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MatFacCurvesP4 :: isInBoijSoederbergCone

isInBoijSoederbergCone -- check whether a Betti table is in the Boij-Soederberg cone

Synopsis

Description

The function returns true if there exists a rational number q such that q*B is the Betti table of some module over a polynomial ring, and false if not

i1 : B=new BettiTally from
       {(0, {1}, 1) => 6,
       (1, {2}, 2) => 10,
       (2, {3}, 3) => 3,
       (1, {3}, 3) => 3,
       (1, {4}, 4) => 1,
       (2, {5}, 5) => 13,
       (3, {6}, 6) => 9,
       (4, {7}, 7) => 1
       }

            0  1  2 3 4
o1 = total: 6 14 16 9 1
         1: 6 10  3 . .
         2: .  3  . . .
         3: .  1 13 9 1

o1 : BettiTally
i2 : isInBoijSoederbergCone B

o2 = true
i3 : B'=new BettiTally from
       {(0, {1}, 1) => 6,
       (1, {2}, 2) => 10,
       (2, {3}, 3) => 3,
       (1, {3}, 3) => 3,
       (1, {4}, 4) => 2,
       (2, {5}, 5) => 13,
       (3, {6}, 6) => 9,
       (4, {7}, 7) => 1
       }

            0  1  2 3 4
o3 = total: 6 15 16 9 1
         1: 6 10  3 . .
         2: .  3  . . .
         3: .  2 13 9 1

o3 : BettiTally
i4 : isInBoijSoederbergCone B'

o4 = false

Ways to use isInBoijSoederbergCone :