bug with power series and/or p-adics

[jbalakrishnan]

Can't manipulate certain elements of a power series ring:

sage: R.<x> = QQ[]
sage: p =11
sage: K = Qp(p,10)
sage: J.<a> = K.extension(x^2-p)
sage: C.<t> = LaurentSeriesRing(J)
sage: D.<s> = PowerSeriesRing(C)
sage: x = (10 + 10*a^2 + 10*a^4 + 10*a^6 + 10*a^8 + 10*a^10 + 10*a^12 + 10*a^14 + 10*a^16 + 10*a^18 + O(a^20)) + (2 + 2*a^4 + 2*a^8 + 2*a^12 + 2*a^16 + O(a^20))*t^2 + (10*a^2 + 5*a^4 + 7*a^6 + 6*a^8 + 3*a^10 + 2*a^12 + 9*a^14 + 3*a^16 + 2*a^18 + O(a^22))*t^4 + (10 + 7*a^2 + 9*a^4 + 8*a^6 + 5*a^8 + 10*a^12 + 3*a^14 + 6*a^16 + 8*a^18 + O(a^20))*t^6 + (6 + 2*a^4 + 8*a^6 + 6*a^8 + 2*a^10 + 6*a^12 + 6*a^14 + 4*a^16 + 5*a^18 + O(a^20))*t^8 + (9 + a^2 + 4*a^4 + 7*a^6 + a^8 + 2*a^10 + 4*a^12 + a^16 + 5*a^18 + O(a^20))*t^10 + (1 + 4*a^2 + 7*a^4 + 7*a^6 + 4*a^8 + 7*a^12 + 4*a^14 + 7*a^16 + 6*a^18 + O(a^20))*t^12 + ((7 + 4*a + 10*a^2 + 6*a^4 + 4*a^5 + 10*a^6 + 6*a^8 + 4*a^9 + 10*a^10 + 6*a^12 + 4*a^13 + 10*a^14 + 6*a^16 + 4*a^17 + 10*a^18 + O(a^20))*t^2 + O(a^20)*t^3 + (2*a + 4*a^2 + 4*a^3 + 9*a^4 + a^5 + 2*a^6 + 6*a^7 + 6*a^8 + 9*a^9 + 7*a^10 + 5*a^11 + a^12 + 4*a^13 + 7*a^14 + 3*a^15 + 6*a^16 + 8*a^17 + a^18 + 9*a^19 + O(a^20))*t^4 + O(a^20)*t^5 + (6 + 8*a + 7*a^2 + 8*a^3 + 7*a^4 + 7*a^5 + a^6 + 7*a^7 + 9*a^8 + 4*a^9 + 7*a^10 + 5*a^11 + 5*a^12 + 5*a^13 + 9*a^14 + 4*a^15 + 5*a^16 + 7*a^17 + 3*a^18 + a^19 + O(a^20))*t^6 + O(a^20)*t^7 + (7 + 2*a + 6*a^2 + 7*a^3 + 5*a^4 + 6*a^5 + 3*a^7 + a^8 + 3*a^9 + a^10 + 5*a^12 + 5*a^13 + 2*a^14 + 7*a^15 + 7*a^16 + 2*a^17 + 8*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 10*a + 3*a^2 + 8*a^3 + 2*a^4 + 2*a^5 + 3*a^6 + 5*a^7 + 5*a^8 + a^9 + 3*a^11 + 2*a^12 + 7*a^14 + a^15 + 8*a^17 + 4*a^18 + 5*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (10 + 7*a + 5*a^2 + 10*a^3 + 10*a^4 + a^5 + 6*a^6 + 3*a^7 + 9*a^8 + 9*a^9 + 5*a^10 + 7*a^11 + 3*a^12 + 7*a^13 + 10*a^14 + 3*a^15 + 9*a^16 + 9*a^17 + 7*a^18 + 4*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + O(t^14))*s + ((2 + 7*a + 2*a^2 + 10*a^3 + 2*a^4 + 6*a^5 + 2*a^6 + 10*a^7 + 2*a^8 + 6*a^9 + 2*a^10 + 10*a^11 + 2*a^12 + 6*a^13 + 2*a^14 + 10*a^15 + 2*a^16 + 6*a^17 + 2*a^18 + 10*a^19 + O(a^20))*t^2 + O(a^20)*t^3 + (9*a + 7*a^2 + 3*a^3 + 4*a^4 + 6*a^5 + 3*a^6 + 10*a^7 + 6*a^8 + 2*a^9 + 9*a^11 + 5*a^12 + 9*a^13 + 9*a^14 + 10*a^15 + 4*a^17 + 8*a^18 + 4*a^19 + O(a^20))*t^4 + O(a^20)*t^5 + (7 + 5*a + 2*a^2 + 3*a^3 + 4*a^5 + 7*a^6 + 7*a^8 + 10*a^9 + a^10 + 2*a^11 + 9*a^12 + a^13 + a^15 + 3*a^16 + a^17 + 7*a^19 + O(a^20))*t^6 + O(a^20)*t^7 + (3 + 