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""" TESTS::
sage: R = Zp(5, prec=5, type='fixed-mod') sage: a = random_matrix(R,5) sage: a.determinant() 1 + 3*5 + 3*5^2 + 2*5^4 + O(5^5) sage: K = Qp(3, 10,'capped-rel'); K.krull_dimension() 0
Computation of logs::
sage: Qp(5)(1).log() O(5^20) sage: Qp(5)(-1).log() O(5^20) sage: Qp(5,prec=5)(7).log() 4*5^2 + 4*5^3 + 3*5^4 + O(5^5) sage: Qp(5,prec=10)(25*8).log(p_branch = 0) 5 + 3*5^3 + 3*5^4 + 2*5^5 + 5^6 + 2*5^7 + 3*5^8 + 3*5^9 + O(5^10) sage: Zp(5,prec=10)(8).log() 5 + 3*5^3 + 3*5^4 + 2*5^5 + 5^6 + 2*5^7 + 3*5^8 + 3*5^9 + O(5^10)
Loading and saving elements of various types::
sage: a = Zp(5)(-3); loads(dumps(a)) == a True
sage: M = MatrixSpace(pAdicField(3,100),2) sage: (M([1,0,0,90]) - (1+O(3^100)) * M(1)).left_kernel() Vector space of degree 2 and dimension 1 over 3-adic Field with capped relative precision 100 Basis matrix: [1 + O(3^100) 0] """ |