I am working with GP and minimum polynomials as follows running on ASUS x75:
(19:25) gp > elt=Mod(a*x^3+b*x^2+c*x+d,('x^5-1)/('x-1))
%122 = Mod(a*x^3 + b*x^2 + c*x + d, x^4 + x^3 + x^2 + x + 1)
(19:25) gp > (poly=minpoly(elt,x='x))
%123 = x^4 + (a + (b + (c - 4*d)))*x^3 + (a^2 + (-3*b + (2*c - 3*d))*a + (b^2 + (2*c - 3*d)*b + (c^2 - 3*d*c + 6*d^2)))*x^2 + (a^3 + (-2*b + (3*c - 2*d))*a^2 + (-2*b^2 + (c + 6*d)*b + (-2*c^2 - 4*d*c + 3*d^2))*a + (b^3 + (-2*c - 2*d)*b^2 + (3*c^2 - 4*d*c + 3*d^2)*b + (c^3 - 2*d*c^2 + 3*d^2*c - 4*d^3)))*x + (a^4 + (-b + (-c - d))*a^3 + (b^2 + (2*c + 2*d)*b + (c^2 - 3*d*c + d^2))*a^2 + (-b^3 + (-3*c + 2*d)*b^2 + (2*c^2 - d*c - 3*d^2)*b + (-c^3 + 2*d*c^2 + 2*d^2*c - d^3))*a + (b^4 + (-c - d)*b^3 + (c^2 + 2*d*c + d^2)*b^2 + (-c^3 - 3*d*c^2 + 2*d^2*c - d^3)*b + (c^4 - d*c^3 + d^2*c^2 - d^3*c + d^4)))
The first command came out successfully, while the second one below did finish successfully and gave an allocatemem() error. How is it possible to get the second command to work, without overheating the computer or program exhaustion? And the WHOLE output to command below this is needed. Thanks for the help.
(19:23) gp > elt=Mod(a*x^5+b*x^4+c*x^3+d*x^2+e*x+f,('x^7-1)/('x-1))
%120 = Mod(a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)
(19:23) gp > (poly=minpoly(elt,x='x))
*** at top-level: poly=minpoly(elt,x='x)
*** ^-----------------
*** minpoly: the PARI stack overflows !
current stack size: 9000000 (8.583 Mbytes)
[hint] you can increase GP stack with allocatemem()
You can increase the PARI/GP's heap up to any limit you want at run-time following the example below (demonstrates how to set heap size to 120000000 bytes):
default(parisize, 120000000)
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