Adapt Frontend/Circom for FCircuit Trait (#71)

* initial

* improved z_i

* improved

* Redefined the .circom and the test code for CircomWrapper

* added test function for wrapper_circuit which has circom_fcircuit, but incompatibility error of Pairing and Pallas

* changed the path in the gitignore

* Remove circom generated path

* improved variable vector

* Pallas::Fr

* improved to the primefield

* mentioned the issues:1. extract z_i1(only public output) 2.constraintsSystem and its Ref

* modified

* public input in circom

* generalized; removed the hardcorded value

* Generalization using FpVar::<Fr>::new_input

* initial

* improved z_i

* improved

* Redefined the .circom and the test code for CircomWrapper

* added test function for wrapper_circuit which has circom_fcircuit, but incompatibility error of Pairing and Pallas

* Remove circom generated path

* improved variable vector

* Pallas::Fr

* improved to the primefield

* mentioned the issues:1. extract z_i1(only public output) 2.constraintsSystem and its Ref

* modified

* Small updates:

- update cubic_circuit.circom: remove extra constraint, remove public
  inputs
- remove allocations of inputs in arkworks
- add return of z_{i+1} at the end of CircomtoFCircuit::generate_step_constraints

With this tmp fix the `test_circom_step_constraints` passes, but needs to be iterated and polished.

* Update circom-compat to re-allocate inputs

* update after rebase to latest main: add usage of self.state_len() to circom frontend

* move circom frontend related structs into frontend/circom dir

* clippy lints

* extract_witness

* add comments

* clean

* fmt, lint, and spell

* CI Check trigger

* fmt

* applied the feedback

---------

Co-authored-by: Y5 <76672645+yugonsan@users.noreply.github.com>
Co-authored-by: arnaucube <root@arnaucube.com>

.gitignore

@@ -1,8 +1,8 @@
 /target
 Cargo.lock
 # Circom generated files
-/src/frontend/circom/test_folder/test_circuit.r1cs
-/src/frontend/circom/test_folder/test_circuit_js/
+folding-schemes/src/frontend/circom/test_folder/cubic_circuit.r1cs
+folding-schemes/src/frontend/circom/test_folder/cubic_circuit_js/
 
 # generated contracts at test time
-solidity-verifiers/generated
+solidity-verifiers/generated