Changes between Initial Version and Version 16 of Ticket #26195


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Timestamp:
09/07/18 18:30:37 (11 months ago)
Author:
caruso
Comment:

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  • Ticket #26195

    • Property Cc TristanVaccon caruso added; vaccon removed
    • Property Commit changed from to 8446736d3e9bb14d60b6688f8d258f8a47cb66f6
    • Property Branch changed from to u/caruso/tate_algebras
  • Ticket #26195 – Description

    initial v16  
    1 We propose to implement Tate algebras over complete discrete valuation rings/fields.
     1This ticket implements Tate algebras over complete discrete valuation rings/fields, together with Gröbner bases for ideals in these algebras.
     2
     3Small demo:
     4{{{
     5sage: R = Zp(2, 10, print_mode='digits')
     6sage: A.<x,y> = TateAlgebra(R)
     7sage: f = x^2 + 2*x + x*y^3 + 4*y + y
     8sage: g = y^2*x^3 + 2*x + x^2 + 2*x^4*y
     9sage: I = A.ideal([f,2*g])
     10sage: J = A.ideal([f,g])
     11sage: I.groebner_basis()
     12[(...0000000001)*x*y^3 + (...0000000001)*x^2 + (...0000000101)*y + (...00000000010)*x,
     13 (...1110001010)*x^2 + (...1010000100)*y^3 + (...1100010100)*x + (...1001101000)*x^2*y^2 + (...0011101000)*y + (...1111110000)*y^2 + (...0000100000)*x^2*y + (...1100100000)*x*y^2 + (...0010100000)*x*y + O(2^10),
     14 (...1111000010)*y + (...1010110100)*y^8 + (...1110011100)*y^3 + (...0100001000)*y^6 + (...0001110000)*y^7 + (...0111010000)*y^5 + (...0011100000)*y^2 + (...1001000000)*y^4 + O(2^10)]
     15sage: J.groebner_basis()
     16[(...0111000101)*x^2 + (...1101000010)*y^3 + (...1110001010)*x + (...0100110100)*x^2*y^2 + (...0001110100)*y + (...0111111000)*y^2 + (...0000010000)*x^2*y + (...1110010000)*x*y^2 + (...0001010000)*x*y + O(2^10),
     17 (...0111100001)*y + (...0101011010)*y^8 + (...0111001110)*y^3 + (...1010000100)*y^6 + (...0000111000)*y^7 + (...0011101000)*y^5 + (...1001110000)*y^2 + (...0100100000)*y^4 + O(2^10)]
     18sage: I.is_saturated()
     19False
     20sage: Io = I.saturate()
     21sage: J.is_saturated()
     22True
     23sage: Io == J
     24}}}