feat: start working on add for polynomial

src/utils/field.rs

@@ -1,6 +1,6 @@
 use std::{
     env::args,
-    ops::{Add, Mul},
+    ops::{Add, BitXor, Mul},
 };
 
 use anyhow::{anyhow, Ok, Result};
@@ -73,9 +73,13 @@ impl Mul for Polynomial {
 impl Add for Polynomial {
     type Output = Self;
     fn add(self, rhs: Self) -> Self::Output {
-        FieldElement::new(
+        for i in 0..self.polynomial.len() {
-            xor_bytes(&self.field_element, rhs.field_element).expect("Error in poly add"),
+            for j in 0..rhs.polynomial.len() {
-        )
+                polynomial[i + j] = &polynomial[i + j]
+                    + &(self.polynomial.get(i).unwrap() * rhs.polynomial.get(j).unwrap());
+            }
+        }
+        Polynomial::new(polynomial)
     }
 }
 
@@ -169,6 +173,14 @@ impl Clone for FieldElement {
     }
 }
 
+/*
+impl BitXor for FieldElement {
+    fn bitxor(self, rhs: Self) -> Self::Output {
+        FieldElement
+    }
+}
+*/
+
 /*
 impl From<Vec<u8>> for FieldElement {
     fn from(item: Vec<u8>) -> Self {