|  |  D.5.10.4 sheafCohBGG Procedure from librarysheafcoh.lib(see  sheafcoh_lib).
 
Example:Usage:
sheafCohBGG(M,l,h); M module, l,h int
Assume:
Mis graded, and it comes assigned with an admissible degree
vector as an attribute,h>=l, and the basering hasn+1variables.
Return:
intmat, cohomology of twists of the coherent sheaf F on P^n
associated to coker(M). The range of twists is determined by l,h.
Display:
The intmat is displayed in a diagram of the following form: 
 A|  |                 l            l+1                      h
  ----------------------------------------------------------
      n:     h^n(F(l))    h^n(F(l+1))   ......    h^n(F(h))
           ...............................................
      1:     h^1(F(l))    h^1(F(l+1))   ......    h^1(F(h))
      0:     h^0(F(l))    h^0(F(l+1))   ......    h^0(F(h))
  ----------------------------------------------------------
    chi:     chi(F(l))    chi(F(l+1))   ......    chi(F(h))
 | 
 '-'in the diagram refers to a zero entry; a'*'refers to a negative entry (= dimension not yet determined).
refers to a not computed dimension.
 
Note:
This procedure is based on the Bernstein-Gel'fand-Gel'fand
correspondence and on Tate resolution ( see [Eisenbud, Floystad,
Schreyer: Sheaf cohomology and free resolutions over exterior
algebras, Trans AMS 355 (2003)] ).
 sheafCohBGG(M,l,h)does not compute all values in the above
table. To determine all values ofh^i(F(d)),d=l..h,
usesheafCohBGG(M,l-n,h+n).
 See also:
 dimH;
 sheafCoh.|  | LIB "sheafcoh.lib";
// cohomology of structure sheaf on P^4:
//-------------------------------------------
ring r=0,x(1..5),dp;
module M=0;
def A=sheafCohBGG(M,-9,4);
==>       -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4
==> ------------------------------------------------------------
==>   4:  70  35  15   5   1   -   -   -   -   -   *   *   *   *
==>   3:   *   -   -   -   -   -   -   -   -   -   -   *   *   *
==>   2:   *   *   -   -   -   -   -   -   -   -   -   -   *   *
==>   1:   *   *   *   -   -   -   -   -   -   -   -   -   -   *
==>   0:   *   *   *   *   -   -   -   -   -   1   5  15  35  70
==> ------------------------------------------------------------
==> chi:   *   *   *   *   1   0   0   0   0   1   *   *   *   *
// cohomology of cotangential bundle on P^3:
//-------------------------------------------
ring R=0,(x,y,z,u),dp;
resolution T1=mres(maxideal(1),0);
module M=T1[3];
intvec v=2,2,2,2,2,2;
attrib(M,"isHomog",v);
def B=sheafCohBGG(M,-8,4);
==>        -8   -7   -6   -5   -4   -3   -2   -1    0    1    2    3    4
==> ---------------------------------------------------------------------
==>   3:  189  120   70   36   15    4    -    -    -    -    *    *    *
==>   2:    *    -    -    -    -    -    -    -    -    -    -    *    *
==>   1:    *    *    -    -    -    -    -    -    1    -    -    -    *
==>   0:    *    *    *    -    -    -    -    -    -    -    6   20   45
==> ---------------------------------------------------------------------
==> chi:    *    *    *  -36  -15   -4    0    0   -1    0    *    *    *
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