KK = ZZ / 30097;
R = KK[l_{0}..l_{4},m_{0}..m_{3}, MonomialOrder=>Lex];
alpha = random(KK^10, KK^10);
beta = random(KK^10, KK^10);
C = random(R^1, R^3);
V = random(R^3, R^10);
E = apply(4, i->apply(3-i, j-> l_{i}^2 + l_{i+j+1}^2 - (2/alpha_(i,i+j+1))*l_{i}*l_{i+j+1} - m_{i}^2 - m_{i+j+1}^2 + (2/beta_(i,i+j+1))*m_{i}*m_{i+j+1} ));
E4 = apply(4, i->l_{i}^2 + l_{4}^2 - (2/alpha_(i,4))*l_{i}*l_{4} - m_{i}^2 - 1 + (2/beta_(i,4))*m_{i} );
H = flatten E | E4;
I = ideal H;
dim I
degree I
gbTrace=3;
Igb = groebnerBasis I;
Ip = gb I
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registering polynomial ring 5 at 0x28b7000
10 10
Matrix KK <--- KK
10 10
Matrix KK <--- KK
1 3
Matrix R <--- R
3 10
Matrix R <--- R
Ideal of R
registering gb 2 at 0x3144c40
[gb]{2}(10)mmmmmmmmmm{3}(20)mmmmmmmmmmmmmmmmmmmm{4}(106)mmmomommmmmmmomo\
mmmmmm
omommoooommoooomoomooomoooooommooooooooooommomoooooooooooooomooooooooo
{5}(137)mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmoomommmmmmmmmommmmmmmmmmmm\
mmoooooooo
ooommmoooomooooooomoommooommmmooooooooooommmm{6}(210)mmmmmmmmmmmmmmmmmmm\
mmm
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmommmmmmmmmmmmmmmooooo\
ooo
ooooooooooooooommmmmmmmmoommoooooooooooommmmmmmmmmoooooooooooomoommmmmmm\
moo
ooooooooo{7}(279)mmmmmmmmmmmmmmmmooooooooooooooooooooooooomooooooooooooo\
ooo
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo\
ooo
oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo\
ooo
ooooooooooooooooooooooooooooooooooooooooooooooo{8}(86)oomooomooooooooooo\
ooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo{9}(21)oo\
ooo
oooooooooooooooo{10}(2)oo
number of (nonminimal) gb elements = 366
number of monomials = 14033
ncalls = 32176
nloop = 184088
nsaved = 1317
registering monomial ideal 2 at 0x31e4100
0
40
1 25
Matrix R <--- R
GroebnerBasis[status: done; S-pairs encountered up to degree 9]
GroebnerBasis
registering polynomial ring 5 at 0x28b7000
10 10
Matrix KK <--- KK
10 10
Matrix KK <--- KK
1 3
Matrix R <--- R
3 10
Matrix R <--- R
Ideal of R
registering gb 2 at 0x3144c40
[gb]{2}(10)mmmmmmmmmm{3}(20)mmmmmmmmmmmmmmmmmmmm{4}(106)mmmomommmmmmmomommmmmm
omommoooommoooomoomooomoooooommooooooooooommomoooooooooooooomooooooooo
{5}(137)mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmoomommmmmmmmmommmmmmmmmmmmmmoooooooo
ooommmoooomooooooomoommooommmmooooooooooommmm{6}(210)mmmmmmmmmmmmmmmmmmmmmm
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmommmmmmmmmmmmmmmoooooooo
ooooooooooooooommmmmmmmmoommoooooooooooommmmmmmmmmoooooooooooomoommmmmmmmoo
ooooooooo{7}(279)mmmmmmmmmmmmmmmmooooooooooooooooooooooooomoooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooo{8}(86)oomooomoooooooooooooo
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo{9}(21)ooooo
oooooooooooooooo{10}(2)oo
number of (nonminimal) gb elements = 366
number of monomials = 14033
ncalls = 32176
nloop = 184088
nsaved = 1317
registering monomial ideal 2 at 0x31e4100
0
40
1 25
Matrix R <--- R
GroebnerBasis[status: done; S-pairs encountered up to degree 9]
GroebnerBasis
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