Add derivative method for rational polynomials

- Fix ncols() in Python API

src/api/python.rs

@@ -8082,6 +8082,36 @@ impl PythonRationalPolynomial {
         }
     }
 
+    /// Take a derivative in `x`.
+    ///
+    /// Examples
+    /// --------
+    ///
+    /// >>> from symbolica import Expression
+    /// >>> x = Expression.symbol('x')
+    /// >>> p = Expression.parse('1/((x+y)*(x^2+x*y+1)(x+1))').to_rational_polynomial()
+    /// >>> print(p.derivative(x))
+    pub fn derivative(&self, x: PythonExpression) -> PyResult<Self> {
+        let x = self
+            .poly
+            .numerator
+            .get_vars_ref()
+            .iter()
+            .position(|v| match (v, x.expr.as_view()) {
+                (Variable::Symbol(y), AtomView::Var(vv)) => *y == vv.get_symbol(),
+                (Variable::Function(_, f) | Variable::Other(f), a) => f.as_view() == a,
+                _ => false,
+            })
+            .ok_or(exceptions::PyValueError::new_err(format!(
+                "Variable {} not found in polynomial",
+                x.__str__()?
+            )))?;
+
+        Ok(Self {
+            poly: self.poly.derivative(x),
+        })
+    }
+
     /// Compute the partial fraction decomposition in `x`.
     ///
     /// Examples
@@ -8366,6 +8396,36 @@ impl PythonFiniteFieldRationalPolynomial {
         }
     }
 
+    /// Take a derivative in `x`.
+    ///
+    /// Examples
+    /// --------
+    ///
+    /// >>> from symbolica import Expression
+    /// >>> x = Expression.symbol('x')
+    /// >>> p = Expression.parse('1/((x+y)*(x^2+x*y+1)(x+1))').to_rational_polynomial()
+    /// >>> print(p.derivative(x))
+    pub fn derivative(&self, x: PythonExpression) -> PyResult<Self> {
+        let x = self
+            .poly
+            .numerator
+            .get_vars_ref()
+            .iter()
+            .position(|v| match (v, x.expr.as_view()) {
+                (Variable::Symbol(y), AtomView::Var(vv)) => *y == vv.get_symbol(),
+                (Variable::Function(_, f) | Variable::Other(f), a) => f.as_view() == a,
+                _ => false,
+            })
+            .ok_or(exceptions::PyValueError::new_err(format!(
+                "Variable {} not found in polynomial",
+                x.__str__()?
+            )))?;
+
+        Ok(Self {
+            poly: self.poly.derivative(x),
+        })
+    }
+
     /// Compute the partial fraction decomposition in `x`.
     ///
     /// Examples
@@ -8718,7 +8778,7 @@ impl PythonMatrix {
 
     /// Return the number of columns.
     pub fn ncols(&self) -> usize {
-        self.matrix.nrows()
+        self.matrix.ncols()
     }
 
     /// Return true iff every entry in the matrix is zero.

src/domains/rational_polynomial.rs

@@ -742,6 +742,39 @@ where
     }
 }
 
+impl<R: EuclideanDomain + PolynomialGCD<E>, E: Exponent> RationalPolynomial<R, E>
+where
+    RationalPolynomial<R, E>: FromNumeratorAndDenominator<R, R, E>,
+{
+    /// Compute the derivative of the rational polynomial in `var`.
+    pub fn derivative(&self, var: usize) -> Self {
+        if self.numerator.degree(var) == E::zero() && self.denominator.degree(var) == E::zero() {
+            return RationalPolynomial {
+                numerator: self.numerator.zero(),
+                denominator: self.denominator.one(),
+            };
+        }
+
+        let dn = self.numerator.derivative(var);
+        let dd = self.denominator.derivative(var);
+
+        let a = RationalPolynomial::from_num_den(
+            dn,
+            self.denominator.clone(),
+            &self.numerator.field,
+            false,
+        );
+        let b = RationalPolynomial::from_num_den(
+            &self.numerator * &dd,
+            &self.denominator * &self.denominator,
+            &self.numerator.field,
+            false,
+        );
+
+        &a - &b
+    }
+}
+
 impl<R: EuclideanDomain + PolynomialGCD<E>, E: Exponent> RationalPolynomial<R, E>
 where
     RationalPolynomial<R, E>: FromNumeratorAndDenominator<R, R, E>,

symbolica.pyi

@@ -2561,6 +2561,18 @@ class RationalPolynomial:
         >>> print((e - p.to_expression()).expand())
         """
 
+    def derivative(self, x: Expression) -> RationalPolynomial:
+        """Take a derivative in `x`.
+
+        Examples
+        --------
+
+        >>> from symbolica import Expression
+        >>> x = Expression.symbol('x')
+        >>> p = Expression.parse('1/((x+y)*(x^2+x*y+1)(x+1))').to_rational_polynomial()
+        >>> print(p.derivative(x))
+        """
+
     def apart(self, x: Expression) -> List[RationalPolynomial]:
         """Compute the partial fraction decomposition in `x`.
 
@@ -2629,6 +2641,18 @@ class FiniteFieldRationalPolynomial:
     def gcd(self, rhs: FiniteFieldRationalPolynomial) -> FiniteFieldRationalPolynomial:
         """Compute the greatest common divisor (GCD) of two rational polynomials."""
 
+    def derivative(self, x: Expression) -> RationalPolynomial:
+        """Take a derivative in `x`.
+
+        Examples
+        --------
+
+        >>> from symbolica import Expression
+        >>> x = Expression.symbol('x')
+        >>> p = Expression.parse('1/((x+y)*(x^2+x*y+1)(x+1))').to_rational_polynomial()
+        >>> print(p.derivative(x))
+        """
+
     def apart(self, x: Expression) -> List[FiniteFieldRationalPolynomial]:
         """Compute the partial fraction decomposition in `x`.