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LogarithmicLaws.scala
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LogarithmicLaws.scala
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/*
* Copyright 2021 Arman Bilge
*
* 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 schrodinger.laws
import schrodinger.math.Logarithmic
import cats.kernel.laws.*
trait LogarithmicLaws[A, L](using val L: Logarithmic[A, L]):
def logarithmRoundTrip(a: A): IsEq[A] =
L.exponential(L.logarithm(a)) <-> a
def exponentialRoundTrip(l: L): IsEq[L] =
L.logarithm(L.exponential(l)) <-> l
def oneIsZero: IsEq[A] =
L.exponential(L.semifield.one) <-> L.divisionRing.zero
def timesIsPlus(x: L, y: L): IsEq[A] =
L.exponential(L.semifield.times(x, y)) <->
L.divisionRing.plus(L.exponential(x), L.exponential(y))
def divIsMinus(x: L, y: L): IsEq[A] =
L.exponential(L.semifield.div(x, y)) <->
L.divisionRing.minus(L.exponential(x), L.exponential(y))
object LogarithmicLaws:
def apply[A, L](using Logarithmic[A, L]): LogarithmicLaws[A, L] = new {}