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.
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 |