Hi

@mmcdara

Thanks for you detailed reply and code.

I have another computation which works well, although it turns out there is no solution.

But it gave me a result without crash.

=========Code begin=============

restart:

with(LinearAlgebra):

U := Vector[row](4, [1, u, u^2, u^3]):

V := Vector[column](4, [1, v, v^2, v^3]):

M := Matrix(4, 4, [[1, 0, 0, 0], [-3, 3, 0, 0], [3, -6, 3, 0], [-1, 3, -3, 1]]):

MT := Transpose(M):

F0 := (f00*v+f01*u)/(u+v):

F1 := ((1-u)*f10+v*f11)/(1-u+v):

F2 := ((1-u)*f21+(1-v)*f20)/(2-u-v):

F3 := (u*f30+(1-v)*f31)/(1+u-v):

G := Matrix(4, 4, [[p0, e00, e31, p3], [e01, F0, F3, e30], [e10, F1, F2, e21], [p1, e11, e20, p2]]):

Gregory := (U . M . G . MT . V):

coefList:=[p0,p1,p2,p3,e00,e01,e10,e11,e20,e21,e30,e31,f00,f01,f10,f11,f20,f21,f30,f31]:

nops(coefList):

for i from 1 to nops(coefList) do

ind:=coefList[i];

BF||ind:=factor(coeff(Gregory,coefList[i],1));

end do:

for i from 1 to nops(coefList) do

ind:=coefList[i];

DBF||ind:=factor(diff(BF||ind,u));

end do:

QR:=x-> w1*subs(u=u1,v=v1,x) + w1*subs(u=u1,v=1-v1,x) + w2*subs(u=u2,v=v2,x) + w2*subs(u=u2,v=1-v2,x) + w3*subs(u=1/2,v=1/2,x):

for i from 1 to nops(coefList) do

ind:=coefList[i];

eqD[i]:=numer(simplify(int(DBF||ind, u=0..1, v=0..1) - QR(DBF||ind)));

end do:

sysD := [seq(eqD[i],i=1..nops(coefList))]:

with(Groebner):

Basis(sysD,plex(u1,v1,w1,u2,v2,w2,w3));

[1]

# number of terms in each eq[i]

seq(nops(eqD[i]),i=1..nops(coefList));

# number of words used to represent each eq[i]

seq(length(eqD[i]),i=1..nops(coefList));

# total degree of each eq[i]

seq(degree(eqD[i]),i=1..nops(coefList));

# maximum number of indeterminates in the monomials of each eq[i]

ni := NULL:

for i from 1 to nops(coefList) do

nj := 0:

for j from 1 to nops(eqD[i]) do

nj := max(nj, numelems(indets(op(j, eqD[i]), name)))

end do;

ni := ni, nj

end do:

ni;

========Code end==============

Here are some "statistics" about the 20 by 20 polynomial system I want to find a Grobner basis of.

**# number of words used to represent each eq[i]:**

**20, 8, 8, 20, 14, 19, 13, 6, 6, 13, 19, 14, 500, 640, 871, 715, 715, 871, 640, 500**

**# total degree of each eq[i]:**

**316, 124, 124, 316, 242, 318, 238, 94, 94, 238, 318, 242, 13817, 18321, 24544, 20048, 20048, 24544, 18321, 13817**

**# total degree of each eq[i]:**

**5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14**

**# maximum number of indeterminates in the monomials of each eq[i]:**

**3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5**

So, this is a computation that Maple could handle?

Then what is the most complex computation Maple can handle?

Best,

jun