┌────────────────────────────────────────────────────────────────────┐
│ Sage Version 6.0, Release Date: 2013-12-17                         │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: 

sage: K = QQ[(-23)^(1/2)]
sage: K.factor(2)
(Fractional ideal (2, 1/2*a - 1/2)) * (Fractional ideal (2, 1/2*a + 1/2))
sage: crt([1,2,3], [3,5,7])
52
sage: crt?
sage: R=QQ[x]
sage: x=R.gen()
sage: crt([1,2], [3, x])
2
sage: crt([1,2,3], [3+x,5+x^2+x,7+x^3])
39/3740*x^5 - 4/935*x^4 - 5/748*x^3 + 273/3740*x^2 - 28/935*x + 2209/748
sage: