mathtools/cmd/primitiveRoot.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 (
	"errors"
	"fmt"
	"log"
	"math/big"

	"github.com/spf13/cobra"
)

var modulus string
var tpf []string

func computeNaive(modulus *big.Int) (*big.Int, error) {
	if modulus.Cmp(big.NewInt(1)) == 0 {
		return big.NewInt(0), nil
	}

	for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
		e := big.NewInt(1)
		exps := make(map[string]big.Int)
		for k := big.NewInt(1); k.Cmp(modulus) == -1; k.Add(k, big.NewInt(1)) {
			e.Mul(e, g)
			e.Mod(e, modulus)
			exps[e.Text(10)] = *k
		}

		isPrimitive := true
		for a := big.NewInt(1); a.Cmp(modulus) == -1; a.Add(a, big.NewInt(1)) {
			gcd := new(big.Int).GCD(nil, nil, a, modulus)
			if gcd.Cmp(big.NewInt(1)) != 0 {
				continue
			}

			_, ok := exps[a.Text(10)]
			if !ok {
				isPrimitive = false
				break
			}
		}

		if isPrimitive {
			return g, nil
		}
	}

	return nil, errors.New("no primitive root")
}

func computeFromFactors(modulus *big.Int, tpf []string) *big.Int {
	return nil
}

func primitiveRoot(cmd *cobra.Command, args []string) {
	m, ok := new(big.Int).SetString(modulus, 10)
	if !ok {
		log.Fatal("invalid input " + modulus)
	}

	root := new(big.Int)
	var err error
	if len(tpf) == 0 {
		root, err = computeNaive(m)
		if err != nil {
			log.Fatal(err)
		}
	} else {
		root = computeFromFactors(m, tpf)
	}

	fmt.Println(root)
}

// primitiveRootCmd represents the primitiveRoot command
var primitiveRootCmd = &cobra.Command{
	Use:   "primitive-root -m M",
	Short: "Compute a primitive root modulo n",
	Long:  `Compute a primitive root modulo n.`,
	Run:   primitiveRoot,
}

func init() {
	rootCmd.AddCommand(primitiveRootCmd)

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

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

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

	primitiveRootCmd.Flags().StringVarP(&modulus, "modulus", "m", "", "modulus")
	primitiveRootCmd.MarkFlagRequired("modulus")

	primitiveRootCmd.Flags().StringSliceVarP(&tpf, "totient-factorization", "t", make([]string, 0), "prime factorization of the totient of the modulus")
}