Allow extending algebraic extensions in Python API

src/api/python.rs

@@ -7816,6 +7816,42 @@ impl PythonNumberFieldPolynomial {
             })
             .into())
     }
+
+    /// Get the minimal polynomial of the algebraic extension.
+    pub fn get_minimal_polynomial(&self) -> PythonPolynomial {
+        PythonPolynomial {
+            poly: self.poly.ring.poly().clone(),
+        }
+    }
+
+    /// Extend the coefficient ring of this polynomial `R[a]` with `b`, whose minimal polynomial
+    /// is `R[a][b]` and form `R[b]`. Also return the new representation of `a` and `b`.
+    ///
+    /// `b`  must be irreducible over `R` and `R[a]`; this is not checked.
+    pub fn extend(&self, b: Self) -> (Self, PythonPolynomial, PythonPolynomial) {
+        let (new_field, map1, map2) = self.poly.ring.extend(&b.poly);
+
+        (
+            Self {
+                poly: self.poly.map_coeff(
+                    |f| {
+                        let mut new_num = new_field.zero();
+                        for (p, coeff) in f.poly.coefficients.iter().enumerate() {
+                            new_field.add_assign(
+                                &mut new_num,
+                                &new_field.pow(&map1, p as u64).mul_coeff(coeff.clone()),
+                            );
+                        }
+
+                        new_num
+                    },
+                    new_field.clone(),
+                ),
+            },
+            PythonPolynomial { poly: map1.poly },
+            PythonPolynomial { poly: map2.poly },
+        )
+    }
 }
 
 /// A Symbolica rational polynomial.

src/domains/algebraic_number.rs

@@ -353,6 +353,12 @@ impl<R: Ring> std::fmt::Display for AlgebraicNumber<R> {
 }
 
 impl<R: Ring> AlgebraicNumber<R> {
+    pub fn mul_coeff(self, c: R::Element) -> Self {
+        AlgebraicNumber {
+            poly: self.poly.mul_coeff(c),
+        }
+    }
+
     pub fn to_finite_field<UField: FiniteFieldWorkspace>(
         &self,
         field: &FiniteField<UField>,
@@ -559,7 +565,7 @@ impl<R: Field + PolynomialGCD<u16>> AlgebraicExtension<R> {
     /// Extend the current algebraic extension `R[a]` with `b`, whose minimal polynomial
     /// is `R[a][b]` and form `R[b]`. Also return the new representation of `a` and `b`.
     ///
-    /// `b`  must be irreducible over `R` and `R[a]`; this is not checked.
+    /// `b` must be irreducible over `R` and `R[a]`; this is not checked.
     pub fn extend(
         &self,
         b: &MultivariatePolynomial<AlgebraicExtension<R>>,

symbolica.pyi

@@ -2363,6 +2363,15 @@ class NumberFieldPolynomial:
         >>> p.replace(x, r)
         """
 
+    def get_minimal_polynomial(self) -> Polynomial:
+        """Get the minimal polynomial of the algebraic extension."""
+
+    def extend(self, b: NumberFieldPolynomial) -> Tuple[NumberFieldPolynomial, Polynomial, Polynomial]:
+        """Extend the coefficient ring of this polynomial `R[a]` with `b`, whose minimal polynomial
+        is `R[a][b]` and form `R[b]`. Also return the new representation of `a` and `b`.
+
+        `b`  must be irreducible over `R` and `R[a]`; this is not checked."""
+
 
 class FiniteFieldPolynomial:
     """A Symbolica polynomial with finite field coefficients."""