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BoijSoederberg :: makePureBettiDiagram

makePureBettiDiagram -- makes a pure Betti diagram given a list of degrees

Synopsis

Description

See pureBetti for a description of the Herzog-Kuhl equations.
i1 : makePureBettiDiagram{0,2,4,5}

            0  1  2 3
o1 = total: 3 10 15 8
         0: 3  .  . .
         1: . 10  . .
         2: .  . 15 8

o1 : BettiTally
i2 : makePureBettiDiagram({0,2,4,5}, TableEntries => HerzogKuhl)

               0    1   2    3
o2 = total: 1/40 1/12 1/8 1/15
         0: 1/40    .   .    .
         1:    . 1/12   .    .
         2:    .    . 1/8 1/15

o2 : BettiTally
i3 : makePureBettiDiagram{0,3,4,5,6,7,10}

            0  1   2   3   4  5 6
o3 = total: 1 50 175 252 175 50 1
         0: 1  .   .   .   .  . .
         1: .  .   .   .   .  . .
         2: . 50 175 252 175 50 .
         3: .  .   .   .   .  . .
         4: .  .   .   .   .  . 1

o3 : BettiTally
i4 : makePureBettiDiagram({0,3,4,5,6,7,10}, TableEntries => RealizationModules)

             0    1    2    3    4    5  6
o4 = total: 36 1800 6300 9072 6300 1800 36
         0: 36    .    .    .    .    .  .
         1:  .    .    .    .    .    .  .
         2:  . 1800 6300 9072 6300 1800  .
         3:  .    .    .    .    .    .  .
         4:  .    .    .    .    .    . 36

o4 : BettiTally
i5 : makePureBettiDiagram{0,3,4,5,6,7,8,11}

            0  1   2   3   4   5  6 7
o5 = total: 1 77 330 616 616 330 77 1
         0: 1  .   .   .   .   .  . .
         1: .  .   .   .   .   .  . .
         2: . 77 330 616 616 330 77 .
         3: .  .   .   .   .   .  . .
         4: .  .   .   .   .   .  . 1

o5 : BettiTally
i6 : makePureBettiDiagram({0,3,4,5,6,7,8,11}, TableEntries => HerzogKuhl)

                   0      1     2     3     4     5      6        7
o6 = total: 1/221760 1/2880 1/672 1/360 1/360 1/672 1/2880 1/221760
         0: 1/221760      .     .     .     .     .      .        .
         1:        .      .     .     .     .     .      .        .
         2:        . 1/2880 1/672 1/360 1/360 1/672 1/2880        .
         3:        .      .     .     .     .     .      .        .
         4:        .      .     .     .     .     .      . 1/221760

o6 : BettiTally
i7 : makePureBettiDiagram({0,3,4,5,6,7,8,11}, TableEntries => RealizationModules)

             0    1     2     3     4     5    6  7
o7 = total: 45 3465 14850 27720 27720 14850 3465 45
         0: 45    .     .     .     .     .    .  .
         1:  .    .     .     .     .     .    .  .
         2:  . 3465 14850 27720 27720 14850 3465  .
         3:  .    .     .     .     .     .    .  .
         4:  .    .     .     .     .     .    . 45

o7 : BettiTally

See also

Ways to use makePureBettiDiagram :

For the programmer

The object makePureBettiDiagram is a method function with options.