resol1

 [ ii v] resol1 r 
array of poly ii; string v;
<< vv >> is a string of variables separated by ,
  
 [ ii v] resol1 r 
array of poly ii; array of strings v;
<< vv >> is an array of variable names. 
  
 [ ii v w] resol1 r 
array of poly ii; string v; array w;
<< w >> is a weight vector.
  
 ii may be array of array of poly.
You can also give a parameter << d >> to specify the truncation depth
of the resolution: [ d ii v] resol1, [d ii v w] resol1
  
resol1 constructs a resolution which is adapted (strict)
to a filtration. So, it is not minimal in general.
 r = [s0, s1, s2 , s3, ...].
 s0 is the groebner basis of ii,
 s1 is the syzygy of s0,
 s2 is the syzygy of s1,
 s3 is the syzygy of s2 and so on.
 s1 s0 mul ==> 0, s2 s1 mul ==>0, ...
For details, see math.AG/9805006
cf. sResolution, tparse, s_ring_..., resol0.cp
resol1.withZeroMap returns a resolution with zero maps of the both sides
   of the resolution.
cf. resol1.zeroMapL, resol1.zeroMapR, resol1.withZeroMap.aux
resol1.syzlist : global variable to keep the raw output of sResolution.
   
Example 1: [ [( x^3-y^2 )  ( 2 x Dx + 3 y Dy + 6 )  ( 2 y Dx + 3 x^2 Dy) ] 
             (x,y) ] resol1 pmat ; 
Example 2: [ [( x^3-y^2 )  ( 2 x Dx + 3 y Dy + 6 )  ( 2 y Dx + 3 x^2 Dy) ] 
             (x,y) [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1 pmat ; 
Example 3: [ [[(2 x Dx + 3 y Dy +6) (0)] 
              [(3 x^2 Dy + 2 y Dx) (0)] 
              [(0) (x^2+y^2)] 
              [(0) (x y )] ] 
             (x,y) [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1 pmat ; 
Example 4:  /resol0.verbose 1 def
          [ [[(x^2+y^2+ x y) (x+y)] [(x y ) ( x^2 + x y^3)] ] (x,y) 
            [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1 pmat ;