construction of some relative quadratic extensions is SERIOUSLY FRICKIN's FOO-bar'd #4782
Description
Try this carefully with your finger on kill -9:
sage: NumberField(x^2 + 79*x - 60, 'a').extension(x^2 - 69*x + 38,'b')
On sage.math top shows pretty quickly over 6.9GB memory usage!
15392 was 25 0 8219m 6.9g 21m R 100 10.9 0:53.76 sage-ipython
The discriminants aren't very big:
sage: R.<x> = QQ[]
sage: disc(x^2 + 79*x-60)
6481
sage: disc(x^2 - 69*x + 38)
4609
Same behavior with Proof false:
sage: proof.all(False)
sage: NumberField(x^2 + 79*x - 60, 'a').extension(x^2 - 69*x + 38,'b')
...hell....
Giving both polys at once (which maybe use polcompositum) works:
sage: NumberField([x^2 + 79*x-60, x^2 - 69*x + 38], 'a')
*** Warning: insufficient precision for fundamental units, not given.
Number Field in a0 with defining polynomial x^2 + 79*x - 60 over its base field
Basically there is something very wrong with how we make relative fields... probably because of something very very wrong in the core of pari itself (and it's relative number fields).
Component: number fields
Reviewer: Robert Bradshaw
Issue created by migration from https://trac.sagemath.org/ticket/4782