f5f1551964
Lucidia Math - Advanced mathematical engines: forge/ - Mathematical Foundations: - consciousness.py (650 lines) - Consciousness modeling - unified_geometry.py (402 lines) - Geometric transformations - advanced_tools.py (356 lines) - Advanced utilities - main.py (209 lines) - CLI orchestration - numbers.py, proofs.py, fractals.py, dimensions.py lab/ - Experimental Mathematics: - unified_geometry_engine.py (492 lines) - Geometry engine - amundson_equations.py (284 lines) - Custom equations - iterative_math_build.py (198 lines) - Iterative construction - trinary_logic.py (111 lines) - Three-valued logic - prime_explorer.py (108 lines) - Prime exploration - quantum_finance.py (83 lines) - Quantum finance models 3,664 lines of Python. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <noreply@anthropic.com>
69 lines
2.1 KiB
Python
69 lines
2.1 KiB
Python
"""Custom symbolic operators for the Lucidia Math Forge.
|
|
|
|
Three playful operators are provided:
|
|
|
|
``paradox_merge`` (⊕)
|
|
Combines two values in a way that remembers both sum and difference.
|
|
``infinite_fold`` (⊗)
|
|
Repeatedly applies a binary function, emulating an infinite folding.
|
|
``collapse`` (↯)
|
|
Reduces a nested structure to a single value.
|
|
|
|
These operators are intentionally whimsical and serve as examples of how
|
|
one might craft new algebraic toys in Python.
|
|
"""
|
|
from __future__ import annotations
|
|
|
|
from functools import reduce
|
|
from typing import Any, Callable, Iterable, Tuple
|
|
|
|
|
|
def paradox_merge(a: Any, b: Any) -> Tuple[Any, Any]:
|
|
"""Paradox merge operator ⊕.
|
|
|
|
Returns a tuple of ``(a + b, a - b)``. The operator is non-
|
|
commutative and non-associative, encouraging exploration of unusual
|
|
algebraic structures.
|
|
"""
|
|
|
|
try:
|
|
return a + b, a - b
|
|
except TypeError as exc: # pragma: no cover - demonstration only
|
|
raise TypeError("operands must support + and -") from exc
|
|
|
|
|
|
def infinite_fold(func: Callable[[Any, Any], Any], values: Iterable[Any]) -> Any:
|
|
"""Infinite fold operator ⊗.
|
|
|
|
Conceptually applies ``func`` across ``values`` endlessly. In
|
|
practice we simply use :func:`functools.reduce` but expose the idea of
|
|
a never-ending fold.
|
|
"""
|
|
|
|
return reduce(func, values)
|
|
|
|
|
|
def collapse(value: Any) -> Any:
|
|
"""Collapse operator ↯.
|
|
|
|
If ``value`` is iterable the items are combined using ``paradox_merge``
|
|
until a single value remains; otherwise it is returned unchanged.
|
|
"""
|
|
|
|
if isinstance(value, Iterable) and not isinstance(value, (str, bytes)):
|
|
items = list(value)
|
|
if not items:
|
|
return None
|
|
result = items[0]
|
|
for item in items[1:]:
|
|
result = paradox_merge(result, item)[0]
|
|
return result
|
|
return value
|
|
|
|
|
|
if __name__ == "__main__":
|
|
# Example usage of the custom operators.
|
|
print("Paradox merge of 3 and 1:", paradox_merge(3, 1))
|
|
print("Infinite fold sum:", infinite_fold(lambda x, y: x + y, [1, 2, 3, 4]))
|
|
print("Collapse list:", collapse([1, 2, 3]))
|