Code:

R = QQ[x, y, z, w]; -- defines a ring
I = monomialCurveIdeal(R, {1, 2, 3})
C = res I -- computes the resolution
betti I -- displays the Betti table

Getting help:

-- quick usage information
? monomialCurveIdeal

-- details and examples
help monomialCurveIdeal

-- documentation on the web
viewHelp monomialCurveIdeal

-- documentation headlines about curves
headlines about "curve"

Also try: (either click or copy & enter in M2)

• help "reading the documentation"
• help "getting help or reporting bugs"
• help "Tutorial: Modules in Macaulay2"
• help "computing Groebner bases"

Result:

i1 : R = QQ[x, y, z, w];

i2 : I = monomialCurveIdeal(R, {1, 2, 3})

             2                    2
o2 = ideal (z  - y*w, y*z - x*w, y  - x*z)

o2 : Ideal of R

i3 : C = res I

      1      3      2
o3 = R  <-- R  <-- R  <-- 0
                           
     0      1      2      3

o3 : ChainComplex

i4 : betti C

            0 1 2
o4 = total: 1 3 2
         0: 1 . .
         1: . 3 2

o4 : BettiTally