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CohomCalg :: CohomCalg

CohomCalg -- an interface to the CohomCalg software for computing cohomology of torus invariant divisors on a toric variety

Description

CohomCalg is software written by Benjamin Jurke and Thorsten Rahn (in collaboration with Ralph Blumenhagen and Helmut Roschy) for computing the cohomology vectors of torus invariant divisors on a (normal) toric variety (see https://github.com/BenjaminJurke/cohomCalg for more information).

CohomCalg is an efficient and careful implementation. One limitation is that the number of rays in the fan and the number of generators of the Stanley-Reisner ideal of the fan must both be no larger than 64.

Here is a sample usage of this package in Macaulay2. Let’s compute the cohomology of some divisors on a smooth Fano toric variety.

i1 : needsPackage "NormalToricVarieties"

o1 = NormalToricVarieties

o1 : Package
i2 : X = smoothFanoToricVariety(3,15)

o2 = X

o2 : NormalToricVariety
i3 : rays X

o3 = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {0, -1, -1}, {0, -1, 0}, {-1, 0, 0},
     ------------------------------------------------------------------------
     {-1, 1, 0}}

o3 : List
i4 : max X

o4 = {{0, 1, 2}, {0, 1, 3}, {0, 2, 4}, {0, 3, 4}, {1, 2, 6}, {1, 3, 6}, {2,
     ------------------------------------------------------------------------
     4, 5}, {2, 5, 6}, {3, 4, 5}, {3, 5, 6}}

o4 : List
i5 : S = ring X

o5 = S

o5 : PolynomialRing
i6 : SR = dual monomialIdeal X

o6 = monomialIdeal (x x , x x , x x , x x , x x , x x )
                     2 3   1 4   0 5   1 5   0 6   4 6

o6 : MonomialIdeal of S
i7 : KX = toricDivisor X

o7 = - X  - X  - X  - X  - X  - X  - X
        0    1    2    3    4    5    6

o7 : ToricDivisor on X
i8 : assert isVeryAmple (-KX)
i9 : cohoms1 = for i from 0 to 6 list X_i => cohomCalg X_i

    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
                                                                           
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.


    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
  0.00% completed (1 sec remaining)...            
                                                                           
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.


    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
                                                                           
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.


    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
                                                                           
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.


    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
  0.00% completed (1 sec remaining)...            
                                                                           
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.


    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
  0.00% completed (1 sec remaining)...            
                                                                           
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.


o9 = {X  => {2, 0, 0, 0}, X  => {1, 0, 0, 0}, X  => {2, 0, 0, 0}, X  => {2,
       0                   1                   2                   3       
     ------------------------------------------------------------------------
     0, 0, 0}, X  => {1, 0, 0, 0}, X  => {1, 0, 0, 0}, X  => {1, 0, 0, 0}}
                4                   5                   6

o9 : List
i10 : cohoms2 = for i from 0 to 6  list X_i => (
          for j from 0 to dim X list rank HH^j(X, OO_X(toSequence degree X_i))
          )

o10 = {X  => {2, 0, 0, 0}, X  => {1, 0, 0, 0}, X  => {2, 0, 0, 0}, X  => {2,
        0                   1                   2                   3       
      -----------------------------------------------------------------------
      0, 0, 0}, X  => {1, 0, 0, 0}, X  => {1, 0, 0, 0}, X  => {1, 0, 0, 0}}
                 4                   5                   6

o10 : List
i11 : assert(cohoms1 === cohoms2)

For efficiency reasons, it is better, if this works for your use, to call CohomCalg by batching together several cohomology requests.

i12 : needsPackage "ReflexivePolytopesDB"

o12 = ReflexivePolytopesDB

o12 : Package
i13 : topes = kreuzerSkarke(21, Limit => 20);
using offline data file: ks21-n100.txt
i14 : A = matrix topes_10

o14 = | 1 0 0 -1 2  0  0 -3 -2 1  |
      | 0 1 0 1  -1 1  0 1  0  -1 |
      | 0 0 1 1  -1 -1 0 4  2  -2 |
      | 0 0 0 0  0  0  1 -1 -1 1  |

