aerobus::zpz< p > Struct Template Reference

congruence classes of integers modulo p (32 bits) More...

#include <aerobus.h>

Classes
struct	val
	values in zpz More...

Public Types
using	inner_type = int32_t
	underlying type for values
template<auto x>
using	inject_constant_t = val< static_cast< int32_t >(x)>
	injects a constant integer into zpz
using	zero = val< 0 >
	zero value
using	one = val< 1 >
	one value
template<typename v1 , typename v2 >
using	add_t = typename add< v1, v2 >::type
	addition operator
template<typename v1 , typename v2 >
using	sub_t = typename sub< v1, v2 >::type
	substraction operator
template<typename v1 , typename v2 >
using	mul_t = typename mul< v1, v2 >::type
	multiplication operator
template<typename v1 , typename v2 >
using	div_t = typename div< v1, v2 >::type
	division operator
template<typename v1 , typename v2 >
using	mod_t = typename remainder< v1, v2 >::type
	modulo operator
template<typename v1 , typename v2 >
using	gt_t = typename gt< v1, v2 >::type
	strictly greater operator (type)
template<typename v1 , typename v2 >
using	lt_t = typename lt< v1, v2 >::type
	strictly smaller operator (type)
template<typename v1 , typename v2 >
using	eq_t = typename eq< v1, v2 >::type
	equality operator (type)
template<typename v1 , typename v2 >
using	gcd_t = gcd_t< i32, v1, v2 >
	greatest common divisor
template<typename v1 >
using	pos_t = typename pos< v1 >::type
	positivity operator (type)

Static Public Attributes
static constexpr bool	is_field = is_prime<p>::value
	true iff p is prime
static constexpr bool	is_euclidean_domain = true
	always true
template<typename v1 , typename v2 >
static constexpr bool	gt_v = gt_t<v1, v2>::value
	strictly greater operator (booleanvalue)
template<typename v1 , typename v2 >
static constexpr bool	lt_v = lt_t<v1, v2>::value
	strictly smaller operator (booleanvalue)
template<typename v1 , typename v2 >
static constexpr bool	eq_v = eq_t<v1, v2>::value
	equality operator (booleanvalue)
template<typename v >
static constexpr bool	pos_v = pos_t<v>::value
	positivity operator (boolean value)

Detailed Description

template<int32_t p>
struct aerobus::zpz< p >

congruence classes of integers modulo p (32 bits)

if p is prime, zpz

is a field

Template Parameters

p

a integer

Examples

examples/modular_arithmetic.cpp, and examples/polynomials_over_finite_field.cpp.

Member Typedef Documentation

add_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::add_t = typename add<v1, v2>::type

addition operator

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

div_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::div_t = typename div<v1, v2>::type

division operator

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

eq_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::eq_t = typename eq<v1, v2>::type

equality operator (type)

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

gcd_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::gcd_t = gcd_t<i32, v1, v2>

greatest common divisor

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

gt_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::gt_t = typename gt<v1, v2>::type

strictly greater operator (type)

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

inject_constant_t

template<int32_t p>

template<auto x>

using aerobus::zpz< p >::inject_constant_t = val<static_cast<int32_t>(x)>

injects a constant integer into zpz

Template Parameters

x	an integer

inner_type

template<int32_t p>

using aerobus::zpz< p >::inner_type = int32_t

underlying type for values

lt_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::lt_t = typename lt<v1, v2>::type

strictly smaller operator (type)

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

mod_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::mod_t = typename remainder<v1, v2>::type

modulo operator

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

mul_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::mul_t = typename mul<v1, v2>::type

multiplication operator

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

one

template<int32_t p>

using aerobus::zpz< p >::one = val<1>

one value

pos_t

template<int32_t p>

template<typename v1 >

using aerobus::zpz< p >::pos_t = typename pos<v1>::type

positivity operator (type)

Template Parameters

v1	a value in zpz::val

sub_t

template<int32_t p>

template<typename v1 , typename v2 >

using aerobus::zpz< p >::sub_t = typename sub<v1, v2>::type

substraction operator

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

zero

template<int32_t p>

using aerobus::zpz< p >::zero = val<0>

zero value

Member Data Documentation

eq_v

template<int32_t p>

template<typename v1 , typename v2 >

constexpr bool aerobus::zpz< p >::eq_v = eq_t<v1, v2>::value

staticconstexpr

equality operator (booleanvalue)

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

gt_v

template<int32_t p>

template<typename v1 , typename v2 >

constexpr bool aerobus::zpz< p >::gt_v = gt_t<v1, v2>::value

staticconstexpr

strictly greater operator (booleanvalue)

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

is_euclidean_domain

template<int32_t p>

constexpr bool aerobus::zpz< p >::is_euclidean_domain = true

staticconstexpr

always true

is_field

template<int32_t p>

constexpr bool aerobus::zpz< p >::is_field = is_prime<p>::value

staticconstexpr

true iff p is prime

lt_v

template<int32_t p>

template<typename v1 , typename v2 >

constexpr bool aerobus::zpz< p >::lt_v = lt_t<v1, v2>::value

staticconstexpr

strictly smaller operator (booleanvalue)

Template Parameters

v1	a value in zpz::val
v2	a value in zpz::val

pos_v

template<int32_t p>

template<typename v >

constexpr bool aerobus::zpz< p >::pos_v = pos_t<v>::value

staticconstexpr

positivity operator (boolean value)

Template Parameters

v1	a value in zpz::val

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

• src/aerobus.h