@Carl Love 

Thanks for your reply.

The computation server has 64GB main memory.

I have many tests to compute on this server.

Some of them ended up with "maple: fatal error, lost connection to kernel"

And some ended up with "Execution Stopped: Unhandled signal caught (UNKNOWN: 1)",

or "

memory used=684574.7MB, alloc=32540.2MB, time=559102.79

Execution stopped: Stack limit reached.

"

Are they all running out of memory?

What can I do to know the exact reasons of those error messages?

Best,

jun

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