betti with degree 0 variables

[lcrantonh]

Macaulay2 seems to give strange betti tables for modules over rings with variables of degree 0.

i1 : S = ZZ/101[x,y,Degrees => {{0},{1}}]

o1 = S

o1 : PolynomialRing

i2 : M = comodule ideal y

o2 = cokernel | y |

                            1
o2 : S-module, quotient of S

i3 : betti M

            0 1
o3 = total: 1 1
        -1: . 1
         0: 1 .

o3 : BettiTally

i4 : F = prune res M

      1      1
o4 = S  <-- S  <-- 0
                    
     0      1      2

o4 : ChainComplex

i5 : degrees F_1

o5 = {{1}}

o5 : List

[DanGrayson]

It's probably related to S having no heft vector. Here is a work-around:

i2 : S = ZZ/101[x,y,Degrees => {{0},{1}}]

o2 = S

o2 : PolynomialRing

i3 : M = comodule ideal y

o3 = cokernel | y |

                            1
o3 : S-module, quotient of S

i4 : betti M

            0 1
o4 = total: 1 1
        -1: . 1
         0: 1 .

o4 : BettiTally

i5 : peek oo

o5 = BettiTally{(0, {0}, 0) => 1}
                (1, {1}, 0) => 1

i6 : betti(M, Weights=>{1})

            0 1
o6 = total: 1 1
         0: 1 1

o6 : BettiTally

i7 : peek oo

o7 = BettiTally{(0, {0}, 0) => 1}
                (1, {1}, 1) => 1