Parse canonical rationals before backend coercion (#775)

* fix(math): parse canonical rationals before backend coercion

* fix(ci): format eval telemetry test signature

Ruff format requires wrapping the long test function signature that
blocked Lint & Format on this branch.

Co-authored-by: morluto <morluto@users.noreply.github.com>

---------

Co-authored-by: morluto <morluto@users.noreply.github.com>

Author: morluto

src/jacobian/domains/arithmetic/operations.py

@@ -109,7 +109,7 @@ def nth_root(request: IntegerNthRootRequest) -> IntegerNthRootResult:
 
 
 def _fraction(value: CanonicalRational) -> Fraction:
-    return Fraction(int(value.num), int(value.den))
+    return value.as_fraction()
 
 
 def _wire(value: Fraction) -> CanonicalRational:

src/jacobian/domains/geometry/operations.py

@@ -56,8 +56,8 @@ def _point(value: RationalPoint2D) -> Any:
     from sympy.geometry import Point2D
 
     return Point2D(
-        sympy.Rational(int(value.x.num), int(value.x.den)),
-        sympy.Rational(int(value.y.num), int(value.y.den)),
+        sympy.Rational(value.x.as_fraction()),
+        sympy.Rational(value.y.as_fraction()),
     )
 
 

src/jacobian/domains/matrix_lattice/operations.py

@@ -42,7 +42,7 @@ def _qq_matrix(matrix: RationalMatrix) -> Any:
 
     return sympy.Matrix(
         [
-            [sympy.Rational(int(value.num), int(value.den)) for value in row]
+            [sympy.Rational(value.as_fraction()) for value in row]
             for row in matrix.entries
         ]
     )
@@ -190,9 +190,7 @@ def compute_rational_linear_solve(
     import sympy
 
     source = _qq_matrix(request.matrix)
-    rhs = sympy.Matrix(
-        [sympy.Rational(int(value.num), int(value.den)) for value in request.rhs]
-    )
+    rhs = sympy.Matrix([sympy.Rational(value.as_fraction()) for value in request.rhs])
     solution, parameters = source.gauss_jordan_solve(rhs)
     if parameters.rows:
         raise ValueError("linear system does not have a unique solution")

src/jacobian/domains/optimization/worker.py

@@ -19,7 +19,7 @@
 def _rational(value: CanonicalRational) -> Any:
     import sympy
 
-    return sympy.Rational(int(value.num), int(value.den))
+    return sympy.Rational(value.as_fraction())
 
 
 def _wire(value: Any) -> dict[str, str]:

src/jacobian/domains/polynomial/elementary_operations.py

@@ -197,15 +197,17 @@ def _partial_fraction_term(
 def _partial_fraction_sort_key(
     term: RationalPartialFractionTerm,
 ) -> tuple[tuple[tuple[tuple[int, ...], int, int], ...], int]:
-    factor_terms = tuple(
-        (
-            factor_term.exponents,
-            int(factor_term.coefficient.num),
-            int(factor_term.coefficient.den),
+    factor_terms: list[tuple[tuple[int, ...], int, int]] = []
+    for factor_term in term.denominator_factor.polynomial.terms:
+        coefficient = factor_term.coefficient.as_fraction()
+        factor_terms.append(
+            (
+                factor_term.exponents,
+                coefficient.numerator,
+                coefficient.denominator,
+            )
         )
-        for factor_term in term.denominator_factor.polynomial.terms
-    )
-    return factor_terms, term.denominator_exponent
+    return tuple(factor_terms), term.denominator_exponent
 
 
 def rational_partial_fraction_decomposition(

src/jacobian/domains/polynomial/jacobian_syzygy.py

@@ -172,11 +172,7 @@ def compute_graded_jacobian_syzygy(
         for factor in request.linear_factors:
             source *= Poly(
                 sum(
-                    Rational(
-                        int(coefficient.num),
-                        int(coefficient.den),
-                    )
-                    * generator
+                    Rational(coefficient.as_fraction()) * generator
                     for coefficient, generator in zip(
                         factor.coefficients,
                         generators,

src/jacobian/domains/polynomial/operations.py

@@ -47,10 +47,7 @@ def _poly(polynomial: RationalPolynomial) -> Any:
 
     generators = _symbols(polynomial.variables)
     coefficients = {
-        term.exponents: Rational(
-            int(term.coefficient.num),
-            int(term.coefficient.den),
-        )
+        term.exponents: Rational(term.coefficient.as_fraction())
         for term in polynomial.polynomial.terms
     }
     return Poly.from_dict(coefficients, *generators, domain=QQ)

src/jacobian/domains/probability/operations.py

@@ -49,7 +49,8 @@ def _wire(value: Any) -> CanonicalRational:
 def _fmpq(value: CanonicalRational) -> Any:
     from flint import fmpq
 
-    return fmpq(int(value.num), int(value.den))
+    fraction = value.as_fraction()
+    return fmpq(fraction.numerator, fraction.denominator)
 
 
 def _complex_wire(value: tuple[Any, Any]) -> ExactComplexRational:

src/jacobian/matrices/capabilities.py

@@ -316,10 +316,7 @@ def _sympy_matrix(matrix: ExactRationalMatrix) -> Matrix:
     from sympy import Matrix, Rational
 
     return Matrix(
-        [
-            [Rational(int(entry.num), int(entry.den)) for entry in row]
-            for row in matrix.entries
-        ]
+        [[Rational(entry.as_fraction()) for entry in row] for row in matrix.entries]
     )
 
 

src/jacobian/polynomial_interval_capabilities.py

@@ -701,10 +701,10 @@ def _bernstein_coefficients(
     degree = polynomial.degree
     sp = _sympy.get()
     generator: Symbol = sp.symbols(polynomial.variable)
-    terms = {
-        term.exponents: sp.QQ(int(term.coefficient.num), int(term.coefficient.den))
-        for term in polynomial.polynomial.terms
-    }
+    terms = {}
+    for term in polynomial.polynomial.terms:
+        coefficient = term.coefficient.as_fraction()
+        terms[term.exponents] = sp.QQ(coefficient.numerator, coefficient.denominator)
     source = sp.Poly.from_dict(terms, generator, domain=sp.QQ)
     shifted = sp.Poly(
         sp.expand(source.as_expr().subs(generator, a + width * generator)),