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/*
 * Copyright 2022 Erik Erlandson
 *
 * 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 coulomb.ops.algebra.cats

import algebra.ring.*
import cats.kernel.*
import coulomb.ops.standard.*
import coulomb.rational.*

object rational:
    given Field[Rational] with
        def zero = Rational.const0
        def one = Rational.const1
        def plus(x: Rational, y: Rational) = x + y
        override def minus(x: Rational, y: Rational) = x - y
        def times(x: Rational, y: Rational) = x * y
        def div(x: Rational, y: Rational) = x / y
        def negate(x: Rational) = -x
        override def pow(x: Rational, n: Int) = x.pow(n)

    given CommutativeGroup[Rational] = summon[Field[Rational]].additive

    given Order[Rational] with Hash[Rational] with
        def hash(x: Rational) = x.hashCode
        def compare(x: Rational, y: Rational) =
            if x == y then 0
            else if x > y then 1
            else -1