next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
NodalCurves :: verifyConjA

verifyConjA -- verify the Prym-Green conjecture

Synopsis

Description

If the answer is true, then the Prym-Green Conjecture Farkas, Ludwig [2010] holds for genus g and level n. In case of false the verification failed, but the conjecture could be still true. The options allow to ask for printing and timing.

Printing=>true results in

1) printing of the expected betti table( of the dual) of the resolution of the Prym-canonical curve

2) betti number of the critical Koszul cohomology matrix and over the ground field and the betti number of its syzygy matrix. No syzygy is the conjecture.

Timings=>true results in the priniting three timings:

1) the time to compute the Koszul matrix as a matrix of polynomials

2) the time to convert this matrix to a matrix over the ground field

3) the time to compute the syzygies of this matrix.

Step 3 takes a lot of time, e.g. for g=16 is took us on our machine 18 days.
i1 : verifyConjA(8,3,Printing=>true)
warning: clearing value of symbol t to allow access to subscripted variables based on it
       : debug with expression   debug 5504   or with command line option   --debug 5504
       0  1  2  3 4 5
total: 8 35 56 35 7 1
    0: 8 35 56 35 . .
    1: .  .  .  . 7 .
    2: .  .  .  . . 1
         0  1          0
(total: 50 40, total: 40)
    -1:  . 40      0: 40
     0: 50  .

o1 = true
i2 : verifyConjA(8,2)

o2 = false
i3 : verifyConjA(10,2,Printing=>true,Timings=>true)
warning: clearing value of symbol t to allow access to subscripted variables based on it
       : debug with expression   debug 5504   or with command line option   --debug 5504
        0  1   2   3   4  5  6 7
total: 10 63 162 210 126 42 18 1
    0: 10 63 162 210 126  .  . .
    1:  .  .   .   .   . 42 18 .
    2:  .  .   .   .   .  .  . 1
     -- used 2.66315 seconds
     -- used 0.017972 seconds
     -- used 1.11351 seconds
          0   1           0
(total: 245 210, total: 210)
    -1:   . 210      0: 210
     0: 245   .

o3 = true

Ways to use verifyConjA :