add primitive root subcommand

cmd/primitiveRoot.go

@@ -0,0 +1,112 @@
+/*
+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) {
+	for g := big.NewInt(2); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
+		e := new(big.Int).Set(g)
+		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")
+}