@ecterrab 

what is the metric for testing whether it is spherical?

i guess

metric is something like x^2*dx+y^2*dy+z^2*dz

@Mac Dude 

when i use wait command, it still hangs, 

any other methods to solve the hang problem and read the table ?

@Mac Dude 

can not close maple 

and then i open maple again and search wait command, 

it can not be terminated with task manager of window too

how to use command wait to improve dead loop

@Mac Dude 

it hangs when would like to display the keys of table in another sheet

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):
T := Table();
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);
T[h] := [op(T[h]), F];
end if:
end if:
od:
end if:
od:
od:

another sheet:
for i in indices(T) do
print(i);
od:

@Mac Dude 

which version has this preference in the menu?

i can not find it in maple 12

@Mac Dude 

how to set table T as global variable and access it in another worksheet?

@Kitonum 

finally solved with

poly1 := 0;
for j in [1..Length(prepoly1[1])] do
zz:=1;
for i in SplitString(String(prepoly1[1][j]), "+" ) do
zz:=zz*EvalString(i);
od;
if zz <> 1 then
poly1 := poly1 + zz;
fi;
od;

then i think again, actually no need to use gap

if allow duplicate to use 3 for loop to solve previous question

i notice gap system's tuples have more combination than maple's one

it takes time to investigate which is missing which is duplicate

@Markiyan Hirnyk 

I have looked the help in maple 12, it use parametrization(f, x,y, t)

it only use 2 variables, x and y, result in parametric form in terms of t

yes in maple 12, command parametrization

how to use this for 3 variables

if know the underlying algorithm in parametrization,

it will be useful to do for 3 variables.

i find some book do parametrization with arclength, 

it seems parametrization has different version.

which version can succeed to do parametrization

@Markiyan Hirnyk 

this function can only for 2 variable, but the a*(b+c) has 3 variables,

any special skill need to make it work for 3 variables?

when i run parametrization(a*b+a*c, a, b, t);

Error, (in parametrization) a*b+a*c is reducible

how can it be further reduce? why it is reducible?

i run Reduce in package algebraic, it is the same, that means it is irreducible in maple 12

@Axel Vogt 

do you mean that substitute h=1 into solution of elimination?

but can not recover  eq2 := a*b*c+a

 how to do elimination of variable with resultant?

@Axel Vogt 

here is the example,

i concatenate list 2 times, for example [a,b,c] become [a,b,c,a,b,c,a,b,c] to get full combination

1. is it correct to get full combination of polynomials with code below? if not, how?

2. can maple run in http://aws.amazon.com/free/ ?

3. how to export the result of full combination of polynomials in maple code text file after run

in supercomputer and expect to use the code run in home computer?

4.

the method in above link has not limited the power of variable. for example, power of variable only allowed 1 or allowed <= 2, or allowed <= 3

 i find example in book algorithm of invariant , using molien theorem to calculate hilbert series

it seems can use the hilbert series form to guess back the matrix group by observation, is it correct?

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:
gaga := polylistresult;
nops(polylistresult);
polylistresult := [op(polylistresult), op(gaga)];
nops(polylistresult);
polylistresult := [op(polylistresult), op(gaga)];
nops(polylistresult);
with(combinat):
gg := permute(polylistresult, 3);
Error, (in combinat:-permute) Maple was unable to allocate enough memory to complete this computation. Please see ?alloc

@Markiyan Hirnyk 

i have two maple question, but no one answer.

http://www.mapleprimes.com/questions/202363-What-Is-The-Function-For-Degree-Reverse

http://www.mapleprimes.com/questions/202362-How-To-Eliminate-The-Variable-H-With

@Markiyan Hirnyk 

This math overflow question actually is my account's question

i guess no one answer this, so, i ask in different places

@Markiyan Hirnyk 

if maple can classify all that with my algorithm in super computer 

and hard code saved in its own database

power 1 , matrix 0,1

power 2 , martix 0,1,2

power 3 , matrix 0,1,2,3

it will be extremely faster and better than repeated compute in user computer

@Alejandro Jakubi 

i meet this error 

http://www.mapleprimes.com/questions/202338-Error-in-Combinatpermute-Maple

i guess maple new too many instance within the function

so use up memory.

i suggest 3 things

1. return part of result before it return out of memory

2. display how long will wait if using No SQL Object database

    as no reason to wait one day without shutdown personal computer

3. if not using NoSQL object database, i suggest it partition the whole result

    partly return the result within the limit of memory and then free the memory of previous part, the final result can be a array.