               4        10
o14 : Matrix ZZ  <--- ZZ
i15 : P = convexHull A

o15 = P

o15 : Polyhedron
i16 : X = normalToricVariety P

o16 = X

o16 : NormalToricVariety
i17 : SR = dual monomialIdeal X

o17 = monomialIdeal (x x , x x x , x x , x x x , x x x , x x x x , x x x ,
                      1 2   0 1 3   0 4   0 2 6   0 3 6   1 3 5 6   1 3 7 
      -----------------------------------------------------------------------
      x x x , x x x x , x x x , x x x , x x x x , x x x x , x x x , x x x x ,
       1 4 7   0 3 5 7   2 4 8   2 6 8   3 5 6 8   4 5 6 8   4 7 8   2 5 7 8 
      -----------------------------------------------------------------------
      x x x x , x x x x , x x x , x x x , x x , x x x , x x x , x x x ,
       3 5 7 8   3 6 7 8   0 1 9   2 4 9   5 9   0 6 9   2 6 9   1 7 9 
      -----------------------------------------------------------------------
      x x x )
       4 7 9

o17 : MonomialIdeal of QQ[x , x , x , x , x , x , x , x , x , x ]
                           0   1   2   3   4   5   6   7   8   9
i18 : D2 = subsets(for i from 0 to #rays X - 1 list (-X_i), 2)

o18 = {{- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
           0     1       0     2       1     2       0     3       1     3  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
          2     3       0     4       1     4       2     4       3     4  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
          0     5       1     5       2     5       3     5       4     5  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
          0     6       1     6       2     6       3     6       4     6  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
          5     6       0     7       1     7       2     7       3     7  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
          4     7       5     7       6     7       0     8       1     8  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
          2     8       3     8       4     8       5     8       6     8  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X },
          7     8       0     9       1     9       2     9       3     9  
      -----------------------------------------------------------------------
      {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }, {- X , - X }}
          4     9       5     9       6     9       7     9       8     9

o18 : List
i19 : D2 = D2/sum/degree

o19 = {{0, 1, -2, -2, 4, 0}, {0, 1, -1, 1, 0, -2}, {2, 2, 3, 1, -4, -6}, {-1,
      -----------------------------------------------------------------------
      0, -4, -2, 5, 3}, {1, 1, 0, -2, 1, -1}, {1, 1, 1, 1, -3, -3}, {-2, 0,
      -----------------------------------------------------------------------
      -3, -1, 4, 2}, {0, 1, 1, -1, 0, -2}, {0, 1, 2, 2, -4, -4}, {-1, 0, -1,
      -----------------------------------------------------------------------
      -1, 1, 1}, {-1, -1, -3, -1, 4, 2}, {1, 0, 1, -1, 0, -2}, {1, 0, 2, 2,
      -----------------------------------------------------------------------
      -4, -4}, {0, -1, -1, -1, 1, 1}, {-1, -1, 0, 0, 0, 0}, {-1, 0, -4, -1,
      -----------------------------------------------------------------------
      4, 2}, {1, 1, 0, -1, 0, -2}, {1, 1, 1, 2, -4, -4}, {0, 0, -2, -1, 1,
      -----------------------------------------------------------------------
      1}, {-1, 0, -1, 0, 0, 0}, {0, -1, -1, 0, 0, 0}, {-1, 0, -3, -2, 4, 2},
      -----------------------------------------------------------------------
      {1, 1, 1, -2, 0, -2}, {1, 1, 2, 1, -4, -4}, {0, 0, -1, -2, 1, 1}, {-1,
      -----------------------------------------------------------------------
      0, 0, -1, 0, 0}, {0, -1, 0, -1, 0, 0}, {0, 0, -1, -1, 0, 0}, {-1, 0,
      -----------------------------------------------------------------------
      -3, -1, 3, 2}, {1, 1, 1, -1, -1, -2}, {1, 1, 2, 2, -5, -4}, {0, 0, -1,
      -----------------------------------------------------------------------
      -1, 0, 1}, {-1, 0, 0, 0, -1, 0}, {0, -1, 0, 0, -1, 0}, {0, 0, -1, 0,
      -----------------------------------------------------------------------
      -1, 0}, {0, 0, 0, -1, -1, 0}, {-1, 0, -3, -1, 4, 1}, {1, 1, 1, -1, 0,
      -----------------------------------------------------------------------
      -3}, {1, 1, 2, 2, -4, -5}, {0, 0, -1, -1, 1, 0}, {-1, 0, 0, 0, 0, -1},
      -----------------------------------------------------------------------
      {0, -1, 0, 0, 0, -1}, {0, 0, -1, 0, 0, -1}, {0, 0, 0, -1, 0, -1}, {0,
      -----------------------------------------------------------------------
      0, 0, 0, -1, -1}}

o19 : List
i20 : elapsedTime hvecs = cohomCalg(X, D2)

    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

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  75.00% completed (5 secs remaining)...            
                                                                           
