2019.sagews

restart
kk = frac(QQ[u_1,u_2,u_3])
R = kk[x_1..x_20]
S = R[y,MonomialOrder=>Lex]
use R
J = ideal (2*x_1-u_1,2*x_2-u_1-u_2,2*x_3-u_3,2*x_4-u_2,2*x_5-u_3,x_17-2*x_15,x_18-2*x_16,u_2+x_17-2*x_13,u_3+x_18-2*x_14,x_17-2*x_11+u_1,x_18-2*x_12,x_7*u_2-x_7*u_1+x_8*u_3,u_2*u_1-u_1*x_6,u_2*x_9-u_2*u_1+u_3*x_10,u_3*x_7-u_3*u_1+x_8*u_1-u_2*x_8,x_9*u_3-x_10*u_2,(x_19-x_4)^2+(x_20-x_5)^2-(x_19-x_1)^2-x_20^2,-(x_19-x_1)^2-x_20^2+(x_19-x_2)^2+(x_20-x_3)^2)
I = J + ideal (x_9*x_18-x_17*x_10+u_1*x_10-u_1*x_18,x_18*x_7-x_8*x_17)
Ibar1 = substitute(I,S) + ideal (1-y*(-(x_19-x_1)^2-x_20^2+(x_19-x_15)^2+(x_20-x_16)^2),1-y*(-(x_19-x_1)^2-x_20^2+(x_19-x_9)^2+(x_20-x_10)^2),1-y*(-(x_19-x_1)^2-x_20^2+(x_19-x_13)^2+(x_20-x_14)^2),1-y*(-(x_19-x_1)^2-x_20^2+(x_19-x_7)^2+(x_20-x_8)^2),1-y*(-(x_19-x_1)^2-x_20^2+(x_19-x_11)^2+(x_20-x_12)^2),1-y*((x_19-x_6)^2-(x_19-x_1)^2))
Ibar1GB = gb Ibar1
netList entries transpose gens Ibar1GB

WARNING: Output truncated!

full_output.txt

rning: Limiting number of mark threads share/Macaulay2/Core/files.m2:18:6:(0):[5]: error: can't make directory "/sagenb/sagenbws/.Macaulay2": Permission denied share/Macaulay2/Core/files.m2:18:6:(0):[5]: --entering debugger (type help to see debugger commands) share/Macaulay2/Core/files.m2:18:6-18:52: --source code: makeDir fold((a,b) -> ( makeDir a; a|"/"|b ), parts)) kk FractionField R PolynomialRing S PolynomialRing R PolynomialRing ideal (2x - u , 2x - u - u , 2x - u , 2x - u , 2x - u , - 2x + x , 1 1 2 1 2 3 3 4 2 5 3 15 17 --------------------------------------------------------------------------- - 2x + x , - 2x + x + u , - 2x + x + u , - 2x + x + u , - 16 18 13 17 2 14 18 3 11 17 1 --------------------------------------------------------------------------- 2x + x , (- u + u )x + u x , - u x + u u , u x + u x - u u , u x 12 18 1 2 7 3 8 1 6 1 2 2 9 3 10 1 2 3 7 --------------------------------------------------------------------------- 2 2 2 + (u - u )x - u u , u x - u x , - x + x + x + 2x x - 2x x - 1 2 8 1 3 3 9 2 10 1 4 5 1 19 4 19 --------------------------------------------------------------------------- 2 2 2 2x x , - x + x + x + 2x x - 2x x - 2x x ) 5 20 1 2 3 1 19 2 19 3 20 Ideal of R ideal (2x - u , 2x - u - u , 2x - u , 2x - u , 2x - u , - 2x + x , 1 1 2 1 2 3 3 4 2 5 3 15 17 --------------------------------------------------------------------------- - 2x + x , - 2x + x + u , - 2x + x + u , - 2x + x + u , - 16 18 13 17 2 14 18 3 11 17 1 --------------------------------------------------------------------------- ... 2 2 2 2x x , - x + x + x + 2x x - 2x x - 2x x , - x x + x x + u x 5 20 1 2 3 1 19 2 19 3 20 10 17 9 18 1 10 --------------------------------------------------------------------------- - u x , - x x + x x ) 1 18 8 17 7 18 Ideal of R ideal (2x - u , 2x - u - u , 2x - u , 2x - u , 2x - u , - 2x + x , 1 1 2 1 2 3 3 4 2 5 3 15 17 --------------------------------------------------------------------------- - 2x + x , - 2x + x + u , - 2x + x + u , - 2x + x + u , - 16 18 13 17 2 14 18 3 11 17 1 --------------------------------------------------------------------------- 2x + x , (- u + u )x + u x , - u x + u u , u x + u x - u u , u x 12 18 1 2 7 3 8 1 6 1 2 2 9 3 10 1 2 3 7 --------------------------------------------------------------------------- 2 2 2 + (u - u )x - u u , u x - u x , - x + x + x + 2x x - 2x x - 1 2 8 1 3 3 9 2 10 1 4 5 1 19 4 19 --------------------------------------------------------------------------- 2 2 2 2x x , - x + x + x + 2x x - 2x x - 2x x , - x x + x x + u x 5 20 1 2 3 1 19 2 19 3 20 10 17 9 18 1 10 --------------------------------------------------------------------------- 2 2 2 - u x , - x x + x x , (x - x - x - 2x x + 2x x + 2x x )y + 1 18 8 17 7 18 1 15 16 1 19 15 19 16 20 --------------------------------------------------------------------------- 2 2 2 2 2 2 1, (x - x - x - 2x x + 2x x + 2x x )y + 1, (x - x - x - 1 9 10 1 19 9 19 10 20 1 13 14 --------------------------------------------------------------------------- 2 2 2 2x x + 2x x + 2x x )y + 1, (x - x - x - 2x x + 2x x + 1 19 13 19 14 20 1 7 8 1 19 7 19 --------------------------------------------------------------------------- 2 2 2 2 2 2x x )y + 1, (x - x - x - 2x x + 2x x + 2x x )y + 1, (x - x 8 20 1 11 12 1 19 11 19 12 20 1 6 --------------------------------------------------------------------------- - 2x x + 2x x )y + 1) 1 19 6 19 Ideal of S GroebnerBasis[status: done; S-pairs encountered up to degree 3] GroebnerBasis +-+ |1| +-+

