aerobus::Quotient< Ring, X > Struct Template Reference

Quotient ring by the principal ideal generated by 'X' With i32 as Ring and i32::val<2> as X, Quotient is Z/2Z. More...

#include <aerobus.h>

Classes
struct	val
	projection values in the quotient ring More...

Public Types
using	zero = val< typename Ring::zero >
	zero value
using	one = val< typename Ring::one >
	one
template<typename v1 , typename v2 >
using	add_t = val< typename Ring::template add_t< typename v1::type, typename v2::type > >
	addition operator
template<typename v1 , typename v2 >
using	mul_t = val< typename Ring::template mul_t< typename v1::type, typename v2::type > >
	substraction operator
template<typename v1 , typename v2 >
using	div_t = val< typename Ring::template div_t< typename v1::type, typename v2::type > >
	division operator
template<typename v1 , typename v2 >
using	mod_t = val< typename Ring::template mod_t< typename v1::type, typename v2::type > >
	modulus operator
template<typename v1 , typename v2 >
using	eq_t = typename Ring::template eq_t< typename v1::type, typename v2::type >
	equality operator (as type)
template<typename v1 >
using	pos_t = std::true_type
	positivity operator always true
template<auto x>
using	inject_constant_t = val< typename Ring::template inject_constant_t< x > >
	inject a 'constant' in quotient ring*
template<typename v >
using	inject_ring_t = val< v >
	projects a value of Ring onto the quotient

Static Public Attributes
template<typename v1 , typename v2 >
static constexpr bool	eq_v = Ring::template eq_t<typename v1::type, typename v2::type>::value
	addition operator (as boolean value)
template<typename v >
static constexpr bool	pos_v = pos_t<v>::value
	positivity operator always true
static constexpr bool	is_euclidean_domain = true
	quotien rings are euclidean domain

Detailed Description

template<typename Ring, typename X>
requires IsRing<Ring>
struct aerobus::Quotient< Ring, X >

Quotient ring by the principal ideal generated by 'X' With i32 as Ring and i32::val<2> as X, Quotient is Z/2Z.

Template Parameters

Ring	A ring type, such as 'i32', must satisfy the IsRing concept
X	a value in Ring, such as i32::val<2>

Member Typedef Documentation

add_t

template<typename Ring , typename X >

template<typename v1 , typename v2 >

using aerobus::Quotient< Ring, X >::add_t = val<typename Ring::template add_t<typename v1::type, typename v2::type> >

addition operator

Template Parameters

v1	a value in quotient ring
v2	a value in quotient ring

div_t

template<typename Ring , typename X >

template<typename v1 , typename v2 >

using aerobus::Quotient< Ring, X >::div_t = val<typename Ring::template div_t<typename v1::type, typename v2::type> >

division operator

Template Parameters

v1	a value in quotient ring
v2	a value in quotient ring

eq_t

template<typename Ring , typename X >

template<typename v1 , typename v2 >

using aerobus::Quotient< Ring, X >::eq_t = typename Ring::template eq_t<typename v1::type, typename v2::type>

equality operator (as type)

Template Parameters

v1	a value in quotient ring
v2	a value in quotient ring

inject_constant_t

template<typename Ring , typename X >

template<auto x>

using aerobus::Quotient< Ring, X >::inject_constant_t = val<typename Ring::template inject_constant_t<x> >

inject a 'constant' in quotient ring*

Template Parameters

x	a 'constant' from Ring point of view

inject_ring_t

template<typename Ring , typename X >

template<typename v >

using aerobus::Quotient< Ring, X >::inject_ring_t = val<v>

projects a value of Ring onto the quotient

Template Parameters

v	a value in Ring

mod_t

template<typename Ring , typename X >

template<typename v1 , typename v2 >

using aerobus::Quotient< Ring, X >::mod_t = val<typename Ring::template mod_t<typename v1::type, typename v2::type> >

modulus operator

Template Parameters

v1	a value in quotient ring
v2	a value in quotient ring

mul_t

template<typename Ring , typename X >

template<typename v1 , typename v2 >

using aerobus::Quotient< Ring, X >::mul_t = val<typename Ring::template mul_t<typename v1::type, typename v2::type> >

substraction operator

Template Parameters

v1	a value in quotient ring
v2	a value in quotient ring

one

template<typename Ring , typename X >

using aerobus::Quotient< Ring, X >::one = val<typename Ring::one>

one

pos_t

template<typename Ring , typename X >

template<typename v1 >

using aerobus::Quotient< Ring, X >::pos_t = std::true_type

positivity operator always true

Template Parameters

v1	a value in quotient ring

zero

template<typename Ring , typename X >

using aerobus::Quotient< Ring, X >::zero = val<typename Ring::zero>

zero value

Member Data Documentation

eq_v

template<typename Ring , typename X >

template<typename v1 , typename v2 >

constexpr bool aerobus::Quotient< Ring, X >::eq_v = Ring::template eq_t<typename v1::type, typename v2::type>::value

staticconstexpr

addition operator (as boolean value)

Template Parameters

v1	a value in quotient ring
v2	a value in quotient ring

is_euclidean_domain

template<typename Ring , typename X >

constexpr bool aerobus::Quotient< Ring, X >::is_euclidean_domain = true

staticconstexpr

quotien rings are euclidean domain

pos_v

template<typename Ring , typename X >

template<typename v >

constexpr bool aerobus::Quotient< Ring, X >::pos_v = pos_t<v>::value

staticconstexpr

positivity operator always true

Template Parameters

v1	a value in quotient ring

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The documentation for this struct was generated from the following file:

• src/aerobus.h