Groups ⊂ Rings ⊂ Modules ⊂ Polynomials. More...

import dedekind.algebra:vectorspace;

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Detailed Description

Groups ⊂ Rings ⊂ Modules ⊂ Polynomials.

Copyright: 2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

The_Restoration

"...قصدت به الجبر والمقابلة، ومسائل من الحساب يحتاج الناس إليها في مواريثهم ووصاياهم..." ("...I have intended it [the book] for the restoration and the balancing, and for those problems of calculation which men require in their inheritances and legacies...")

Derived from 'al-jabr' (الجبر), meaning "the restoration" or "reunion." Algebra in the Dedekind topos is the study of operations that preserve structural symmetry.

This module reifies the fundamental algebraic species, ensuring that every mapping (Morphism) respects the laws of composition, identity, and inversion. By 'restoring' these laws to C++ primitives, we enable the compiler to perform symbolic reductions—the automated 'balancing' of the mathematical equation.

algebra__The_Algebraic_Stack

Group (group): The logic of Inversion and Symmetry.
Rings (ring): The dual structure of Addition and Multiplication.
Division (division): The Euclidean Algorithm and the GCD Morphism.
Modules (modules): Linear actions of Rings on additive Groups.
Polynomials (polynomial): The monoid algebra R[M], and the normal form of a ring's terms.

Note: * "الكتاب المختصر في حساب الجبر والمقابلة" (The Compendious Book on Calculation by Completion and Balancing) — Muḥammad ibn Mūsā al-Khwārizmī