8*a + 2*a^3 + 9*a^4 + 8*a^5 + 10*a^6 + a^7 + 2*a^8 + 8*a^10 + 3*a^11 + 6*a^12 + 5*a^13 + 3*a^14 + 8*a^15 + 6*a^16 + 3*a^18 + 7*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 2*a + 6*a^2 + 5*a^3 + 10*a^4 + 10*a^5 + a^6 + a^7 + 10*a^8 + 10*a^10 + a^11 + 3*a^12 + 10*a^13 + 3*a^14 + a^15 + 6*a^16 + a^17 + 2*a^18 + 9*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (7*a + 6*a^3 + 5*a^4 + 3*a^5 + 9*a^6 + 9*a^7 + 4*a^9 + 7*a^10 + 5*a^11 + 4*a^12 + 9*a^13 + a^14 + 3*a^16 + 5*a^18 + 10*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + O(t^14))*s^2 + ((4*a^2 + 10*a^3 + 10*a^4 + 8*a^6 + 4*a^7 + 3*a^8 + 4*a^10 + 4*a^11 + 2*a^12 + 9*a^13 + a^14 + 9*a^15 + 6*a^16 + 5*a^17 + 10*a^18 + 10*a^19 + 3*a^20 + O(a^22))*t^4 + O(a^22)*t^5 + (9 + 6*a + 8*a^3 + 3*a^4 + 9*a^5 + 8*a^6 + 10*a^7 + 3*a^8 + 6*a^9 + 4*a^10 + 6*a^12 + a^13 + 7*a^14 + 8*a^15 + 2*a^16 + 2*a^17 + 7*a^18 + a^19 + O(a^20))*t^6 + O(a^20)*t^7 + (5 + 10*a + 10*a^3 + 9*a^4 + 4*a^5 + 10*a^6 + 5*a^7 + 6*a^8 + a^10 + 7*a^11 + 6*a^12 + 4*a^13 + 8*a^14 + a^15 + 7*a^16 + 6*a^17 + 8*a^18 + 6*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 3*a + 5*a^2 + 9*a^5 + 4*a^6 + 9*a^7 + 6*a^9 + 6*a^10 + 7*a^11 + 9*a^13 + 4*a^14 + 8*a^15 + 6*a^16 + a^17 + 5*a^18 + 5*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (7*a + a^2 + 2*a^3 + 9*a^4 + 10*a^6 + 8*a^7 + a^8 + 9*a^9 + 4*a^10 + 4*a^11 + 10*a^12 + 8*a^13 + 7*a^14 + a^15 + 7*a^16 + 10*a^17 + 5*a^18 + 6*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (9*a^2 + 7*a^3 + 2*a^4 + 2*a^5 + 10*a^6 + 10*a^7 + 5*a^8 + 4*a^9 + 2*a^11 + 2*a^12 + 6*a^13 + 6*a^14 + 4*a^15 + a^16 + 6*a^17 + 7*a^18 + 2*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + O(t^16))*s^3 + ((10*a^2 + 4*a^3 + 10*a^4 + 2*a^5 + 8*a^6 + a^7 + 2*a^8 + 9*a^9 + 7*a^10 + 2*a^11 + 8*a^12 + 9*a^13 + 4*a^14 + 8*a^15 + 6*a^16 + 2*a^17 + a^18 + 8*a^19 + 7*a^20 + O(a^22))*t^4 + O(a^22)*t^5 + (7 + 5*a + 6*a^2 + 5*a^3 + 3*a^6 + 6*a^7 + 3*a^10 + 10*a^11 + 6*a^12 + 4*a^13 + 5*a^14 + 7*a^15 + 9*a^17 + 6*a^18 + 2*a^19 + O(a^20))*t^6 + O(a^20)*t^7 + (2 + 4*a^2 + 2*a^3 + 9*a^4 + 2*a^5 + 3*a^6 + 9*a^7 + 7*a^8 + 10*a^9 + 2*a^10 + 7*a^11 + 10*a^12 + 5*a^13 + 6*a^14 + 10*a^15 + 2*a^16 + 10*a^17 + 9*a^18 + 9*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 5*a + 9*a^2 + 8*a^5 + 10*a^6 + 4*a^7 + 5*a^8 + 8*a^9 + 8*a^10 + 3*a^11 + 5*a^12 + 3*a^13 + 2*a^14 + 5*a^15 + 3*a^16 + a^17 + 6*a^18 + 6*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (2*a + 2*a^2 + 10*a^3 + 3*a^4 + 7*a^5 + 7*a^6 + 2*a^7 + 2*a^8 + 5*a^9 + a^10 + 5*a^11 + a^12 + 8*a^14 + 7*a^16 + 4*a^17 + 5*a^18 + 10*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (2*a + 8*a^2 + 2*a^3 + 8*a^4 + 7*a^5 + 6*a^6 + 3*a^7 + 6*a^9 + 10*a^10 + 4*a^11 + 2*a^12 + 6*a^13 + 7*a^14 + 5*a^15 + 8*a^16 + 2*a^17 + 3*a^18 + 10*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + O(t^16))*s^4 + ((6 + 3*a + a^2 + a^3 + 3*a^4 + a^5 + 6*a^6 + 6*a^7 + 9*a^8 + 6*a^9 + 8*a^10 + 10*a^11 + 8*a^12 + 4*a^13 + 6*a^14 + 8*a^15 + 8*a^16 + a^17 + 10*a^18 + 2*a^19 + O(a^20))*t^6 + O(a^20)*t^7 + (5 + 4*a + 2*a^2 + 5*a^3 + 2*a^4 + 8*a^7 + 10*a^8 + 9*a^9 + 10*a^10 + 2*a^11 + 2*a^12 + 10*a^13 + 5*a^15 + 4*a^16 + 6*a^18 + 7*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 8*a + 6*a^2 + 7*a^3 + 9*a^4 + 7*a^5 + 9*a^6 + 7*a^7 + 10*a^8 + 9*a^9 + 5*a^10 + 3*a^12 + 4*a^13 + 5*a^15 + 6*a^16 + 4*a^17 + 6*a^18 + 3*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (9*a + 10*a^2 + 9*a^3 + 2*a^4 + 8*a^5 + 10*a^6 + 9*a^7 + 10*a^8 + 8*a^9 + 4*a^11 + 6*a^13 + 5*a^14 + 5*a^15 + 5*a^16 + 7*a^17 + 10*a^18 + 2*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (5*a + 9*a^2 + 7*a^3 + 7*a^4 + 7*a^5 + 3*a^6 + 9*a^7 + 3*a^8 + 7*a^9 + 10*a^10 + a^11 + 4*a^12 + 10*a^13 + 8*a^14 + 3*a^15 + 2*a^16 + 3*a^17 + 8*a^18 + 10*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (9*a^2 + 10*a^5 + 9*a^6 + 8*a^7 + 10*a^8 + 10*a^9 + 5*a^10 + 9*a^11 + 3*a^12 + 4*a^13 + 9*a^14 + 10*a^15 + 6*a^16 + 8*a^17 + 3*a^18 + 6*a^19 + O(a^20))*t^16 + O(a^20)*t^17 + O(t^18))*s^5 + ((10 + 6*a + 3*a^2 + 5*a^3 + 3*a^4 + 9*a^5 + 8*a^6 + a^7 + 6*a^8 + 4*a^9 + 10*a^10 + 3*a^11 + 3*a^12 + 4*a^13 + 3*a^14 + 3*a^15 + 7*a^16 + 10*a^17 + 7*a^18 + 6*a^19 + O(a^20))*t^6 + O(a^20)*t^7 + (3 + 7*a + a^2 + 9*a^3 + 8*a^4 + 8*a^5 + 5*a^6 + 4*a^7 + 6*a^8 + 8*a^9 + a^10 + 10*a^11 + 2*a^12 + 5*a^14 + 7*a^15 + 6*a^16 + 8*a^17 + 3*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 2*a + 4*a^2 + 10*a^3 + 3*a^4 + 10*a^5 + 8*a^6 + 6*a^7 + 8*a^8 + 4*a^9 + 3*a^10 + 7*a^11 + 10*a^12 + 10*a^13 + 5*a^14 + 6*a^15 + 6*a^17 + 10*a^18 + 2*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (5*a + 4*a^2 + 5*a^3 + 9*a^4 + 4*a^5 + 10*a^6 + 7*a^7 + 4*a^8 + 9*a^9 + 8*a^10 + 3*a^11 + 10*a^12 + 9*a^13 + 6*a^14 + a^15 + 3*a^16 + 8*a^17 + 8*a^18 + 9*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (a + 7*a^2 + 10*a^3 + 9*a^4 + 3*a^5 + 2*a^6 + 5*a^7 + 6*a^10 + 10*a^11 + 7*a^13 + 5*a^14 + 5*a^15 + 8*a^16 + 6*a^17 + 2*a^18 + 5*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (5*a + 8*a^2 + 4*a^4 + 2*a^5 + 7*a^6 + 4*a^7 + 8*a^8 + 8*a^9 + 6*a^10 + 10*a^11 + 8*a^12 + 2*a^13 + 6*a^15 + 10*a^16 + 9*a^17 + a^19 + O(a^20))*t^16 + O(a^20)*t^17 + O(t^18))*s^6 + ((7 + 6*a + 10*a^2 + 5*a^3 + 4*a^4 + 10*a^5 + 3*a^6 + 5*a^7 + a^8 + 4*a^9 + 3*a^10 + 5*a^11 + 2*a^12 + 2*a^13 + a^14 + 3*a^16 + 8*a^17 + 10*a^18 + 4*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 6*a + 7*a^2 + 8*a^3 + 3*a^4 + 2*a^5 + 4*a^6 + 2*a^7 + 5*a^8 + 9*a^9 + 6*a^10 + 8*a^12 + 6*a^14 + 5*a^15 + 9*a^16 + 2*a^17 + 2*a^18 + a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (6*a + 3*a^2 + 4*a^4 + 2*a^5 + 3*a^6 + a^7 + 3*a^8 + 3*a^9 + 9*a^10 + 5*a^11 + 7*a^13 + 9*a^14 + 5*a^15 + 10*a^17 + 7*a^18 + 4*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (a + 3*a^2 + 9*a^4 + 10*a^5 + 4*a^6 + 6*a^7 + 10*a^8 + 4*a^9 + 7*a^10 + 7*a^11 + 7*a^12 + 5*a^13 + 5*a^14 + 5*a^15 + 3*a^18 + 6*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (2*a^2 + 2*a^3 + 8*a^4 + 8*a^5 + 7*a^6 + 10*a^7 + 4*a^8 + 9*a^9 + 10*a^10 + 7*a^11 + 4*a^12 + 4*a^13 + 4*a^14 + 10*a^15 + 10*a^16 + a^17 + 7*a^18 + O(a^20))*t^16 + O(a^20)*t^17 + (9*a + 5*a^2 + 7*a^3 + 5*a^4 + 3*a^5 + 5*a^6 + 6*a^7 + 6*a^8 + 8*a^9 + 8*a^10 + a^11 + 9*a^12 + 3*a^13 + 3*a^14 + 4*a^15 + 9*a^16 + a^17 + 3*a^18 + 9*a^19 + O(a^20))*t^18 + O(a^20)*t^19 + O(t^20))*s^7 + ((6 + 7*a + 3*a^2 + 8*a^4 + 2*a^5 + 7*a^6 + 5*a^7 + 4*a^8 + 6*a^9 + 8*a^10 + 6*a^11 + a^12 + 9*a^13 + 2*a^15 + a^16 + 6*a^17 + a^18 + 7*a^19 + O(a^20))*t^8 + O(a^20)*t^9 + (9 + 3*a + 6*a^2 + 10*a^3 + 4*a^4 + 2*a^5 + 10*a^6 + 2*a^7 + 9*a^9 + a^10 + 7*a^11 + 10*a^12 + 4*a^14 + 9*a^15 + 8*a^16 + 7*a^17 + 10*a^18 + 7*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (5*a + 8*a^2 + a^3 + 10*a^4 + a^5 + 7*a^6 + 2*a^7 + 8*a^8 + 5*a^9 + 10*a^10 + 4*a^11 + 3*a^12 + 7*a^13 + 4*a^14 + 4*a^15 + 10*a^16 + 2*a^17 + 3*a^18 + 7*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (2*a^2 + a^3 + 3*a^4 + 7*a^5 + 7*a^6 + 3*a^7 + 4*a^8 + 10*a^9 + 7*a^10 + 5*a^11 + 2*a^12 + a^13 + 9*a^14 + 7*a^15 + 10*a^16 + 7*a^17 + 3*a^18 + 3*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (10*a + 8*a^2 + 5*a^3 + a^4 + 5*a^5 + 10*a^6 + 2*a^7 + 7*a^8 + 3*a^9 + 2*a^10 + 7*a^11 + 8*a^12 + 9*a^13 + 2*a^14 + 4*a^15 + 4*a^16 + 10*a^17 + 7*a^18 + O(a^20))*t^16 + O(a^20)*t^17 + (2*a^2 + 9*a^3 + 8*a^5 + 8*a^6 + 10*a^7 + 2*a^8 + 9*a^9 + a^10 + 2*a^12 + 5*a^13 + 3*a^14 + 6*a^15 + 8*a^16 + 4*a^17 + 5*a^18 + 4*a^19 + O(a^20))*t^18 + O(a^20)*t^19 + O(t^20))*s^8 + ((9 + 7*a + 8*a^2 + a^3 + 8*a^4 + 9*a^5 + 4*a^6 + 2*a^7 + 4*a^8 + 10*a^9 + 2*a^10 + 3*a^11 + 9*a^12 + 3*a^13 + 9*a^14 + 4*a^15 + 10*a^16 + a^17 + 8*a^18 + 