mathtools/cmd/pell.go

/*
Copyright © 2025 filifa

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package cmd

import (
	"fmt"
	"math/big"

	"github.com/spf13/cobra"
	"scm.dairydemon.net/filifa/mathtools/internal/lib"
)

var pellCoeff string

func isPellSolution(h, k, d *big.Int) bool {
	foo := new(big.Int).Exp(k, big.NewInt(2), nil)
	foo.Mul(d, foo)

	bar := new(big.Int).Exp(h, big.NewInt(2), nil)
	bar.Sub(bar, foo)

	return bar.Cmp(big.NewInt(1)) == 0
}

func pell(cmd *cobra.Command, args []string) {
	d, ok := new(big.Int).SetString(pellCoeff, 10)
	if !ok {
		cobra.CheckErr("invalid input " + args[0])
	}

	a0 := new(big.Int).Sqrt(d)

	repetend, err := lib.SqrtRepetend(d)
	if err != nil {
		cobra.CheckErr(pellCoeff + " is a perfect square")
	}

	hch := gaussianBrackets(a0, big.NewInt(1), cycle(repetend))
	kch := gaussianBrackets(big.NewInt(1), big.NewInt(0), cycle(repetend))

	for {
		h, k := <-hch, <-kch
		if isPellSolution(h, k, d) {
			fmt.Println(h, k)
		}
	}
}

// pellCmd represents the pell command
var pellCmd = &cobra.Command{
	Use:   "pell",
	Short: "Find solutions to a Pell equation",
	Long:  `Find solutions to a Pell equation.`,
	Run:   pell,
}

func init() {
	rootCmd.AddCommand(pellCmd)

	// Here you will define your flags and configuration settings.

	// Cobra supports Persistent Flags which will work for this command
	// and all subcommands, e.g.:
	// pellCmd.PersistentFlags().String("foo", "", "A help for foo")

	// Cobra supports local flags which will only run when this command
	// is called directly, e.g.:
	// pellCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")

	pellCmd.Flags().StringVarP(&pellCoeff, "coefficient", "d", "", "coefficient")
	pellCmd.MarkFlagRequired("coefficient")

	// TODO: add support for generalized Pell equations
}