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 (
	"fmt"
	"log"
	"math/big"

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

var modulus string
var tpf []string

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 = lib.PrimitiveRoot(m)
		if err != nil {
			log.Fatal(err)
		}
	} else {
		root, err = lib.PrimitiveRootFast(m, tpf)
		if err != nil {
			log.Fatal(err)
		}
	}

	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.

This command computes a value g such that, for all integers a coprime to n, g^k = a (mod n) for some k. In other words, this command computes a generator for the multiplicative group of integers modulo n.

For improved performance, provide the prime factorization of the totient of n with the -t flag.

Note that primitive roots only exist for the moduli 1, 2, 4, p^k, and 2p^k, where p is an odd prime. The totients of these numbers are 1, 1, 2, (p-1)*p^(k-1), and (p-1)*p^(k-1), respectively.`,
	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")
	// TODO: add a check flag for verifying -t input is the totient, test for performance
}