# 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.

## Ways to use arcs :

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

## For the programmer

The object arcs is .