package odin-algebra:algebraic_structures/ring
Source

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    Overview

    Interface for a Ring and CommutativeRing add - called to perform the operation ans = left + right sub - called to perform the operation ans = left - right mul - called to perform the operation ans = left * right neg - called to perform the operation ans = -left add_identity - a + additive_identity == a for all a mul_identity - a * mul_identity == a for all a all functions can be called where 2 or 3 input parameters point to the same piece of memory

    Types

    CommutativeRing ¶
    Source

    CommutativeRing :: struct($T: typeid) {
	… // See source for fields
}
     

    Has no additional operations above what Ring has just indicates to the type system that addition is commutative

    Related Procedures With Parameters

    Ring ¶
    Source

    Ring :: struct($T: typeid) {
	… // See source for fields
}
     

    Interface for a ring: add - called to perform the operation ans = left + right sub - called to perform the operation ans = left - right mul - called to perform the operation ans = left * right neg - called to perform the operation ans = -left add_identity - a + additive_identity == a for all a mul_identity - a * mul_identity == a for all a all functions can be called where 2 or 3 input parameters point to the same piece of memory

    Related Procedures With Parameters

    Constants

    RING_F32 ¶
    Source

    RING_F32: CommutativeRing($T=f32) : CommutativeRing(f32){Ring(f32){base.BASE_F32, add_f32, sub_f32, mul_f32, neg_f32, 0, 1}}

    RING_I32 ¶
    Source

    RING_I32: CommutativeRing($T=i32) : CommutativeRing(i32){Ring(i32){base.BASE_I32, add_i32, sub_i32, mul_i32, neg_i32, 0, 1}}

    RING_I64 ¶
    Source

    RING_I64: CommutativeRing($T=i64) : CommutativeRing(i64){Ring(i64){base.BASE_I64, add_i64, sub_i64, mul_i64, neg_i64, 0, 1}}

    RING_U32 ¶
    Source

    RING_U32: CommutativeRing($T=u32) : CommutativeRing(u32){Ring(u32){base.BASE_U32, add_u32, sub_u32, mul_u32, neg_u32, 0, 1}}

    Variables

    This section is empty.

    Procedures

    add_f32 ¶
    Source

    add_f32 :: proc(a: ^f32, l: f32, r: f32) {…}

    add_i32 ¶
    Source

    add_i32 :: proc(a: ^i32, l: i32, r: i32) {…}

    add_i64 ¶
    Source

    add_i64 :: proc(a: ^i64, l: i64, r: i64) {…}

    add_u32 ¶
    Source

    add_u32 :: proc(a: ^u32, l: u32, r: u32) {…}

    integer_pow ¶
    Source

    integer_pow :: proc(ans: ^$T, x: $T, power: uint, ring: Ring($T)) {…}
     

    sets ans = x^power for any ring

    mul_f32 ¶
    Source

    mul_f32 :: proc(a: ^f32, l: f32, r: f32) {…}

    mul_i32 ¶
    Source

    mul_i32 :: proc(a: ^i32, l: i32, r: i32) {…}

    mul_i64 ¶
    Source

    mul_i64 :: proc(a: ^i64, l: i64, r: i64) {…}

    mul_u32 ¶
    Source

    mul_u32 :: proc(a: ^u32, l: u32, r: u32) {…}

    neg_f32 ¶
    Source

    neg_f32 :: proc(a: ^f32, l: f32) {…}

    neg_i32 ¶
    Source

    neg_i32 :: proc(a: ^i32, l: i32) {…}

    neg_i64 ¶
    Source

    neg_i64 :: proc(a: ^i64, l: i64) {…}

    neg_u32 ¶
    Source

    neg_u32 :: proc(a: ^u32, l: u32) {…}

    sub_f32 ¶
    Source

    sub_f32 :: proc(a: ^f32, l: f32, r: f32) {…}

    sub_i32 ¶
    Source

    sub_i32 :: proc(a: ^i32, l: i32, r: i32) {…}

    sub_i64 ¶
    Source

    sub_i64 :: proc(a: ^i64, l: i64, r: i64) {…}

    sub_u32 ¶
    Source

    sub_u32 :: proc(a: ^u32, l: u32, r: u32) {…}

    test_commutative_ring_axioms ¶
    Source

    test_commutative_ring_axioms :: proc(t: ^testing.T, generator: prop_test.Generator($T), ring: CommutativeRing($T)) {…}
     

    called to run prop based tests to see if a ring implementation violates the commutative ring axioms

    test_memory_safety_axioms ¶
    Source

    test_memory_safety_axioms :: proc(t: ^testing.T, generator: prop_test.Generator($T), ring: Ring($T)) {…}
     

    called to run prop based tests to see if a ring implementation is memory safe

    test_ring_axioms ¶
    Source

    test_ring_axioms :: proc(t: ^testing.T, generator: prop_test.Generator($T), ring: Ring($T)) {…}
     

    called to run prop based tests to see if a ring implementation violates the ring axioms

    Procedure Groups

    This section is empty.

    Source Files

    Generation Information

    Generated with odin version dev-2025-04 (vendor "odin") Linux_amd64 @ 2025-05-13 09:15:55.503356514 +0000 UTC