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module field_m
!! field is a unit_ring that also has a division or inverse operation
use unit_ring_m, only: unit_ring
implicit none
private
public :: &
field_only_division, &
field_only_inverse, &
field, &
derive_field_from_division, &
derive_field_from_inverse
requirement field_only_division(T, plus, zero, mult, one, minus, negate, divide)
require :: unit_ring(T, plus, zero, mult, one, minus, negate)
elemental function divide(x, y) result(quotient)
type(T), intent(in) :: x, y
type(T) :: quotient
end function
end requirement
requirement field_only_inverse(T, plus, zero, mult, one, minus, negate, invert)
require :: unit_ring(T, plus, zero, mult, one, minus, negate)
elemental function invert(x) result(inverse)
type(T), intent(in) :: x
type(T) :: inverse
end function
end requirement
requirement field(T, plus, zero, mult, one, minus, negate, divide, invert)
require :: field_only_division(T, plus, zero, mult, one, minus, negate, divide)
require :: field_only_inverse(T, plus, zero, mult, one, minus, negate, invert)
end requirement
template derive_field_from_division(T, plus, zero, mult, one, minus, negate, divide)
require :: field_only_division(T, plus, zero, mult, one, minus, negate, divide)
private
public :: invert
contains
elemental function invert(x) result(inverse)
type(T), intent(in) :: x
type(T) :: inverse
inverse = divide(one(), x)
end function
end template
template derive_field_from_inverse(T, plus, zero, mult, one, minus, negate, invert)
require :: field_only_inverse(T, plus, zero, mult, one, minus, negate, invert)
private
public :: divide
contains
elemental function divide(x, y) result(quotient)
type(T), intent(in) :: x, y
type(T) :: quotient
quotient = mult(x, invert(y))
end function
end template
end module
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