Macaulay2 » Documentation
Packages » FunctionFieldDesingularization :: arcs
next | previous | forward | backward | up | index | toc

# arcs -- prints node labels for the desingularization tree

- 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.

## Ways to use arcs:

- arcs(RingElement,Ideal,List,File) (missing documentation)

## For the programmer

The object arcs is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/FunctionFieldDesingularization.m2:652:0.