WARNING: The Serre dualization reduction was unable to uniquely resolve 86 of the original 90 ambiguous monoms.
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 45 (0.0% done)...       
Computing target cohomology 2 of 45 (2.2% done)...       
Computing target cohomology 3 of 45 (4.4% done)...       
Computing target cohomology 4 of 45 (6.7% done)...       
Computing target cohomology 5 of 45 (8.9% done)...       
Computing target cohomology 6 of 45 (11.1% done)...       
Computing target cohomology 7 of 45 (13.3% done)...       
Computing target cohomology 8 of 45 (15.6% done)...       
Computing target cohomology 9 of 45 (17.8% done)...       
Computing target cohomology 10 of 45 (20.0% done)...       
Computing target cohomology 11 of 45 (22.2% done)...       
Computing target cohomology 12 of 45 (24.4% done)...       
Computing target cohomology 13 of 45 (26.7% done)...       
Computing target cohomology 14 of 45 (28.9% done)...       
Computing target cohomology 15 of 45 (31.1% done)...       
Computing target cohomology 16 of 45 (33.3% done)...       
Computing target cohomology 17 of 45 (35.6% done)...       
Computing target cohomology 18 of 45 (37.8% done)...       
Computing target cohomology 19 of 45 (40.0% done)...       
Computing target cohomology 20 of 45 (42.2% done)...       
Computing target cohomology 21 of 45 (44.4% done)...       
Computing target cohomology 22 of 45 (46.7% done)...       
Computing target cohomology 23 of 45 (48.9% done)...       
Computing target cohomology 24 of 45 (51.1% done)...       
Computing target cohomology 25 of 45 (53.3% done)...       
Computing target cohomology 26 of 45 (55.6% done)...       
Computing target cohomology 27 of 45 (57.8% done)...       
Computing target cohomology 28 of 45 (60.0% done)...       
Computing target cohomology 29 of 45 (62.2% done)...       
Computing target cohomology 30 of 45 (64.4% done)...       
Computing target cohomology 31 of 45 (66.7% done)...       
Computing target cohomology 32 of 45 (68.9% done)...       
Computing target cohomology 33 of 45 (71.1% done)...       
Computing target cohomology 34 of 45 (73.3% done)...       
Computing target cohomology 35 of 45 (75.6% done)...       
Computing target cohomology 36 of 45 (77.8% done)...       
Computing target cohomology 37 of 45 (80.0% done)...       
Computing target cohomology 38 of 45 (82.2% done)...       
Computing target cohomology 39 of 45 (84.4% done)...       
Computing target cohomology 40 of 45 (86.7% done)...       
Computing target cohomology 41 of 45 (88.9% done)...       
Computing target cohomology 42 of 45 (91.1% done)...       
Computing target cohomology 43 of 45 (93.3% done)...       
Computing target cohomology 44 of 45 (95.6% done)...       
Computing target cohomology 45 of 45 (97.8% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.

     -- 7.84052 seconds elapsed

o20 = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 0, 0, 0},
      -----------------------------------------------------------------------
      {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 0, 0, 0}, {0,
      -----------------------------------------------------------------------
      0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0,
      -----------------------------------------------------------------------
      0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0,
      -----------------------------------------------------------------------
      0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0,
      -----------------------------------------------------------------------
      0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
      -----------------------------------------------------------------------
      {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0,
      -----------------------------------------------------------------------
      0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0,
      -----------------------------------------------------------------------
      0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0,
      -----------------------------------------------------------------------
      0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1, 0, 0,
      -----------------------------------------------------------------------
      0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}

