Missing (?) final std (redSB) in primdec

[gorzel]

Why does primdec not peforms a final std on the radical components? It does not cost too much to do this, but it will often clearify the result.

Example, the solution is just the point x=2,y=2:

> LIB "primdec.lib";
// ** loaded /usr/local/bin/../share/singular/LIB/primdec.lib (4.0.2.0,Apr_2015)
> ring r =0,(x,y),dp;
> ideal I = y^4-8*y^3+24*y^2-32*y+16,
. 1/32*y^3-15/64*y^2+x+1/8*y-25/16;

> radical(I);
_[1]=y-2
_[2]=x-2

> primdecGTZ(I);
[1]:
   [1]:
      _[1]=y4-8y3+24y2-32y+16
      _[2]=1/32y3-15/64y2+x+1/8y-25/16
   [2]:
      _[1]=y-2
      _[2]=1/32y3-15/64y2+x+1/8y-25/16
> option(redSB);
> primdecGTZ(I);
[1]:
   [1]:
      _[1]=y4-8y3+24y2-32y+16
      _[2]=1/32y3-15/64y2+x+1/8y-25/16
   [2]:
      _[1]=y-2
      _[2]=1/32y3-15/64y2+x+1/8y-25/16    // <-- simplify this !
> ideal J = _[1][2];
> std(J);
_[1]=y-2
_[2]=x-2

Compare:

> facstd(I);
[1]:
   _[1]=-128xy+65y2+64x+80y-36
   _[2]=1024x2-259y2-2752x+448y+1548
   _[3]=2y3-15y2+64x+8y-100
> primdecSY(I);
[1]:
   [1]:
      _[1]=128xy-65y2-64x-80y+36
      _[2]=1024x2-259y2-2752x+448y+1548
      _[3]=2y3-15y2+64x+8y-100
   [2]:
      _[1]=y-2
      _[2]=x-2

[hannes]

std/groebner is a costly operation and should only be used if required.