + 807*y^36 + 16275*y^33 + 137418*y^30 + 657468*y^27 + 2022132*y^24 + 4261593*y^21 + 6359517*y^18 + 6807642*y^15 + 5208588*y^12 + 2786064*y^9 + 991221*y^6 + 210987*y^3 + 20349)*x^48 + (236*y^45 + 10130*y^42 + 142440*y^39 + 1059310*y^36 + 4967272*y^33 + 16031256*y^30 + 37415280*y^27 + 64990980*y^24 + 85322700*y^21 + 85096274*y^18 + 64192184*y^15 + 36072150*y^12 + 14650240*y^9 + 4067140*y^6 + 691152*y^3 + 54264)*x^45 + (30*y^54 + 4170*y^51 + 98604*y^48 + 1096212*y^45 + 7375134*y^42 + 33698790*y^39 + 111511296*y^36 + 277898400*y^33 + 534570894*y^30 + 805740078*y^27 + 959080980*y^24 + 903085092*y^21 + 669797778*y^18 + 386941962*y^15 + 170623944*y^12 + 55503720*y^9 + 12559716*y^6 + 1766232*y^3 + 116280)*x^42 + (1170*y^60 + 48816*y^57 + 802116*y^54 + 7499664*y^51 + 46409274*y^48 + 206049600*y^45 + 689210928*y^42 + 1792490688*y^39 + 3701668932*y^36 + 6154136352*y^33 + 8306864280*y^30 + 9140627808*y^27 + 8200118628*y^24 + 5973694272*y^21 + 3503549232*y^18 + 1630491840*y^15 + 588491946*y^12 + 158875056*y^9 + 30200004*y^6 + 3605904*y^3 + 203490)*x^39 + (205*y^69 + 17700*y^66 + 437490*y^63 + 5610920*y^60 + 45819735*y^57 + 263784410*y^54 + 1136433510*y^51 + 3806861850*y^48 + 10175478690*y^45 + 22094802080*y^42 + 39460102500*y^39 + 58445545080*y^36 + 72146756110*y^33 + 74377242300*y^30 + 63989355580*y^27 + 45778331340*y^24 + 27047062305*y^21 + 13054330380*y^18 + 5063587210*y^15 + 1540401360*y^12 + 354006795*y^9 + 57792410*y^6 + 5973630*y^3 + 293930)*x^36 + (15*y^78 + 4686*y^75 + 183381*y^72 + 3229248*y^69 + 34295493*y^66 + 250373046*y^63 + 1351480515*y^60 + 5645741244*y^57 + 18820148622*y^54 + 51148149492*y^51 + 115082515614*y^48 + 216745997520*y^45 + 344371973946*y^42 + 463955273628*y[+++]
(16:09) gp > "sobre Q(a):  x^5-x-a"
"sobre Q(a):  x^5-x-a"