implement Nova's AugmentedFCircuit (#33)

* impl AugmentedFCircuit non-base case

* add multiple iterations to AugmentedFCircuit test

* implement base case on AugmentedFCircuit and test

* Update cmE of E=0-vec to work as zero point

Update cmE of E=0-vec to work as zero point instead of as cm(0-vec)

* patch r1cs-std dep to a cherry-picked version with the zero-scalar-mult fix

* refactor FCircuit to make it more suitable inside the AugmentedFCircuit

Cargo.toml

@@ -10,7 +10,7 @@ ark-poly = "^0.4.0"
 ark-std = "^0.4.0"
 ark-crypto-primitives = { version = "^0.4.0", default-features = false, features = ["r1cs", "sponge", "crh"] }
 ark-relations = { version = "^0.4.0", default-features = false }
-ark-r1cs-std = { version = "^0.4.0", default-features = false }
+ark-r1cs-std = { default-features = false } # use latest version from the patch
 ark-circom = { git = "https://github.com/gakonst/ark-circom.git" }
 thiserror = "1.0"
 rayon = "1.7.0"
@@ -26,6 +26,8 @@ espresso_transcript = {git="https://github.com/EspressoSystems/hyperplonk", pack
 ark-pallas = {version="0.4.0", features=["r1cs"]}
 ark-vesta = {version="0.4.0"}
 ark-bn254 = "0.4.0"
+tracing = { version = "0.1", default-features = false, features = [ "attributes" ] }
+tracing-subscriber = { version = "0.2" }
 
 [features]
 default = ["parallel", "nova", "hypernova"]
@@ -37,3 +39,11 @@ parallel = [
     "ark-ff/parallel",  
     "ark-poly/parallel", 
     ]
+
+# The following patch is to use a version of ark-r1cs-std compatible with
+# v0.4.0 but that includes a cherry-picked commit from after v0.4.0 which fixes
+# the in-circuit scalar multiplication of the zero point. The commit is from
+# https://github.com/arkworks-rs/r1cs-std/pull/124, without including other
+# changes done between v0.4.0 and this fix which would break compatibility.
+[patch.crates-io]
+ark-r1cs-std = { git = "https://github.com/arnaucube/ark-r1cs-std-cherry-picked/" }