how to calculate the curvature of discrete data?

if discrete data have curvature, does it mean that it has quantum gravity?

but it may be some random data, it seems contradicts the fact

how to quantization of this curvature in maple?

how to compute non-reduced hilbert series?

hilbertseries return a simplified version of hilbert series,

how to output non-simplified version of hilbert series?

M := Matrix([[0,1,1,1,1],[1,0,1,1,1],[1,1,0,1,1],[1,1,1,0,1],[1,1,1,1,0]]);

how to multiply M[1] which is [0,1,1,1,1] with Matrix([[x0], [x1], [x2], [x3], [x4]])
to become [0,x1,x2,x3,x4]

may not use Matrix([[x0], [x1], [x2], [x3], [x4]])

just want to use first element as x0 when it is not 0

second element as x1, etc

LM:=proc(n)
local L;
uses combinat;
L:=permute([1$(n*(n-1)/2), 0$(n*(n-1)/2)], n*(n-1)/2);
[seq(Matrix(n,{seq(seq((i+1,j)=L[k][(i-1)*i/2+j], j=1..i), i=1..n-1)}, shape=symmetric), k=1..nops(L))];
end proc:
M := LM(5);
N := nops(M);
append("E:\\mm.txt");
for i from 1 to N do
ExportMatrix( "E://mm.txt", M[i]);
od:

hope to export to a text file

and show

for example

matrix([[1,1,1],[1,1,0],[0,0,0]]);

matrix([[1,1,1],[1,1,0],[0,0,0]]);

matrix([[1,1,1],[1,1,0],[0,0,0]]);

...

etc

is it possible to generalize a function to a combinatorial level for approximate axioms

for example, first 100 or 1000 data points satisfy axioms

or 100% satisfy a axioms which means satisfy to infinity

because i find data always not exactly satisfy the axioms,
i guess it only satisfy to some limit, this may explain why data has decimal number

or conversely is it possible to generalize some axioms which approximate the original exact axioms
then data can exactly satisfy the approximate axioms

can generalize a nested forloop to achieve this goal?

how can it be done in algebra point of view?

For example:

x*y = for loop -> for loop -> i*j

it can change for loop expression into algebra

for i from 1 to 10 do
for j from 1 to 10 do
print i*j
od:
od: