primdec.lib: newZero_decomp() seems to expect redSB option

[jakobkroeker]

origin: https://github.com/surface-smoothers/lipmanresolve/issues/284

newZero_decomp seems to expect redSB option and that is not documented. Look at all newZero_decomp calls: shortly before the calls the option 'redSB' is set.

At least in zeroSp() (which is called by insepDecomp()) parameter i has to be reduced groebner basis.

Anne: -check also that in newZero_decomp the input ideal is a standard basis. (sure that is mandatory?)

• Anne: check ordering in newZero_decomp (which ordering is expected?)

proposal to ordering check:

// checks only straight ordering, no block and no weighted degree orderings.
static proc orderingIs(def R, string ordstring)
{
    ASSUME(1, "lp"==ordstring ||
              "dp"==ordstring ||
              "rp"==ordstring ||
              "Dp"==ordstring ||
              "ds"==ordstring ||
              "ls"==ordstring ||
              "Ds"==ordstring ||
              "rs"==ordstring );

    list rl = ringlist(R);
    ASSUME(1, size(rl[3])==2 );
    intvec v  = 1;
    if (rl[3][1][1]=="C")
    {
       if (ordstring != rl[3][2][1]) {      return (0); }
       if ( v != rl[3][2][2] )       {      return (0); }
    }
    else
    {
        ASSUME(1, "C"==rl[3][2][1] );

        if (ordstring != rl[3][1][1]) {     return (0); }
        if ( v != rl[3][1][2] )       {     return (0); }
    }
    return (1);
}

proc ordering_is_certainly_lp( def R )  { return ( orderingIs(R,"lp") ); }
example
{
   ring R = 0,(x,y,z),lp;
   ordering_is_certainly_lp(R);

   // not ordering_is_certainly_lp() is not equivalent to 'ordering is not lp':
   // therefore the naming contains the word 'certainly'
   ring R = 0,(x,y,z),( lp(1), lp(1), lp(1));
   ordering_is_certainly_lp(R);    
}

proc ordering_is_certainly_dp( def R )  { return ( orderingIs(R,"dp") ); }
proc ordering_is_certainly_rp( def R )  { return ( orderingIs(R,"rp") ); }
proc ordering_is_certainly_Dp( def R )  { return ( orderingIs(R,"Dp") ); }
proc ordering_is_certainly_ls( def R )  { return ( orderingIs(R,"ls") ); }
proc ordering_is_certainly_ds( def R )  { return ( orderingIs(R,"ds") ); }
proc ordering_is_certainly_rs( def R )  { return ( orderingIs(R,"rs") ); }
proc ordering_is_certainly_Ds( def R )  { return ( orderingIs(R,"Ds") ); }

[jakobkroeker]

asked Gerhard Pfister and Hans Schoenemann, if newZero_decomp() expects the option 'redSB' . Waiting for an answer

Also open a proposed feature ticket (giving this example) where all developers asked to check their library code if the required preconditions are documented and/or if the preconditions are checked

[jakobkroeker]

asked Gerhard Pfister and Hans Schoenemann, if newZero_decomp() expects the option 'redSB' .

Answer:

Das ist keine Voraussetzung, hat sich aber als gut erwiesen.

I do not believe that (see zeroSp()) => find a counterexample?