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resonanceDet -- compute the resonance determinant of the crucial constant strand of a degenerate K3 X_e(a,a)

Synopsis

Description

We compute the minimal resolution F of degenerate K3 X_e(a,a) over ZZ[e_1,e_2] where deg e_i =i and the variables x_0,..x_a,y_0..y_b have degrees deg x_i=i+1 and deg y_i=1. The equations of X_e(a,b) are homogeneous with respect to this grading. Viewed as a resolution over QQ(e_1,e_2), this resolution is non-minimal and carries further gradings. We decompose the crucial map of the a-th strand into blocks, compute their determinants, and factor the product.

i1 : a=4

o1 = 4
 
i2 : (d1,d2)=resonanceDet(a)
 -- .0106374s elapsed
 -- .000025324s elapsed
 -- .000072161s elapsed
 -- .000056083s elapsed
 -- .000061701s elapsed
 -- .000070377s elapsed
 -- .000076651s elapsed
 -- .000029398s elapsed
 -- .00008556s elapsed
 -- .000068501s elapsed
 -- .000071237s elapsed
 -- .000079195s elapsed
 -- .000084826s elapsed
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(number of blocks= , 18)
(size of the matrices, Tally{1 => 4})
                             2 => 6
                             3 => 2
                             4 => 6
       0 1
total: 1 1
    7: 1 1
(e )(-1)
  1
       0 1
total: 2 2
    7: 2 .
    8: . 2
    2
(e ) (e )(-1)
  1    2
       0 1
total: 2 2
    7: 2 .
    8: . .
    9: . 2
    2    2
(e ) (e )
  1    2
       0 1
total: 3 3
    7: 2 .
    8: 1 .
    9: . 1
   10: . 2
    2    4
(e ) (e ) (-3)
  1    2
       0 1
total: 4 4
    7: 1 .
    8: 1 .
    9: 2 2
   10: . 1
   11: . 1
    2    4
(e ) (e ) (3)
  1    2
       0 1
total: 4 4
    8: 1 .
    9: 2 1
   10: 1 2
   11: . 1
    2    3
(e ) (e ) (3)
  1    2
       0 1
total: 1 1
    9: 1 1
(e )(-1)
  1
       0 1
total: 2 2
    9: 1 1
   10: 1 1
    2
(e )
  1
       0 1
total: 4 4
    9: 2 1
   10: 1 1
   11: 1 2
    2    2
(e ) (e ) (-1)
  1    2
       0 1
total: 4 4
    9: 1 .
   10: 2 1
   11: 1 2
   12: . 1
    2    3
(e ) (e ) (3)
  1    2
       0 1
total: 4 4
    9: 1 .
   10: 1 .
   11: 2 2
   12: . 1
   13: . 1
    2    4
(e ) (e ) (3)
  1    2
       0 1
total: 4 4
    9: 2 1
   10: 1 1
   11: 1 2
    2    2
(e ) (e ) (-1)
  1    2
       0 1
total: 3 3
   10: 2 .
   11: 1 .
   12: . 1
   13: . 2
    2    4
(e ) (e ) (3)
  1    2
       0 1
total: 2 2
   10: 1 1
   11: 1 1
    2
(e )
  1
       0 1
total: 2 2
   11: 2 .
   12: . .
   13: . 2
    2    2
(e ) (e )
  1    2
       0 1
total: 1 1
   11: 1 1
(e )
  1
       0 1
total: 2 2
   12: 2 .
   13: . 2
    2
(e ) (e )(-1)
  1    2
       0 1
total: 1 1
   13: 1 1
(e )
  1

       6      32    32
o2 = (3 , (e )  (e )  )
            1     2

o2 : Sequence

See also

Ways to use resonanceDet:

For the programmer

The object resonanceDet is a method function.