486 lines
10 KiB
Plaintext
486 lines
10 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"source": [
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"# Permutation Algebra\n",
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"This notebook is a prerequisite to following the DARC tutorial"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"outputs": [],
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"source": [
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"from src.models import OuterKey, InnerKey, SubstitutionKey"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.906547Z",
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"start_time": "2024-07-03T16:38:57.867931Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"## Key Generation Parameters\n",
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"- block size: The number of characters we encode in a block. Block size isn't using in this notebook\n",
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"- key height: The alphabet length. If we want to encode bytes, our alphabet length is 256.\n",
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" If we want to encode lowercase letters a-z our alphabet length is 26. NKodes 10 key 7 attribute alphabet is 70.\n",
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"- key width: The number of bytes an encrypted charter is in our alphabet.\n"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"outputs": [],
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"source": [
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"height = 4\n",
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"width = 3"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.907029Z",
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"start_time": "2024-07-03T16:38:57.872544Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"## Operand Types\n",
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"### Inner Key\n",
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"An inner key is a list of `height` rows, each a random permutation of an identity arrary of length `width`"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"outputs": [
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{
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"data": {
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"text/plain": "[[2, 0, 1], [0, 2, 1], [0, 2, 1], [1, 2, 0]]"
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},
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"execution_count": 37,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"i0 = InnerKey.init_matrix(width, height)\n",
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"i1 = InnerKey.init_matrix(width, height)\n",
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"i2 = InnerKey.init_matrix(width, height)\n",
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"\n",
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"i0.matrix"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.907507Z",
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"start_time": "2024-07-03T16:38:57.876023Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"### Outer Key\n",
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"An outer key is ..."
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"outputs": [
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{
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"data": {
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"text/plain": "[[3, 2, 1, 0]]"
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},
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"execution_count": 38,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"o0 = OuterKey.init_matrix(height)\n",
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"o1 = OuterKey.init_matrix(height)\n",
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"o2 = OuterKey.init_matrix(height)\n",
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"\n",
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"o0.matrix"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.954081Z",
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"start_time": "2024-07-03T16:38:57.880359Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"### Substitution Key (formerly AlphabetKey or alpha_key)\n",
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"Sub key is ..."
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"outputs": [
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{
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"data": {
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"text/plain": "[[21, 62, 42], [151, 171, 33], [31, 131, 141], [100, 202, 161]]"
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},
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"execution_count": 39,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"a0 = SubstitutionKey.init_matrix(width, height)\n",
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"a1 = SubstitutionKey.init_matrix(width, height)\n",
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"a0.matrix"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.954770Z",
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"start_time": "2024-07-03T16:38:57.884556Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"## Operators Types\n",
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"### ***<<*** Inner Permutation"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"outputs": [],
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"source": [],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.955162Z",
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"start_time": "2024-07-03T16:38:57.887640Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"### ***<*** Outer Permutation"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"outputs": [],
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"source": [],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.955526Z",
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"start_time": "2024-07-03T16:38:57.890158Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"### ***^*** Substitution"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"outputs": [],
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"source": [],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.957721Z",
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"start_time": "2024-07-03T16:38:57.892476Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"## dddd"
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],
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"metadata": {
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"collapsed": false
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}
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},
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{
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"cell_type": "code",
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"execution_count": 40,
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"outputs": [
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{
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"data": {
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"text/plain": "True"
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},
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"execution_count": 40,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"a0_i0_o0_v0 = a0 << (i0 < o0)\n",
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"a0_i0_o0_v1 = ((a0 < ~o0) << i0) < o0\n",
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"\n",
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"a0_i0_o0_v0 == a0_i0_o0_v1"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.957791Z",
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"start_time": "2024-07-03T16:38:57.896696Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 41,
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"outputs": [
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{
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"data": {
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"text/plain": "True"
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},
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"execution_count": 41,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"a0_o0_i0_v0 = (a0 < o0) << i0\n",
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"a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0\n",
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"a0_i0_o0_v0 == a0_i0_o0_v1"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.958249Z",
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"start_time": "2024-07-03T16:38:57.900751Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 42,
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"outputs": [
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{
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"data": {
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"text/plain": "True"
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},
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"execution_count": 42,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"a0_o0_i0_v0 = (a0 < o0) << i0\n",
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"a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0\n",
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"a0_o0_i0_v0 == a0_o0_i0_v1"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.958404Z",
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"start_time": "2024-07-03T16:38:57.903708Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"outputs": [
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{
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"data": {
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"text/plain": "True"
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},
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"execution_count": 50,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"(~(i0 << i1)) == (~i1 << ~i0)"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:42:45.756613Z",
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"start_time": "2024-07-03T16:42:45.746766Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 44,
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"outputs": [
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{
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"data": {
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"text/plain": "True"
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},
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"execution_count": 44,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"i0_i1_i2_v0 = i0 << i1 << i2\n",
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"i0_i1_i2_v1 = i0 << (i1 << i2)\n",
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"i0_i1_i2_v2 = (i0 << i1) << i2\n",
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"i0_i1_i2_v0 == i0_i1_i2_v1 == i0_i1_i2_v2"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.958613Z",
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"start_time": "2024-07-03T16:38:57.910939Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"outputs": [
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{
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"data": {
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"text/plain": "True"
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},
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"execution_count": 49,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"i0 == ((i0 << i2 << i1) << ~(i2 << i1)) == ((i0 << i2 << i1) << ~i1 << ~i2)"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:41:01.725294Z",
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"start_time": "2024-07-03T16:41:01.718345Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 46,
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"outputs": [
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{
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"data": {
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"text/plain": "True"
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},
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"execution_count": 46,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"i0_o0_o1_o2_v1 = ((i0 < o0) < o1) < o2\n",
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"i0_o0_o1_o2_v2 = (i0 < (o0 << o1)) < o2\n",
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"i0_o0_o1_o2_v3 = (i0 < o0) < (o1 << o2)\n",
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"i0_o0_o1_o2_v4 = (i0 < (o0 << o1 << o2))\n",
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"\n",
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"i0_o0_o1_o2_v1 == i0_o0_o1_o2_v2 == i0_o0_o1_o2_v3 == i0_o0_o1_o2_v4"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2024-07-03T16:38:57.958859Z",
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"start_time": "2024-07-03T16:38:57.915888Z"
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}
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}
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},
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{
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"cell_type": "markdown",
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"source": [
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"### Becareful about your order of operation\n",
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"***Always use parenthesis to control the order of operations***"
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],
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"metadata": {
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"collapsed": false
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|
}
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},
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{
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"cell_type": "code",
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"execution_count": 47,
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|
"outputs": [
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|
{
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|
"data": {
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|
"text/plain": "True"
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|
},
|
|
"execution_count": 47,
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|
"metadata": {},
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"output_type": "execute_result"
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}
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|
],
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"source": [
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"i0 < (o0 << o1 << o2) != (i0 < (o0 << o1 << o2)) # not equal !!!!!!"
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],
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"metadata": {
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"collapsed": false,
|
|
"ExecuteTime": {
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|
"end_time": "2024-07-03T16:38:57.958925Z",
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"start_time": "2024-07-03T16:38:57.920831Z"
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|
}
|
|
}
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 2
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|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython2",
|
|
"version": "2.7.6"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 0
|
|
}
|