taka@orange:~/this08/Dmodules$ M2
Macaulay 2, version 1.1
with packages: Classic, Core, Elimination, IntegralClosure, LLLBases, Parsing, PrimaryDecomposition, SchurRings, TangentCone

i1 : load "Dmodules.m2"

i2 : S=QQ[x,y]

o2 = S

o2 : PolynomialRing

i3 : f=x*y*(x-y)

      2       2
o3 = x y - x*y

o3 : S

i4 : logCohomology f
 2       2
x y - x*y
{3} | -3 -x+2y |
{2} | x  0     |
{2} | y  xy-y2 |
                             2
{{x*dx + y*dy + 3, x*y*dy - y dy + x - 2y}}
iAllt (integrationAllWithTransfer) in trans.m2
cokernel | xdx+ydy+3 xydy-y2dy+x-2y |
                   1                        5                        9                        7                        2
(QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- 0 <-- 0
                                                                                                                                    
0                        1                        2                        3                        4                        5     6
{0, 0, | x |}
       | 1 |
{0, 0, | xydy-y2dy+x-2y |, | xy-y2 |}
       | xdx+ydy+2      |  | y     |
       | 0              |  | 0     |
                           | 0     |
                           | x     |
                           | 0     |
{0, 1, | x2ydx-xy2dx+2xy-y2  |, | -x2y+xy2 |}
       | -x2ydy+xy2dy-x2+2xy |
{1, 0, | -x -y 0  |}
       | 0  0  -1 |
       | 0  0  0  |
{1, 0, | x2dx+xydy+3x xydx+y2dy+3y -xydy+y2dy-x+2y |, | xy y2 -xy+y2 |}
                                                      | x2 xy 0      |
{2, 0, | -y -x |}

o4 = HashTable{BFunction => (s - 1)                                                                       }
                                                    1
               CohomologyGroups => HashTable{0 => QQ }
                                                    3
                                             1 => QQ
                                                    2
                                             2 => QQ
               Input => cokernel | xdx+ydy+3 xydy-y2dy+x-2y |
               LocalizeMap => LocMap
                                              1                        2                        1
               OmegaRes => (QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- 0
                                                                                                       
                           0                        1                        2                        3
               PreCycles => HashTable{0 => | x |       }
                                           | 1 |
                                      1 => | -x -y 0  |
                                           | 0  0  -1 |
                                           | 0  0  0  |
                                      2 => | -y -x |
               TransferCycles => HashTable{0 => | -x2y+xy2 |    }
                                           1 => | xy y2 -xy+y2 |
                                                | x2 xy 0      |
                                           2 => | -y -x |
                                                 1                        3                        2
               VResolution => (QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- (QQ [x, y, dx, dy])  <-- 0
                                                                                                          
                              0                        1                        2                        3

o4 : HashTable

i5 : quit
taka@orange:~/this08/Dmodules$