Mathematics Core
Declared invariant-enforced mathematical calculations.
Declared surface as of v0.9.
General guarantees
- All calculations are deterministic
- Exact representations are used by default
- Approximation is explicit and opt-in
- Boundary states are returned as data
- Refusal occurs only when an invariant is undefined or violated
Arithmetic
Representation
- Number systems: integers, rationals, floats
- Default mode: symbolic / exact
Supported operations
- add
- subtract
- multiply
- divide (Euclidean)
- sqrt (symbolic)
- power
- mod
- abs
- sign
Explicit approximation operations
- add float
- subtract float
- multiply float
- divide float
- divide decimal
- long division
- approximate
- approximate root
- iterate until
- solve numeric system
Invariant notes
- Division returns quotient and remainder
- Exact arithmetic is the default
- Floating-point behaviour is explicit and opt-in
Algebra
Representation
- Symbolic
- Exact
Supported operations
- Equation solving (single variable)
- Linear multi-variable systems
- Factorisation
- Expansion
- Simplification
- Substitution
- Evaluation
- Approximate root (iterative, requires initial guess)
- Iterative numeric systems
Invariant notes
- Multi-variable solving is limited to linear systems
- Evaluation remains exact unless forced otherwise
Calculus
- Differentiation
- Integration
- Limits
- Jacobian
- Hessian
- ODE solving (symbolic)
All calculus operations are symbolic and exact.
Vector Calculus
- Gradient
- Divergence
- Curl
- Laplacian
All operations are symbolic and exact.
Number Theory
Representation
- Integers only
- Exact
Supported operations
- Primes
- Factorisation
- GCD / LCM
- Diophantine equations
- Bounded Thue equations
- Quadratic residues
- Legendre symbol
- Modular inverse
- Euler totient
- Primitive roots
- Discrete logarithm
Not supported
- Probabilistic primality tests
- Analytic number theory
- Floating-point methods
Completeness is declared only when bounds are specified.
Elliptic Curves
Field
- Finite prime fields
Supported operations
- Point addition, subtraction, negation
- Point doubling
- Scalar multiplication
- Curve order
- Point order
- Subgroup inspection
- Discrete logarithm
- Curve validation & discriminant
- Trace of Frobenius
- Random point generation
The point at infinity is represented as a valid result state. Boundary conditions are returned as data, not refusals.