Format canonical rational results beyond Python's digit limit (#778)

* fix: format canonical rational results safely

* refactor: simplify canonical output architecture check

Author: morluto

src/jacobian/domains/arithmetic/operations.py

@@ -16,6 +16,7 @@
 from fractions import Fraction
 from typing import Literal
 
+from jacobian.canonical import format_canonical_integer
 from jacobian.contracts.arithmetic import (
     IntegerBaseDigitsRequest,
     IntegerBaseDigitsResult,
@@ -114,8 +115,8 @@ def _fraction(value: CanonicalRational) -> Fraction:
 
 def _wire(value: Fraction) -> CanonicalRational:
     return CanonicalRational(
-        num=str(value.numerator),
-        den=str(value.denominator),
+        num=format_canonical_integer(value.numerator),
+        den=format_canonical_integer(value.denominator),
     )
 
 

src/jacobian/domains/combinatorics/operations.py

@@ -5,6 +5,7 @@
 from functools import reduce
 from operator import mul
 
+from jacobian.canonical import format_canonical_integer
 from jacobian.contracts.combinatorics import (
     FibonacciPairRequest,
     FibonacciPairResult,
@@ -168,7 +169,10 @@ def bernoulli(request: NonnegativeIntegerRequest) -> RationalResult:
     n = request.n
     value = sympy.bernoulli(n)
     return RationalResult(
-        value=CanonicalRational(num=str(value.p), den=str(value.q)),
+        value=CanonicalRational(
+            num=format_canonical_integer(int(value.p)),
+            den=format_canonical_integer(int(value.q)),
+        ),
     )
 
 

src/jacobian/domains/geometry/operations.py

@@ -6,6 +6,7 @@
 from fractions import Fraction
 from typing import Any, cast
 
+from jacobian.canonical import format_canonical_integer
 from jacobian.contracts.exact import CanonicalRational
 from jacobian.contracts.geometry import (
     ClosedSegment2D,
@@ -46,8 +47,8 @@ def _fraction(value: Any) -> Fraction:
 def _wire_rational(value: Any) -> CanonicalRational:
     fraction = _fraction(value)
     return CanonicalRational(
-        num=str(fraction.numerator),
-        den=str(fraction.denominator),
+        num=format_canonical_integer(fraction.numerator),
+        den=format_canonical_integer(fraction.denominator),
     )
 
 

src/jacobian/domains/graph_optimization/minimum_spanning_tree.py

@@ -5,6 +5,7 @@
 from fractions import Fraction
 from typing import TYPE_CHECKING
 
+from jacobian.canonical import format_canonical_integer
 from jacobian.contracts.capabilities import (
     CapabilityDiagnostic,
     CapabilityInvocationExample,
@@ -43,7 +44,10 @@
 
 
 def _rational(value: Fraction) -> CanonicalRational:
-    return CanonicalRational(num=str(value.numerator), den=str(value.denominator))
+    return CanonicalRational(
+        num=format_canonical_integer(value.numerator),
+        den=format_canonical_integer(value.denominator),
+    )
 
 
 def _canonical_endpoints(left: str, right: str) -> tuple[str, str]:

src/jacobian/domains/matrix_lattice/operations.py

@@ -5,6 +5,7 @@
 from fractions import Fraction
 from typing import Any
 
+from jacobian.canonical import format_canonical_integer
 from jacobian.contracts.matrix_operations import (
     CharacteristicPolynomialResult,
     IntegerMatrixRequest,
@@ -32,8 +33,8 @@
 def _rational(value: Any) -> OutputRational:
     fraction = Fraction(value)
     return OutputRational(
-        num=str(fraction.numerator),
-        den=str(fraction.denominator),
+        num=format_canonical_integer(fraction.numerator),
+        den=format_canonical_integer(fraction.denominator),
     )
 