o20 : List
i21 : peek cohomCalg X

o21 = MutableHashTable{{-1, -1, -3, -1, 4, 2} => {{0, 0, 0, 0, 0}, {}}          }
                       {-1, -1, 0, 0, 0, 0} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, -1, -1, 1, 1} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, -1, 0, 0, 0} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, -3, -1, 3, 2} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, -3, -1, 4, 1} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, -3, -2, 4, 2} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, -4, -1, 4, 2} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, -4, -2, 5, 3} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, 0, -1, 0, 0} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, 0, 0, -1, 0} => {{0, 0, 0, 0, 0}, {}}
                       {-1, 0, 0, 0, 0, -1} => {{0, 0, 0, 0, 0}, {}}
                       {-2, 0, -3, -1, 4, 2} => {{0, 1, 0, 0, 0}, {{1, 1x0*x4}}}
                       {0, -1, -1, -1, 1, 1} => {{0, 0, 0, 0, 0}, {}}
                       {0, -1, -1, 0, 0, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, -1, 0, -1, 0, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, -1, 0, 0, -1, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, -1, 0, 0, 0, -1} => {{0, 1, 0, 0, 0}, {{1, 1x5*x9}}}
                       {0, 0, -1, -1, 0, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, -1, -1, 0, 1} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, -1, -1, 1, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, -1, -2, 1, 1} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, -1, 0, -1, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, -1, 0, 0, -1} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, -2, -1, 1, 1} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, 0, -1, -1, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, 0, -1, 0, -1} => {{0, 0, 0, 0, 0}, {}}
                       {0, 0, 0, 0, -1, -1} => {{0, 0, 0, 0, 0}, {}}
                       {0, 1, -1, 1, 0, -2} => {{0, 0, 0, 0, 0}, {}}
                       {0, 1, -2, -2, 4, 0} => {{0, 0, 0, 0, 0}, {}}
                       {0, 1, 1, -1, 0, -2} => {{0, 0, 0, 0, 0}, {}}
                       {0, 1, 2, 2, -4, -4} => {{0, 0, 0, 0, 0}, {}}
                       {1, 0, 1, -1, 0, -2} => {{0, 0, 0, 0, 0}, {}}
                       {1, 0, 2, 2, -4, -4} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 0, -1, 0, -2} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 0, -2, 1, -1} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 1, -1, -1, -2} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 1, -1, 0, -3} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 1, -2, 0, -2} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 1, 1, -3, -3} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 1, 2, -4, -4} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 2, 1, -4, -4} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 2, 2, -4, -5} => {{0, 0, 0, 0, 0}, {}}
                       {1, 1, 2, 2, -5, -4} => {{0, 0, 0, 0, 0}, {}}
                       {2, 2, 3, 1, -4, -6} => {{0, 1, 0, 0, 0}, {{1, 1x1*x2}}}
i22 : degree(X_3 + X_7 + X_8)

o22 = {0, 0, 1, 2, 0, -1}

o22 : List
i23 : elapsedTime cohomvec1 = cohomCalg(X_3 + X_7 + X_8)

    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
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  75.00% completed (5 secs remaining)...            
                                                                           
WARNING: The Serre dualization reduction was unable to uniquely resolve 86 of the original 90 ambiguous monoms.
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.

     -- 3.21506 seconds elapsed

o23 = {1, 0, 0, 0, 0}

o23 : List
i24 : elapsedTime cohomvec2 = for j from 0 to dim X list rank HH^j(X, OO_X(0,0,1,2,0,-1))
     -- 14.9908 seconds elapsed

o24 = {1, 0, 0, 0, 0}

o24 : List
i25 : assert(cohomvec1 == cohomvec2)
i26 : degree(X_3 + X_7 - X_8)

o26 = {0, 0, 1, 2, -2, -1}

o26 : List
i27 : elapsedTime cohomvec1 = cohomCalg(X_3 + X_7 - X_8)

    cohomCalg v0.31b
    (compiled on May 27 2019 @ 14:43:32 for Linux/Unix x86-64 / 64 bit)
    author: Benjamin Jurke (mail@benjaminjurke.net)
    Based on the algorithm presented in arXiv:1003.5217


Usage and generation of intermediate monomial files deactivated.

Starting computation of secondary sequences...
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WARNING: The Serre dualization reduction was unable to uniquely resolve 86 of the original 90 ambiguous monoms.
Computation of secondary cohomologies and contributions complete.
Computing target cohomology 1 of 1 (0.0% done)...       
Computation of the target cohomology group dimensions complete.

    All done. Programm run successfully completed.

     -- 3.20817 seconds elapsed

o27 = {0, 0, 0, 0, 0}

o27 : List
i28 : elapsedTime cohomvec2 = elapsedTime for j from 0 to dim X list rank HH^j(X, OO_X(0,0,1,2,-2,-1))
     -- 0.278541 seconds elapsed
     -- 0.278556 seconds elapsed

o28 = {0, 0, 0, 0, 0}

o28 : List
i29 : assert(cohomvec1 == cohomvec2)

cohomCalg computes cohomology vectors by calling CohomCalg. It also stashes it’s results in the toric variety’s cache table, so computations need not be performed twice.

See also

Author

Version

This documentation describes version 0.8 of CohomCalg.

Source code

The source code from which this documentation is derived is in the file CohomCalg.m2.

Exports

  • Functions and commands
    • cohomCalg -- compute cohomology vectors using the CohomCalg software
  • Symbols
    • Silent, see cohomCalg -- compute cohomology vectors using the CohomCalg software
  • Other things