arcs -- prints node labels for the desingularization tree

Synopsis

• Usage:

  (prevlist,levellist,clist,blist,nlist,elist,philist,leaflist,Philist) = arcs(b0,n0e0,fout)

• Inputs:
  • polyb, irreducible polynomial for the domain A_k
  • ineq, list of inequality constraints for the part
  • eq, ideal of equality constraints for the part
  • fout, output file to which results are written
• Outputs:
  • prevlist, a list, previous node in tree list
  • levellist, a list, level determines the rings being used
  • clist, a list, irreducible mod x_d
  • blist, a list, irreducible
  • nlist, a list, inequality constraints
  • elist, a list, ideal of equality constraints
  • philist, a list, birational change of variables maps between node and previous node
  • leaflist, a list, leaf of tree or not
  • Philist, a list, birational change of variables maps between node and root node

Description

i1 : fout = openOut "curve_example0";

i2 : F = QQ;

i3 : d = 1;

i4 : P0 = F[a_{0,0}..a_{0,d}];

i5 : R0 = P0[x_{0,0}..x_{0,d},
     Weights=> entries negLexMatrix(d),Global=>false];

i6 : b0 = x_{0,0}^3+x_{0,0}*x_{0,1}+x_{0,1}^5;

i7 : n0 = {};

i8 : e0 = ideal(a_{0,0}^3+a_{0,0}*a_{0,1}+a_{0,1}^5);

o8 : Ideal of P0

i9 : tree = arcs(b0,e0,n0,fout);

i10 : b1 = x_{0,0}^3+x_{0,0}^2*x_{0,1}^4+x_{0,1}^5;

i11 : n1 = {};

i12 : e1 = ideal(a_{0,0},a_{0,1});

o12 : Ideal of P0

i13 : tree = arcs(b1,e1,n1,fout);     

i14 : fout << close;

i15 : 

Each node is described by an irreducible polynomial bnew, cnew its reduction mod x_d, a list of inequality constraints, an ideal of equality constraints, a birational change-of-variables from its previous node, and one from the root as well. See the test examples for syntax.