#### D.5.5.1 BINresol

Procedure from library `resbinomial.lib` (see resbinomial_lib).

Usage:
  BINresol(J); J ideal

Return:
  E-resolution of singularities of a binomial ideal J in terms of the affine charts, see example

Example:

    LIB "resbinomial.lib";
    ring r = 0,(x(1..2)),dp;
    ideal J=x(1)^2-x(2)^3;
    list B=BINresol(J);
    B[1]; // list of final charts
    ==> [1]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) y(2)
    ==> //        block   2 : ordering C
    ==> [2]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) y(2)
    ==> //        block   2 : ordering C
    ==> [3]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) x(2)
    ==> //        block   2 : ordering C
    ==> [4]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) y(2)
    ==> //        block   2 : ordering C
    B[2]; // list of all charts
    ==> [1]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2)
    ==> //        block   2 : ordering C
    ==> [2]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) y(2)
    ==> //        block   2 : ordering C
    ==> [3]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2)
    ==> //        block   2 : ordering C
    ==> [4]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) y(2)
    ==> //        block   2 : ordering C
    ==> [5]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2)
    ==> //        block   2 : ordering C
    ==> [6]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) x(2)
    ==> //        block   2 : ordering C
    ==> [7]:
    ==>    //   characteristic : 0
    ==> //   number of vars : 2
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) y(2)
    ==> //        block   2 : ordering C
    ring r = 2,(x(1..3)),dp;
    ==> // ** redefining r **
    ideal J=x(1)^2-x(2)^2*x(3)^2;
    list B=BINresol(J);
    ==> // ** redefining B **
    B[2]; // list of all charts
    ==> [1]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2) x(3)
    ==> //        block   2 : ordering C
    ==> [2]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) y(2) y(3)
    ==> //        block   2 : ordering C
    ==> [3]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2) x(3)
    ==> //        block   2 : ordering C
    ==> [4]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2) x(3)
    ==> //        block   2 : ordering C
    ==> [5]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) y(2) y(3)
    ==> //        block   2 : ordering C
    ==> [6]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2) x(3)
    ==> //        block   2 : ordering C
    ==> [7]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) y(2) y(3)
    ==> //        block   2 : ordering C
    ==> [8]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2) x(3)
    ==> //        block   2 : ordering C
    ==> [9]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) y(2) x(3)
    ==> //        block   2 : ordering C
    ==> [10]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) x(2) x(3)
    ==> //        block   2 : ordering C
    ==> [11]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    x(1) x(2) y(3)
    ==> //        block   2 : ordering C
    ==> [12]:
    ==>    //   characteristic : 2
    ==> //   number of vars : 3
    ==> //        block   1 : ordering dp
    ==> //                  : names    y(1) x(2) x(3)
    ==> //        block   2 : ordering C

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