Integrate the calcium library to enhance symbolic computation capabilities, focusing on real and complex numbers, exact algebraic numbers, and providing exact results.
Details
Exact Algebraic Numbers:
Use ca types to represent elements in an extended field that includes rational numbers, algebraic numbers (roots of polynomials with rational coefficients), complex numbers, and transcendental numbers like π and e.
Representation:
Algebraic numbers represented as roots of a minimal polynomial, with isolating intervals or other identifiers.
Use dynamic field extensions to handle numbers as solutions to polynomial equations with previously defined algebraic numbers.
Arithmetic and Simplification:
Support arithmetic operations and automatic simplification to the simplest form within the defined field.
Recognize and simplify expressions representing the same number.
Rigorous Results:
Provide rigorously verified results, exact equalities or inequalities, determine rationality, and fully simplify expressions.
Applications:
Suitable for tasks requiring exact and symbolic computation, such as simplifying algebraic expressions, solving equations symbolically, and exact integrations and differentiations.
Goal
Enhance the capability to handle complex mathematical constructs with high precision and correctness in symbolic computations.
Wrap Calcium Types
Overview
Integrate the calcium library to enhance symbolic computation capabilities, focusing on real and complex numbers, exact algebraic numbers, and providing exact results.
Details
Exact Algebraic Numbers: Use
catypes to represent elements in an extended field that includes rational numbers, algebraic numbers (roots of polynomials with rational coefficients), complex numbers, and transcendental numbers like π and e.Representation:
Arithmetic and Simplification:
Rigorous Results:
Applications:
Goal
Enhance the capability to handle complex mathematical constructs with high precision and correctness in symbolic computations.