input : a*b+a*c

output: (a+b)*(a+c)

convert sum of product to product of sum

how to find the homomorphism between prime ideal and space?

how to find the homomorphism between prime ideal and distributive lattice?

which homomorphism result in space if given prime ideal?

how to save the session of maple worksheet so that no need to calculate again after restart computer

after calculated 70 million result for a long time, how to save the result and session so that no need to recalculate again?

 in maple 12, it can not read table T in another worksheet.

i just want to read table T whenever i want during the running of big loop in procedure manman

restart;
with(Groebner):
AllMatrices := proc (A::set, k::posint, n::posint)
local B, C, E:
B := [[]]:
C := proc ()
B := [seq(seq([A[i], op(B[j])], i = 1 .. nops(A)), j = 1 .. nops(B))]:
end proc:
E := (C@@(k*n))(B):
seq(Matrix(k, n, E[m]), m = 1 .. nops(A)^(k*n));
end proc:
mm := AllMatrices({0, 1}, 3, 3);
GetRing := proc(sol)
ringequation := 0;
mono1 := 0;
for j from 1 to 3 do
mono1 := 1;
for i from 1 to nops(sol[1][j]) do
mono1 := mono1*op(i, sol[1][j]);
od:
ringequation := ringequation + mono1;
od:
return ringequation;
end proc;
with(LinearAlgebra):
polylistresult := [];
for i from 1 to nops([mm]) do
sol := MatrixMatrixMultiply(Matrix([[a,b,c]]), op(i,[mm]));
sol := GetRing(sol);
polylistresult := [op(polylistresult), sol];
od:
with(Groebner):
with(Threads):
T := Table();
m := Threads[Mutex][Create]();
manman := proc(T2, m2);
indexlistresult := [];
for i from 2 to nops(polylistresult) do
for j from 2 to nops(polylistresult) do
if i < j then
for k from 2 to nops(polylistresult) do

if j < k then
print("find");
F := [polylistresult[i], polylistresult[j], polylistresult[k]];
h := HilbertSeries(F, {x, y, z}, s);
if h <> 0 then
#if not assigned(T[h]) then
print(h);
Threads[Mutex][Lock]( m2 );
T2[h] := [op(T2[h]), F];
Threads[Mutex][Unlock]( m2 );
end if:
end if:
od:
end if:
od:
od:
end proc:
manman(T, m);
Threads[Mutex][Destroy](m);

another sheet:
Threads[Mutex][Lock]( m );
for i in indices(T) do
print(i);
od:
Threads[Mutex][Unlock]( m );

n=512, what is number = nops(T) without actual running code?

n := 512;
T := [];
for i from 1 to n do
for j from 1 to n do
if i < j then
for k from 1 to n do
if j < k then
T := [op(T), [i,j,k]];
end:
od:
end if:
od:
od:
nops(T);
T;