-- File used during the meeting 2014-01-27
--
S = QQ[s,t]
R = QQ[x,y,z]
F = matrix {{t^3,t^2*s,s^3}}
M = gens power (ideal vars R,3)
sub(M,F)
M*sub(compress sub(gens ker sub(M,F),0*vars S),R)

equation = F -> (
    M := gens power (ideal vars R,3);
    M*sub(compress sub(gens ker sub(M,F),0*vars ring F),R)
    )

equation(F)
equation(random(S^{3},S^3))

-- 
restart
S = QQ[x,y,z,a_0..a_9,MonomialOrder=> Eliminate 2]
F = (gens power (ideal (x,y,z),3))*genericMatrix(S,a_0,10,1)
J = ideal diff(matrix{{x,y,z}},F)
F_0_0%J
time I = ideal selectInSubring(1,gens gb J);
f = substitute(I,{z=>1});
# terms det gens f
F
T = QQ[x,y,z,Degrees => entries id_(ZZ^3)]
degrees vars T
degree x
L = -last degrees gens power(ideal vars T,3)
A = QQ[x,y,z,a_0..a_9,Degrees=> entries id_(ZZ^3)|L]
degree a_2
isHomogeneous sub(F,A)
g = sub(f,A);
degrees g
degrees f
degree x
degree y
degree z
B = QQ[a_0..a_9,Degrees=>L]
g = sub(f,B);
numcols basis({ -12,-12,-12},B)
(a,b) = coefficients gens g;
mons = set first entries a;
#mons
allmons = set first entries basis({ -12,-12,-12},B);
#allmons
#(allmons - mons)