isPure(BettiTally) -- is a Betti diagram pure?

i1 : R = ZZ/101[a..e];

i2 : B = betti res ideal"ab,ac,bd,be,ae,cd,ce,a3,b3,c3,d3,e3"

            0  1  2  3  4 5
o2 = total: 1 12 29 30 15 3
         0: 1  .  .  .  . .
         1: .  7 11  6  1 .
         2: .  5 14 13  4 .
         3: .  .  1  2  1 .
         4: .  .  3  9  9 3

o2 : BettiTally

i3 : B1 = pureBettiDiagram highestDegrees B

            0  1   2   3   4   5
o3 = total: 5 42 420 810 567 140
         0: 5  .   .   .   .   .
         1: .  .   .   .   .   .
         2: . 42   .   .   .   .
         3: .  .   .   .   .   .
         4: .  . 420 810 567 140

o3 : BettiTally

i4 : isPure B

o4 = false

i5 : isPure B1

o5 = true