*******************************
**Macaulay2 does Hassett 2.10 *
**We first do revlex.   *******
*******************************

i2 :  R = QQ[a..d] 

o2 = R

o2 : PolynomialRing



i5 : gens gb ideal(c-a^5,b-a^3)

o5 = | b2-ac a2b-c a3-b |      **Here is the gb! **

             1       3
o5 : Matrix R  <--- R

i23 : f'=a*b*c

o23 = a*b*c

o23 : R

i24 : f' % ideal(c-a^5,b-a^3)

o24 = a*b*c                   ** Here is the normal form **

o24 : R

********************
** Now we use Lex **
********************

i9 :  QQ[x,y,z, MonomialOrder => Lex]

o9 = QQ [x, y, z]

o9 : PolynomialRing

i10 :  gens gb ideal(z-x^5,y-x^3)

o10 = | y5-z3 xz-y2 xy3-z2 x2y-z x3-y |  ** Here is the gb**

                           1                    5
o10 : Matrix (QQ [x, y, z])  <--- (QQ [x, y, z])


i20 : f=x*y*z

o20 = x*y*z

o20 : QQ [x, y, z]

i21 : f %  ideal(z-x^5,y-x^3)

       3
o21 = y                      ** here is the normal form **

o21 : QQ [x, y, z]

i22 : R

o22 = R

o22 : PolynomialRing