GCD

Greatest common divisors (GCD) over algebraic number fields are computed by cr_gcda() function. This function computes GCD by using modular computation and Chinese remainder theorem and it works for the case where the ground field is a multiple extension.

[63] A=newalg(t^9-15*t^6-87*t^3-125);
(#0)
[64] B=newalg(75*s^2+(10*A^7-175*A^4-470*A)*s+3*A^8-45*A^5-261*A^2);
(#1)
[65] P1=75*x^2+(150*B+10*A^7-175*A^4-395*A)*x+(75*B^2+(10*A^7-175*A^4-395*A)*B
+13*A^8-220*A^5-581*A^2)$
[66] P2=x^2+A*x+A^2$
[67] cr_gcda(P1,P2);
27*x+((#0^6-19*#0^3-65)*#1-#0^7+19*#0^4+38*#0)

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