7*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (9*a + 7*a^2 + 10*a^3 + 6*a^4 + 9*a^5 + 6*a^6 + 9*a^8 + 3*a^9 + 4*a^10 + a^12 + 4*a^13 + 2*a^14 + 4*a^15 + 10*a^16 + 10*a^17 + 5*a^18 + 4*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (8*a + 6*a^2 + 5*a^3 + 3*a^4 + 7*a^5 + 5*a^6 + 10*a^7 + 7*a^8 + 5*a^9 + a^10 + 5*a^11 + 3*a^12 + 3*a^13 + 3*a^14 + 7*a^15 + 7*a^16 + a^17 + 7*a^18 + 6*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (10*a + 9*a^2 + 2*a^3 + a^4 + a^5 + 3*a^6 + a^8 + 8*a^10 + 7*a^11 + 5*a^12 + 3*a^14 + 9*a^16 + 3*a^17 + 7*a^18 + 8*a^19 + O(a^20))*t^16 + O(a^20)*t^17 + (6*a + 9*a^2 + 8*a^3 + 7*a^4 + 2*a^5 + 5*a^6 + 3*a^7 + 6*a^8 + 2*a^9 + a^10 + 4*a^12 + 8*a^13 + 10*a^14 + 5*a^15 + 4*a^16 + 3*a^17 + 9*a^18 + 7*a^19 + O(a^20))*t^18 + O(a^20)*t^19 + (2*a + 10*a^2 + a^3 + 2*a^4 + 8*a^5 + 3*a^6 + 4*a^7 + a^8 + 6*a^9 + a^10 + a^11 + a^12 + 10*a^13 + 8*a^14 + 3*a^15 + 2*a^16 + 7*a^19 + O(a^20))*t^20 + O(a^20)*t^21 + O(t^22))*s^9 + ((9 + 9*a + 10*a^2 + a^3 + 6*a^4 + 2*a^5 + 2*a^6 + 4*a^8 + 6*a^9 + 7*a^10 + 7*a^11 + a^12 + a^13 + 8*a^14 + 7*a^15 + 3*a^16 + 8*a^17 + 6*a^19 + O(a^20))*t^10 + O(a^20)*t^11 + (10*a + 4*a^2 + a^4 + 4*a^5 + 5*a^6 + 5*a^7 + 9*a^8 + 3*a^9 + 7*a^11 + 4*a^12 + 2*a^13 + 2*a^14 + 5*a^15 + 3*a^16 + 3*a^17 + 8*a^18 + 4*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (4*a + 2*a^2 + 7*a^3 + 8*a^4 + 10*a^5 + 3*a^6 + 10*a^7 + 5*a^8 + 6*a^9 + a^10 + 9*a^11 + 6*a^12 + 2*a^13 + 10*a^14 + 8*a^15 + a^16 + 5*a^17 + 6*a^18 + 9*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (5*a + 3*a^2 + 10*a^3 + 9*a^4 + 7*a^6 + 3*a^7 + 9*a^8 + 5*a^9 + 8*a^10 + 10*a^11 + 10*a^12 + 10*a^13 + 10*a^14 + 3*a^15 + 2*a^16 + 8*a^17 + a^18 + 10*a^19 + O(a^20))*t^16 + O(a^20)*t^17 + (3*a + 3*a^2 + 9*a^3 + 9*a^4 + a^5 + 2*a^6 + 7*a^7 + 7*a^9 + 3*a^10 + 7*a^11 + 2*a^12 + a^13 + 8*a^14 + 3*a^15 + 8*a^16 + 10*a^17 + 9*a^19 + O(a^20))*t^18 + O(a^20)*t^19 + (a + 7*a^2 + 10*a^3 + 2*a^4 + 6*a^5 + 7*a^6 + 5*a^7 + 4*a^8 + 8*a^9 + 10*a^10 + 5*a^14 + a^15 + 2*a^16 + 9*a^17 + 8*a^18 + O(a^20))*t^20 + O(a^20)*t^21 + O(t^22))*s^10 + ((10 + 5*a^2 + a^3 + 5*a^4 + 9*a^5 + 6*a^6 + 8*a^7 + 10*a^8 + a^9 + 6*a^10 + 9*a^11 + 9*a^12 + 8*a^13 + 3*a^14 + a^15 + 8*a^16 + 8*a^17 + 2*a^18 + 2*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (6*a^3 + 6*a^4 + 10*a^5 + 4*a^6 + 2*a^7 + 7*a^8 + 3*a^9 + 8*a^11 + 10*a^12 + a^13 + 4*a^14 + 10*a^15 + 4*a^16 + 2*a^17 + 3*a^18 + 7*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (9*a^3 + 5*a^4 + 3*a^5 + 7*a^6 + 3*a^7 + 10*a^9 + 2*a^10 + a^11 + 8*a^12 + a^14 + 3*a^15 + 3*a^16 + 2*a^17 + 7*a^18 + 7*a^19 + O(a^20))*t^16 + O(a^20)*t^17 + (3*a^3 + 2*a^4 + a^5 + 2*a^6 + 2*a^8 + 4*a^9 + 10*a^10 + 10*a^11 + 3*a^12 + 7*a^13 + 7*a^14 + 3*a^15 + 8*a^16 + a^17 + 3*a^18 + 5*a^19 + O(a^20))*t^18 + O(a^20)*t^19 + (4*a^3 + 2*a^4 + 4*a^6 + 5*a^7 + 3*a^8 + 7*a^10 + 7*a^12 + a^13 + 4*a^15 + 7*a^17 + 8*a^18 + 7*a^19 + O(a^20))*t^20 + O(a^20)*t^21 + (5*a^3 + a^4 + 9*a^5 + 8*a^6 + 3*a^7 + 2*a^8 + 2*a^9 + 3*a^10 + 10*a^11 + 2*a^12 + 3*a^13 + 8*a^14 + 3*a^15 + 8*a^16 + 2*a^17 + 3*a^18 + 5*a^19 + O(a^20))*t^22 + O(a^20)*t^23 + O(t^24))*s^11 + ((1 + 10*a + 4*a^2 + 5*a^3 + 2*a^4 + a^5 + 7*a^7 + 9*a^8 + a^9 + 7*a^10 + 7*a^11 + 2*a^12 + 4*a^13 + 2*a^14 + 8*a^15 + 2*a^16 + 2*a^17 + 3*a^18 + 8*a^19 + O(a^20))*t^12 + O(a^20)*t^13 + (5*a + 6*a^3 + 6*a^4 + a^5 + 6*a^6 + 4*a^7 + 2*a^8 + 3*a^9 + 9*a^10 + 8*a^11 + 7*a^12 + 5*a^13 + 5*a^14 + a^15 + 10*a^16 + 7*a^17 + 4*a^18 + 3*a^19 + O(a^20))*t^14 + O(a^20)*t^15 + (2*a + 8*a^3 + 5*a^4 + 5*a^5 + 3*a^6 + 5*a^7 + 3*a^8 + 9*a^9 + 5*a^11 + 9*a^12 + 5*a^13 + 3*a^14 + 9*a^15 + 3*a^16 + 5*a^17 + a^18 + 8*a^19 + O(a^20))*t^16 + O(a^20)*t^17 + (8*a + 5*a^3 + 2*a^4 + 8*a^5 + 3*a^6 + 9*a^7 + 7*a^8 + 8*a^9 + 6*a^10 + 8*a^11 + 9*a^12 + 9*a^13 + 8*a^14 + 8*a^15 + 7*a^16 + 8*a^17 + 7*a^19 + O(a^20))*t^18 + O(a^20)*t^19 + (7*a + 4*a^3 + 2*a^4 + 5*a^5 + 5*a^6 + 8*a^7 + 9*a^8 + 2*a^9 + 6*a^10 + 10*a^11 + 10*a^12 + 6*a^13 + 10*a^14 + 5*a^15 + 7*a^16 + 7*a^17 + 9*a^18 + O(a^20))*t^20 + O(a^20)*t^21 + (6*a + 9*a^3 + a^4 + 8*a^5 + a^6 + a^7 + 2*a^8 + a^10 + 4*a^11 + 3*a^12 + 7*a^13 + 5*a^14 + 8*a^15 + 4*a^17 + 9*a^18 + 5*a^19 + O(a^20))*t^22 + O(a^20)*t^23 + O(t^24))*s^12
sage: y = (1 + O(a^20))*t + ((10 + a + 10*a^2 + 10*a^4 + 10*a^6 + 10*a^8 + 10*a^10 + 10*a^12 + 10*a^14 + 10*a^16 + 10*a^18 + O(a^20))*t + O(a^21)*t^2 + (6*a + 7*a^3 + 7*a^5 + 5*a^7 + 9*a^9 + 3*a^11 + 2*a^15 + 2*a^17 + O(a^21))*t^3 + O(a^21)*t^4 + (9*a + a^3 + 2*a^5 + 6*a^7 + 2*a^11 + 4*a^13 + 2*a^17 + a^19 + O(a^21))*t^5 + O(a^21)*t^6 + (3*a + a^3 + 5*a^5 + a^11 + 4*a^13 + 9*a^15 + 4*a^17 + 9*a^19 + O(a^21))*t^7 + O(a^21)*t^8 + (4*a + 8*a^3 + 4*a^5 + a^11 + 10*a^13 + 7*a^15 + 2*a^17 + 3*a^19 + O(a^21))*t^9 + O(a^21)*t^10 + (5*a + 9*a^3 + 2*a^5 + 5*a^9 + 8*a^11 + 5*a^13 + 3*a^15 + 5*a^17 + 8*a^19 + O(a^21))*t^11 + O(t^13))*s
sage: f = x/y                 #ok
sage: g = x*derivative(x)     #ok
sage: h = x*derivative(x)/y  
---------------------------------------------------------------------------
<type 'exceptions.TypeError'>             Traceback (most recent call last)

