Changes between Version 17 and Version 53 of Ticket #26195


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Timestamp:
09/30/18 15:09:47 (10 months ago)
Author:
caruso
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  • Ticket #26195

    • Property Status changed from new to needs_review
    • Property Authors changed from to Xavier Caruso, Thibaut Verron
    • Property Cc roed added
    • Property Commit changed from 8446736d3e9bb14d60b6688f8d258f8a47cb66f6 to 408512dee2f068e87131cf118b59ffb52882bd2e
  • Ticket #26195 – Description

    v17 v53  
    11This ticket implements Tate algebras over complete discrete valuation rings/fields, together with Gröbner bases for ideals in these algebras.
    22
    3 Small demo:
    4 {{{
    5 sage: R = Zp(2, 10, print_mode='digits')
    6 sage: A.<x,y> = TateAlgebra(R)
    7 sage: f = x^2 + 2*x + x*y^3 + 4*y + y
    8 sage: g = y^2*x^3 + 2*x + x^2 + 2*x^4*y
    9 sage: I = A.ideal([f,2*g])
    10 sage: J = A.ideal([f,g])
    11 sage: 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)]
    15 sage: 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)]
    18 sage: I.is_saturated()
    19 False
    20 sage: Io = I.saturate()
    21 sage: J.is_saturated()
    22 True
    23 sage: Io == J
    24 True
    25 }}}
     3See the documentation of `sage.rings.tate_algebra` for details.