* test: compute_path

* refactor: path computation

- Improve path concatenation by utilizing built-in `join` method

* refactor: replace `PartialEq` with derived instance

- Derive `PartialEq` for `SatisfyingAssignment` struct
- Remove redundant manual implementation of `PartialEq`

Cargo-expand generates:
```
        #[automatically_derived]
        impl<G: ::core::cmp::PartialEq + Group> ::core::cmp::PartialEq
        for SatisfyingAssignment<G>
        where
            G::Scalar: PrimeField,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
        {
            #[inline]
            fn eq(&self, other: &SatisfyingAssignment<G>) -> bool {
                self.a_aux_density == other.a_aux_density
                    && self.b_input_density == other.b_input_density
                    && self.b_aux_density == other.b_aux_density && self.a == other.a
                    && self.b == other.b && self.c == other.c
                    && self.input_assignment == other.input_assignment
                    && self.aux_assignment == other.aux_assignment
            }
        }
```

* refactor: avoid default for PhantomData Unit type

* refactor: replace fold with sum where applicable

- Simplify code by replacing `fold` with `sum` in various instances

* refactor: decompression method in sumcheck.rs

* refactor: test functions to use slice instead of vector conversion

* refactor: use more references in functions

- Update parameter types to use references instead of owned values in various functions that do not need them
- Replace cloning instances with references