/home/jen/<ipython console> in <module>()

/home/jen/element.pyx in sage.structure.element.RingElement.__div__()

/home/jen/coerce.pxi in sage.structure.element._div_c()

/home/jen/power_series_ring_element.pyx in sage.rings.power_series_ring_element.PowerSeries._div_c_impl()

/home/jen/element.pyx in sage.structure.element.RingElement.__mul__()

/home/jen/coerce.pxi in sage.structure.element._mul_c()

/home/jen/power_series_poly.pyx in sage.rings.power_series_poly.PowerSeries_poly._mul_c_impl()

/home/jen/element.pyx in sage.structure.element.RingElement.__mul__()

/home/jen/coerce.pxi in sage.structure.element._mul_c()

/home/jen/element.pyx in sage.structure.element.RingElement._mul_()

/home/jen/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial._mul_c_impl()

/home/jen/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial._mul_karatsuba()

/home/jen/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.do_karatsuba()

/home/jen/polynomial_element.pyx in sage.rings.polynomial.polynomial_element._karatsuba_sum()

/home/jen/element.pyx in sage.structure.element.ModuleElement.__add__()

/home/jen/coerce.pxi in sage.structure.element._add_c()

/home/jen/laurent_series_ring_element.pyx in sage.rings.laurent_series_ring_element.LaurentSeries._add_c_impl()

/home/jen/laurent_series_ring_element.pyx in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()

/home/jen/power_series_poly.pyx in sage.rings.power_series_poly.PowerSeries_poly.valuation()

/home/jen/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial.valuation()

<type 'exceptions.TypeError'>: The polynomial, p, must have the same parent as self.

