-- -*- M2-comint -*- hash: 12985912031503996553

i1 : R = ZZ/1277[x,y];

i2 : I = ideal(x^3 - 2*x*y, x^2*y - 2*y^2 + x);

o2 : Ideal of R

i3 : g = gb I

o3 = GroebnerBasis[status: done; S-pairs encountered up to degree 8]

o3 : GroebnerBasis

i4 : gens g

o4 = | y2+638x xy x2 |

             1      3
o4 : Matrix R  <-- R

i5 : R = ZZ/1277[x,y,z,w];

i6 : I = ideal(x*y-z^2,y^2-w^2);

o6 : Ideal of R

i7 : g2 = gb(I,DegreeLimit => 2)

o7 = GroebnerBasis[status: DegreeLimit; all S-pairs handled up to degree 2]

o7 : GroebnerBasis

i8 : gens g2

o8 = | y2-w2 xy-z2 |

             1      2
o8 : Matrix R  <-- R

i9 : g3 = gb(I,DegreeLimit => 3);

i10 : gens g3

o10 = | y2-w2 xy-z2 yz2-xw2 |

              1      3
o10 : Matrix R  <-- R

i11 : g2

o11 = GroebnerBasis[status: DegreeLimit; all S-pairs handled up to degree 3]

o11 : GroebnerBasis

i12 : g2 === g3

o12 = true

i13 : I = ideal(x*y-z^2,y^2-w^2)

                    2   2    2
o13 = ideal (x*y - z , y  - w )

o13 : Ideal of R

i14 : gb(I,PairLimit => 2)

o14 = GroebnerBasis[status: PairLimit; all S-pairs handled up to degree 1]

o14 : GroebnerBasis

i15 : gb(I,PairLimit => 3)

o15 = GroebnerBasis[status: PairLimit; all S-pairs handled up to degree 2]

o15 : GroebnerBasis

i16 : I = ideal(x*y-z^2,y^2-w^2)

                    2   2    2
o16 = ideal (x*y - z , y  - w )

o16 : Ideal of R

i17 : gb(I,BasisElementLimit => 2)

o17 = GroebnerBasis[status: BasisElementLimit; all S-pairs handled up to degree 1]

o17 : GroebnerBasis

i18 : gb(I,BasisElementLimit => 3)

o18 = GroebnerBasis[status: BasisElementLimit; all S-pairs handled up to degree 2]

o18 : GroebnerBasis

i19 : R = ZZ/1277[t,F,G,MonomialOrder => Eliminate 1];

i20 : I = ideal(F - (t^3 + t^2 + 1), G - (t^4 - t))

                3    2             4
o20 = ideal (- t  - t  + F - 1, - t  + t + G)

o20 : Ideal of R

i21 : transpose gens gb (I, SubringLimit => 1)

o21 = {-4} | F4-7F3-2F2G-4FG2-G3+18F2+3FG+6G2-21F-G+9 |
      {-3} | tG2-tF+6tG+5t-F3+3F2+3FG+3G2+G-2         |
      {-3} | tFG+tF-4tG-3t+F2-FG-G2-4F-G+3            |
      {-3} | tF2-4tF+tG+5t-F2-FG+3F+3G-2              |
      {-2} | t2+tF-2t-F-G+1                           |

              5      1
o21 : Matrix R  <-- R

i22 : gbTrace = 3

o22 = 3

i23 : I = ideal(x*y-z^2,y^2-w^2)

                    2   2    2
o23 = ideal (x*y - z , y  - w )

                ZZ
o23 : Ideal of ----[x..z, w]
               1277

i24 : gb I

   -- registering gb 5 at 0x7fdd15223540

   -- [gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber of (nonminimal) gb elements = 4
   -- number of monomials                = 8
   -- #reduction steps = 2
   -- #spairs done = 6
   -- ncalls = 0
   -- nloop = 0
   -- nsaved = 0
   -- 
o24 = GroebnerBasis[status: done; S-pairs encountered up to degree 4]

o24 : GroebnerBasis

i25 : gbTrace = 0

o25 = 0

i26 : R = ZZ/1277[x..z];

i27 : I = ideal(x*y+y*z, y^2, x^2);

o27 : Ideal of R

i28 : g = gb(I, StopBeforeComputation => true)

o28 = GroebnerBasis[status: not started; all S-pairs handled up to degree -1]

o28 : GroebnerBasis

i29 : gens g

o29 = 0

              1
o29 : Matrix R  <-- 0

i30 : R = ZZ/1277[a..e];

i31 : T = (degreesRing R)_0

o31 = T

o31 : ZZ[T]

i32 : f = random(R^1,R^{-3,-3,-5,-6});

              1      4
o32 : Matrix R  <-- R

i33 : time betti gb f
 -- used 0.311301s (cpu); 0.264159s (thread); 0s (gc)

             0  1
o33 = total: 1 53
          0: 1  .
          1: .  .
          2: .  2
          3: .  1
          4: .  2
          5: .  3
          6: .  5
          7: .  5
          8: .  8
          9: .  9
         10: .  8
         11: .  6
         12: .  3
         13: .  1

o33 : BettiTally

i34 : remove(f.cache,{false,0})

i35 : poincare cokernel f = (1-T^3)*(1-T^3)*(1-T^5)*(1-T^6) -- cache poincare

            3    5     8     9    12     14    17
o35 = 1 - 2T  - T  + 2T  + 2T  - T   - 2T   + T

o35 : ZZ[T]

i36 : time betti gb f
 -- used 0.00299608s (cpu); 0.00303459s (thread); 0s (gc)

             0  1
o36 = total: 1 53
          0: 1  .
          1: .  .
          2: .  2
          3: .  1
          4: .  2
          5: .  3
          6: .  5
          7: .  5
          8: .  8
          9: .  9
         10: .  8
         11: .  6
         12: .  3
         13: .  1

o36 : BettiTally

i37 : 
