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>

folding-schemes/Cargo.toml

@@ -14,7 +14,7 @@ ark-relations = { version = "^0.4.0", default-features = false }
 ark-r1cs-std = { version = "0.4.0", default-features = false } # this is patched at the workspace level
 ark-snark = { version = "^0.4.0"}
 ark-serialize = "^0.4.0"
-ark-circom = { git = "https://github.com/gakonst/ark-circom.git" }
+ark-circom = { git = "https://github.com/arnaucube/circom-compat.git" }
 thiserror = "1.0"
 rayon = "1.7.0"
 num-bigint = "0.4"