CC: @roed314

Component: number theory

Keywords: power series, p-adic extensions

Author: Kiran Kedlaya

Reviewer: Mike Hansen

Merged: sage-4.3.rc0

Issue created by migration from https://trac.sagemath.org/ticket/2943

[jbalakrishnan]

comment:1

This is strange:

sage: (derivative(x)).parent()
Power Series Ring in s over Laurent Series Ring in t over Eisenstein Extension of 11-adic Field with capped relative precision 10 in a defined by (1 + O(11^10))*x^2 + (10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + 10*11^10 + O(11^11))
sage: y.parent()
Power Series Ring in s over Laurent Series Ring in t over Eisenstein Extension of 11-adic Field with capped relative precision 10 in a defined by (1 + O(11^10))*x^2 + (10*11 + 10*11^2 + 10*11^3 + 10*11^4 + 10*11^5 + 10*11^6 + 10*11^7 + 10*11^8 + 10*11^9 + 10*11^10 + O(11^11))
sage: (derivative(x)).parent == y.parent()
False

[sagetrac-dmharvey]

comment:2

Here is a much smaller example that triggers the bug:

sage: R.<u> = QQ[]
sage: p = 11
sage: K = Qp(p,10)
sage: J.<a> = K.extension(u^2-p)
sage: C.<t> = LaurentSeriesRing(J)
sage: D.<s> = PowerSeriesRing(C)

sage: y = t + (t^2 + O(t^3))*s
sage: h = y / y
[boom]

Interestingly, if we use the vanilla p-adics instead of a ramified extension, we get a different traceback, which seems to indicate a different (possibly related?) bug:

sage: R.<u> = QQ[]
sage: p = 11
sage: K = Qp(p,10)
sage: C.<t> = LaurentSeriesRing(K)
sage: D.<s> = PowerSeriesRing(C)

sage: y = t + (t^2 + O(t^3))*s

sage: h = y / y
Traceback (most recent call last):
...
File "/Users/david/sage-2.11/local/lib/python2.5/site-packages/sage/rings/polynomial/padics/polynomial_padic_capped_relative_dense.py", line 379, in __getslice__
    raise IndexError, "list index out of range"
IndexError: list index out of range

[sagetrac-dmharvey]

comment:3

Even series inversion gives the list index breakage:

sage: p = 11
sage: K = Qp(p,10)
sage: C.<t> = LaurentSeriesRing(K)
sage: D.<s> = PowerSeriesRing(C)
sage: z = 1 + (t^3 + O(t^13))*s
sage: 1/z

[sagetrac-dmharvey]

comment:4

Actually even just squaring something really simple can break:

sage: K = Qp(p,10)
sage: C.<t> = LaurentSeriesRing(K)
sage: D.<s> = PowerSeriesRing(C)
sage: z = (1 + O(t)) + t*s^2
sage: z * z
[boom]

[sagetrac-dmharvey]

comment:5

ok, the bug is in the polynomial mult instead of the power series mult:

sage: K = Qp(p,10)
sage: C.<t> = LaurentSeriesRing(K)
sage: D.<s> = PolynomialRing(C)
sage: z = (1 + O(t)) + t*s^2
sage: z * z
[boom]

[sagetrac-dmharvey]

comment:6

At least part of this bug is caused by some broken code in p-adic polynomial getslice. Here is the example from the docstring:

sage: K = Qp(13,7)
sage: R.<t> = K[]       
sage: a = 13^7*t^3 + K(169,4)*t - 13^4
sage: a[1:2]
(13^2 + O(13^4))*t

but this one dies:

sage: t[0:1]
[boom]

[sagetrac-dmharvey]

comment:7

A smaller example of the original bug (this example involves only multiplication, no division):

sage: R.<u> = QQ[]
sage: p = 11
sage: K = Qp(p,10)
sage: J.<a> = K.extension(u^2-p)
sage: C.<t> = LaurentSeriesRing(J)
sage: D.<s> = PowerSeriesRing(C)
sage: x = t + (t^2 + O(t^3))*s
sage: y = t^(-1) + (-1 + O(t))*s + O(s^2)
sage: x * y
[boom]