Consider

```
uu=[
[ ((1, 2), (3, -2)), ((1, 3), (3, -3))],
[ ((1, -1), (2, 1))],
[((1, 1), (2, -1)), ((1, -1), (2, 1))],
[ ((2, -2), (4, 2)), ((2, -3), (4, 3))],
[((3, 1), (4, -1)), ((3, 4), (4, -4))],
[((3, 1), (4, -1)), ((3, 2), (4, -2)), ((3, 3), (4, -3))]
]
```

and the following algorithm

```
function sum_exp(uu)
sum_dict = Dict{Int, Int}()
for pairs in uu
for pair in pairs
first_elem = pair[1]
second_elem = pair[2]
if haskey(sum_dict, first_elem)
sum_dict[first_elem] += second_elem
else
sum_dict[first_elem] = second_elem
end
end
end
return sum_dict
end
function cartesian_product
(uu)
res = []
g = Iterators.product(uu...)
for gi in g
if all(values(sum_exp(gi)) .== 0)
push!(res, gi)
end
end
return res
end
```

This code works fine but it is slow and take a lot of memory.

I suspect the root cause lies in the execution of `g = Iterators.product(uu...)`

prior to calculating `sum_exp(gi)) .== 0`

within the `cartesian_product`

function

**Code Functionality:**

- Each tuple within
`uu`

represents a polynomial, with`((1, 2), (3, -2))`

corresponding to`x1^2 * x3^(-2)`

. - The code aims to multiply each tuple in
`uu[1]`

by all tuples within`uu[i]`

for`i > 1`

. - The
`sum_exp`

function returns terms with zero exponents.