tutorial/GenSeqExtend.cc

This example shows how to append digits to the left of a component of a generating vector in order to extend the number of points of a lattice.

This example shows how to append digits to the left of a component of a generating vector in order to extend the number of points of a lattice.

// This file is part of LatNet Builder.
//
// Copyright (C) 2012-2021  The LatNet Builder author's, supervised by Pierre L'Ecuyer, Universite de Montreal.
//
// 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.
 
#include "latbuilder/GenSeq/Extend.h"
#include "latbuilder/Util.h"
#include "latbuilder/TextStream.h"
#include "latbuilder/Digits.h"
 
#include "Path.h"
 
#include <iostream>
 
using namespace LatBuilder;
using TextStream::operator<<;
 
template <typename SEQ>
void showSeq(uInteger base, const SEQ& seq)
{
   for (auto x : seq) {
      Digits<uInteger> digits(base, x);
      std::cout << "    " << digits << std::endl;
   }
}
 
int main()
{
   SET_PATH_TO_LATNETBUILDER_FOR_EXAMPLES();
   uInteger m = 2;

   for (uInteger b : {2, 3, 5}) {
      uInteger numPoints = intPow(b, m); // n = b^m
      uInteger gen = numPoints - 2;      // a_j = n - 2 for this example
      std::cout << "base: " << b << std::endl;
      GenSeq::Extend<LatticeType::ORDINARY> seq(b * numPoints, numPoints, gen);
      std::cout << "  one level: " << seq << std::endl;
      showSeq(b, seq);
   }
 
   Polynomial base = PolynomialFromInt(7);
   Polynomial P = intPow(base,3);
   Polynomial generator = PolynomialFromInt(5);
   GenSeq::Extend<LatticeType::POLYNOMIAL> seq(base * P, P, generator);
 
   return 0;
}