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builtin.go
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builtin.go
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/*
Copyright 2021 Josh Deprez
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
package algebra
var (
// ℤ is a ring.
_ Ring[int] = Integer{}
// ℝ is a field.
_ Field[float64] = Real{}
// ℂ is a field.
_ Field[complex128] = Cmplx{}
)
// Integer implements ℤ using int.
type Integer = BuiltinRing[int]
// Real implements ℝ using float64.
type Real = BuiltinField[float64]
// Cmplx implements ℂ using complex128 (not with the Complex type).
type Cmplx = BuiltinField[complex128]
// Fieldable matches types with built-in arithmetic that can support a field.
type Fieldable interface {
~float32 | ~float64 | ~complex64 | ~complex128
}
// Ringable matches types with built-in arithmetic that can support a ring.
type Ringable interface {
~int | ~int8 | ~int16 | ~int32 | ~int64 | Fieldable
}
// BuiltinField implements a ring over T using built-in arithmetic.
type BuiltinRing[T Ringable] struct{}
// Add returns x+y.
func (BuiltinRing[T]) Add(x, y T) T { return x + y }
// Neg returns -x.
func (BuiltinRing[T]) Neg(x T) T { return -x }
// Zero returns 0.
func (BuiltinRing[T]) Zero() T { return 0 }
// Mul returns x*y.
func (BuiltinRing[T]) Mul(x, y T) T { return x * y }
// Identity returns 1.
func (BuiltinRing[T]) Identity() T { return 1 }
// BuiltinField implements a field over T using built-in arithmetic.
type BuiltinField[T Fieldable] struct{}
// Add returns x+y.
func (BuiltinField[T]) Add(x, y T) T { return x + y }
// Neg returns -x.
func (BuiltinField[T]) Neg(x T) T { return -x }
// Zero returns 0.
func (BuiltinField[T]) Zero() T { return 0 }
// Mul returns x*y.
func (BuiltinField[T]) Mul(x, y T) T { return x * y }
// Identity returns 1.
func (BuiltinField[T]) Identity() T { return 1 }
// Inv returns 1/x. This panics if x is zero.
func (BuiltinField[T]) Inv(x T) T { return 1 / x }