https://www.mathworks.com/help/matlab/ref/conv.html?s_tid=gn_loc_drop conv Convolution and polynomial multiplication Syntax w = conv(u,v) example w = conv(u,v,shape) example Description example w = conv(u,v) returns the convolution of vectors u and v…

Intro: 本篇博客将会从朴素乘法讲起,经过分治乘法,到达FFT和NTT 旨在能够让读者(也让自己)充分理解其思想 模板题入口:洛谷 P3803 [模板]多项式乘法(FFT) 朴素乘法 约定:两个多项式为\(A(x)=\sum_{i=0}^{n}a_ix^i,B(x)=\sum_{i=0}^{m}b_ix^i\) Prerequisite knowledge: 初中数学知识(手动滑稽) 最简单的多项式方法就是逐项相乘再合并同类项,写成公式: 若\(C(x)=A(x)B(x)\),那么\(C(x…

转自:https://blog.csdn.net/dkcgx/article/details/46652021 转自:https://blog.csdn.net/Reborn_Lee/article/details/83279843 conv(向量卷积运算) 所谓两个向量卷积,说白了就是多项式乘法. 比如:p=[1 2 3],q=[1 1]是两个向量,p和q的卷积如下: 把p的元素作为一个多项式的系数,多项式按升幂(或降幂)排列,比如就按升幂吧,写出对应的多项式:1+2x+3x^2;同样的,把q…

头文件: /* * Copyright (c) 2008-2011 Zhang Ming (M. Zhang), zmjerry@163.com * * 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, e…

作者:王子旭链接:https://zhuanlan.zhihu.com/p/21463650来源:知乎著作权归作者所有.商业转载请联系作者获得授权,非商业转载请注明出处. 2016.7.5 更新:长文多图代码预警,电脑食用效果更佳. 完整版代码已上传 GitHub,后续一些有的没的的代码更新也都在GitHub上(https://github.com/LaytonW/qrcode) 给结尾的几个被自动识别的QR码做了防自动识别..顺便也检测一下我们这不怎么高的容错率(7%).要是再被知乎自动识别了…

本篇文章翻译于CKKS EXPLAINED, PART 3: ENCRYPTION AND DECRYPTION,主要介绍CKKS方案的加密和解密. 介绍 在上一篇 CKKS Part2: CKKS的编码和解码 中,我们看到了如何实现CKKS的编码器和解码器,这使我们能够将向量转换为多项式,反之亦然.这一步是必要的,因为我们将看到,与直接使用向量相比,使用多项式构建同态加密方案要高效得多. 在本文中,我们将看到如何使用困难问题,例如LWE或RLWE来构建近似同态加密方案.CKKS使用近似算法而不…

Description 题目描述 You are given an polynomial of x consisting of only addition marks, multiplication marks, brackets, single digit numbers, and of course the letter x. For example, a valid polynomial would be: (1+x)*(1+x*x+x+5)+1*x*x. You are required…

Understanding Convolution in Deep Learning Convolution is probably the most important concept in deep learning right now. It was convolution and convolutional nets that catapulted deep learning to the forefront of almost any machine learning task the…

https://en.wikipedia.org/wiki/Time_complexity#Polynomial_time An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm, i.e., T(n) = O(nk) for some consta…

Modular multiplication of polynomials Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 3239   Accepted: 1459 Description Consider polynomials whose coefficients are 0 and 1. Addition of two polynomials is achieved by 'adding' the coeffici…