field: require TryInto<Base> for ExtensionField

src/primitives/field.rs

@@ -2,6 +2,7 @@
 
 //! Generic Field Traits
 
+use core::convert::TryInto;
 use core::iter::{Skip, Take};
 use core::{fmt, hash, iter, ops};
 
@@ -153,7 +154,7 @@ pub trait Field:
 
 /// Trait describing a simple extension field (field obtained from another by
 /// adjoining one element).
-pub trait ExtensionField: Field + From<Self::BaseField> {
+pub trait ExtensionField: Field + From<Self::BaseField> + TryInto<Self::BaseField> {
     /// The type of the base field.
     type BaseField: Field;
 

src/primitives/gf32_ext.rs

@@ -37,6 +37,19 @@ impl<const DEG: usize> From<Fe32> for Fe32Ext<DEG> {
     }
 }
 
+impl<const DEG: usize> core::convert::TryFrom<Fe32Ext<DEG>> for Fe32 {
+    type Error = ();
+
+    fn try_from(ext: Fe32Ext<DEG>) -> Result<Self, Self::Error> {
+        for elem in &ext.inner[1..] {
+            if *elem != Fe32::Q {
+                return Err(());
+            }
+        }
+        Ok(ext.inner[0])
+    }
+}
+
 impl<const DEG: usize> fmt::Debug for Fe32Ext<DEG> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { fmt::Display::fmt(self, f) }
 }