restart
R = QQ[t_1..t_3,x_1..x_4,MonomialOrder=>Lex]
use R
I = ideal (x_1-t_1^3*t_2^4*t_3^2,x_2-t_1^2*t_2^3*t_3^4,x_3-t_1^1*t_2^1*t_3^2,x_4-t_1^2*t_3)
Igb= gb I
netList entries transpose gens Igb

rning: Limiting number of mark threads share/Macaulay2/Core/files.m2:18:6:(0):[5]: error: can't make directory "/sagenb/sagenbws/.Macaulay2": Permission denied share/Macaulay2/Core/files.m2:18:6:(0):[5]: --entering debugger (type help to see debugger commands) share/Macaulay2/Core/files.m2:18:6-18:52: --source code: makeDir fold((a,b) -> ( makeDir a; a|"/"|b ), parts)) R PolynomialRing R PolynomialRing 3 4 2 2 3 4 2 2 ideal (- t t t + x , - t t t + x , - t t t + x , - t t + x ) 1 2 3 1 1 2 3 2 1 2 3 3 1 3 4 Ideal of R GroebnerBasis[status: done; S-pairs encountered up to degree 34] GroebnerBasis +---------------+ | 3 21 11 4 | |x x - x x | | 1 3 2 4 | +---------------+ | 8 3 2 16 | |t x x - x x | | 3 2 4 1 3 | +---------------+ | 5 3 | |t x x - x x | | 3 1 3 2 4 | +---------------+ | 2 5 2 11 | |t x x - x x | | 3 2 4 1 3 | +---------------+ | 3 2 6 | |t x x - x | | 3 2 4 3 | +---------------+ | 4 | |t x - x x | | 3 1 2 3 | +---------------+ | 2 | |t x - x | | 2 3 2 | +---------------+ | 2 3| |t x x - t x x | | 2 2 4 3 1 3| +---------------+ | 3 4 | |t t x x - x | | 2 3 2 4 3 | +---------------+ | 2 | |t x x - t x x | | 2 2 4 3 1 3| +---------------+ | 2 3 2 | |t t x - x | | 2 3 4 3 | +---------------+ | 3 | |t x x - t x | | 2 3 4 3 1 | +---------------+ | 5 2 2 | |t t x - x x | | 2 3 4 1 3 | +---------------+ | 8 3 2 | |t t x - x | | 2 3 4 1 | +---------------+ |t x - t t x | | 1 3 2 3 4 | +---------------+ | 2 | |t x - t t x x | | 1 2 2 3 3 4| +---------------+ | 4 2 | |t x - t x | | 1 1 2 4 | +---------------+ | 2 | |t t t - x | | 1 2 3 3 | +---------------+ | 4 | |t t t x - x | | 1 2 3 4 1 | +---------------+ | 2 | |t t - x | | 1 3 4 | +---------------+

t_1^10*t_2^11*t_3^10 % Igb

2 t x x x 3 1 2 4 R