 

src/jacobian/domains/optimization/worker.py

@@ -10,6 +10,7 @@
 from jacobian.canonical import (
     CanonicalizationError,
     canonicalize_json,
+    format_canonical_integer,
     loads_strict_json,
 )
 from jacobian.contracts.exact import CanonicalRational
@@ -26,7 +27,10 @@ def _wire(value: Any) -> dict[str, str]:
     import sympy
 
     rational = sympy.Rational(value)
-    return {"num": str(rational.p), "den": str(rational.q)}
+    return {
+        "num": format_canonical_integer(int(rational.p)),
+        "den": format_canonical_integer(int(rational.q)),
+    }
 
 
 def _linear_program(request: RationalLinearProgramRequest) -> dict[str, Any]:

src/jacobian/domains/polynomial/jacobian_syzygy.py

@@ -7,7 +7,7 @@
 from math import gcd
 from typing import Any, Literal, cast
 
-from jacobian.canonical import canonicalize_json
+from jacobian.canonical import canonicalize_json, format_canonical_integer
 from jacobian.contracts.capabilities import (
     CapabilityInvocationExample,
     CapabilityMode,
@@ -40,7 +40,10 @@ def _homogeneous_basis(degree: int) -> tuple[tuple[int, int, int], ...]:
 
 def _fraction_text(value: Any) -> str:
     fraction = Fraction(value)
-    return f"{fraction.numerator}/{fraction.denominator}"
+    return (
+        f"{format_canonical_integer(fraction.numerator)}/"
+        f"{format_canonical_integer(fraction.denominator)}"
+    )
 
 
 def _matrix_digest(
@@ -97,8 +100,8 @@ def _multiplier_polynomial(
             terms=tuple(
                 RationalPolynomialTerm(
                     coefficient=CanonicalRational(
-                        num=str(coefficient.numerator),
-                        den=str(coefficient.denominator),
+                        num=format_canonical_integer(coefficient.numerator),
+                        den=format_canonical_integer(coefficient.denominator),
                     ),
                     exponents=exponents,
                 )
@@ -269,8 +272,8 @@ def compute_graded_jacobian_syzygy(
                 multiplier_degree=multiplier_degree,
                 coefficient_vector=tuple(
                     CanonicalRational(
-                        num=str(value.numerator),
-                        den=str(value.denominator),
+                        num=format_canonical_integer(value.numerator),
+                        den=format_canonical_integer(value.denominator),
                     )
                     for value in vector
                 ),

src/jacobian/domains/polynomial/operations.py

@@ -5,6 +5,7 @@
 from fractions import Fraction
 from typing import Any
 
+from jacobian.canonical import format_canonical_integer
 from jacobian.contracts.exact import CanonicalRational
 from jacobian.contracts.polynomial_operations import (
     PolynomialBezoutIdentity,
@@ -55,7 +56,10 @@ def _poly(polynomial: RationalPolynomial) -> Any:
 
 def _rational(value: Any) -> CanonicalRational:
     fraction = Fraction(value)
-    return CanonicalRational(num=str(fraction.numerator), den=str(fraction.denominator))
+    return CanonicalRational(
+        num=format_canonical_integer(fraction.numerator),
+        den=format_canonical_integer(fraction.denominator),
+    )
 
 
 def _wire(poly: Any, variables: tuple[str, ...]) -> RationalPolynomial:

src/jacobian/domains/polynomial_nullstellensatz/singular.py

@@ -10,7 +10,7 @@
 
 from pydantic import ValidationError
 
-from jacobian.canonical import canonicalize_json
+from jacobian.canonical import canonicalize_json, format_canonical_integer
 from jacobian.capability_service import CapabilityInvocationError
 from jacobian.contracts.capabilities import (
     CapabilityAssurance,
@@ -125,7 +125,10 @@ def _parse_coefficient(value: str) -> CanonicalRational:
     if _INTEGER_OR_RATIONAL.fullmatch(value) is None:
         raise ValueError("Singular returned a non-rational coefficient")
     parsed = Fraction(value)
-    return CanonicalRational(num=str(parsed.numerator), den=str(parsed.denominator))
+    return CanonicalRational(
+        num=format_canonical_integer(parsed.numerator),
+        den=format_canonical_integer(parsed.denominator),
+    )
 
 
 class _TaggedOutputParser:

src/jacobian/domains/polynomial_nullstellensatz/system.py

@@ -6,6 +6,7 @@
 from fractions import Fraction
 from typing import Literal
 
+from jacobian.canonical import format_canonical_integer
 from jacobian.contracts.exact import CanonicalRational
 from jacobian.contracts.nullstellensatz import (
     BoundedRationalPolynomial,
@@ -57,8 +58,8 @@ def _polynomial(
         terms=tuple(
             BoundedRationalPolynomialTerm(
                 coefficient=CanonicalRational(
-                    num=str(coefficient.numerator),
-                    den=str(coefficient.denominator),
+                    num=format_canonical_integer(coefficient.numerator),
+                    den=format_canonical_integer(coefficient.denominator),
                 ),
                 exponents=exponent,
             )