diff --git a/math/src/circle/errors.rs b/math/src/circle/errors.rs
new file mode 100644
index 000000000..51dcb720b
--- /dev/null
+++ b/math/src/circle/errors.rs
@@ -0,0 +1,4 @@
+#[derive(Debug)]
+pub enum CircleError {
+    PointDoesntSatisfyCircleEquation,
+}
diff --git a/math/src/circle/mod.rs b/math/src/circle/mod.rs
index f5a65721f..ac576194f 100644
--- a/math/src/circle/mod.rs
+++ b/math/src/circle/mod.rs
@@ -1,5 +1,6 @@
 pub mod cfft;
 pub mod cosets;
+pub mod errors;
 pub mod point;
 pub mod polynomial;
 pub mod twiddles;
diff --git a/math/src/circle/point.rs b/math/src/circle/point.rs
index 9c6e0662c..24759a043 100644
--- a/math/src/circle/point.rs
+++ b/math/src/circle/point.rs
@@ -1,3 +1,4 @@
+use super::errors::CircleError;
 use crate::field::traits::IsField;
 use crate::field::{
     element::FieldElement,
@@ -9,16 +10,73 @@ use core::ops::{Add, Mul};
 /// x in F, y in F and x^2 + y^2 = 1, i.e. the Circle. The operation of the group will have
 /// additive notation and is as follows:
 /// (a, b) + (c, d) = (a * c - b * d, a * d + b * c)
-
 #[derive(Debug, Clone)]
 pub struct CirclePoint<F: IsField> {
     pub x: FieldElement<F>,
     pub y: FieldElement<F>,
 }
 
-#[derive(Debug)]
-pub enum CircleError {
-    PointDoesntSatisfyCircleEquation,
+impl<F: IsField + HasCircleParams<F>> CirclePoint<F> {
+    pub fn new(x: FieldElement<F>, y: FieldElement<F>) -> Result<Self, CircleError> {
+        if x.square() + y.square() == FieldElement::one() {
+            Ok(Self { x, y })
+        } else {
+            Err(CircleError::PointDoesntSatisfyCircleEquation)
+        }
+    }
+
+    /// Neutral element of the Circle group (with additive notation).
+    pub fn zero() -> Self {
+        Self::new(FieldElement::one(), FieldElement::zero()).unwrap()
+    }
+
+    /// Computes 2(x, y) = (2x^2 - 1, 2xy).
+    pub fn double(self) -> Self {
+        Self::new(
+            self.x.square().double() - FieldElement::one(),
+            self.x.double() * self.y,
+        )
+        .unwrap()
+    }
+
+    /// Computes 2^n * (x, y).
+    pub fn repeated_double(self, n: u32) -> Self {
+        let mut res = self;
+        for _ in 0..n {
+            res = res.double();
+        }
+        res
+    }
+
+    /// Computes the inverse of the point.
+    /// We are using -(x, y) = (x, -y), i.e. the inverse of the group opertion is conjugation
+    /// because the norm of every point in the circle is one.
+    pub fn conjugate(self) -> Self {
+        Self {
+            x: self.x,
+            y: -self.y,
+        }
+    }
+
+    pub fn antipode(self) -> Self {
+        Self {
+            x: -self.x,
+            y: -self.y,
+        }
+    }
+
+    pub const GENERATOR: Self = Self {
+        x: F::CIRCLE_GENERATOR_X,
+        y: F::CIRCLE_GENERATOR_Y,
+    };
+
+    /// Returns the generator of the subgroup of order n = 2^log_2_size.
+    /// We are using that 2^k * g is a generator of the subgroup of order 2^{31 - k}.
+    pub fn get_generator_of_subgroup(log_2_size: u32) -> Self {
+        Self::GENERATOR.repeated_double(31 - log_2_size)
+    }
+
+    pub const ORDER: u128 = F::ORDER;
 }
 
 /// Parameters of the base field that we'll need to define its Circle.
@@ -119,69 +177,6 @@ impl<F: IsField + HasCircleParams<F>> Mul<u128> for CirclePoint<F> {
     }
 }
 
-impl<F: IsField + HasCircleParams<F>> CirclePoint<F> {
-    pub fn new(x: FieldElement<F>, y: FieldElement<F>) -> Result<Self, CircleError> {
-        if x.square() + y.square() == FieldElement::one() {
-            Ok(Self { x, y })
-        } else {
-            Err(CircleError::PointDoesntSatisfyCircleEquation)
-        }
-    }
-
-    /// Neutral element of the Circle group (with additive notation).
-    pub fn zero() -> Self {
-        Self::new(FieldElement::one(), FieldElement::zero()).unwrap()
-    }
-
-    /// Computes 2(x, y) = (2x^2 - 1, 2xy).
-    pub fn double(self) -> Self {
-        Self::new(
-            self.x.square().double() - FieldElement::one(),
-            self.x.double() * self.y,
-        )
-        .unwrap()
-    }
-
-    /// Computes 2^n * (x, y).
-    pub fn repeated_double(self, n: u32) -> Self {
-        let mut res = self;
-        for _ in 0..n {
-            res = res.double();
-        }
-        res
-    }
-
-    /// Computes the inverse of the point.
-    /// We are using -(x, y) = (x, -y), i.e. the inverse of the group opertion is conjugation
-    /// because the norm of every point in the circle is one.
-    pub fn conjugate(self) -> Self {
-        Self {
-            x: self.x,
-            y: -self.y,
-        }
-    }
-
-    pub fn antipode(self) -> Self {
-        Self {
-            x: -self.x,
-            y: -self.y,
-        }
-    }
-
-    pub const GENERATOR: Self = Self {
-        x: F::CIRCLE_GENERATOR_X,
-        y: F::CIRCLE_GENERATOR_Y,
-    };
-
-    /// Returns the generator of the subgroup of order n = 2^log_2_size.
-    /// We are using that 2^k * g is a generator of the subgroup of order 2^{31 - k}.
-    pub fn get_generator_of_subgroup(log_2_size: u32) -> Self {
-        Self::GENERATOR.repeated_double(31 - log_2_size)
-    }
-
-    pub const ORDER: u128 = F::ORDER;
-}
-
 #[cfg(test)]
 mod tests {
     use super::*;