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# Evaluating Functions Worksheet Pdf

F Worksheet by Kuta Software LLC. I can write and graph piecewise-definied functions. arctan 1 7. If it is a function, give the domain. A Jeopardy Game that helps you learn about Functions. Please change your browser settings and reload. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Except for a few people who think Excel is a word processor, all Excel users incorporate worksheet functions in their formulas. * 1) lim x→3 2x2−5x−3 x−3 2) lim x→2 x4−16 x−2 3) lim x→−1 x4+3x3−x2+x+4 x+1. By the end of this section you should be able to use exponential functions evaluate. The following figures give examples of the standard angle and the reference angle for the different quadrants. linear function worksheets with answers algebra pdf exponential domain and range of a worksheet,collection of math worksheets function notation download them and rational worksheet algebra 2 tables 8th grade answers linear 8,quadratic function worksheets with answers evaluating functions worksheet parent algebra 2 exponential,function. To determine whether a relation is a function, we use the vertical line test (VLT). 3x2 +2x 33;x = 2 2. Start your 14-day trial for £1 to track progress, measure results and access thousands of educational activities in English, maths and science. Worksheet 4. All worksheets are included in the index count, even if they're hidden. If it is a function, state the domain and range. Based on information in an issue of Time magazine, the cost varies linearly with the distance, and is $366 per month for 300 km per month, and$510 per month for 1500 km per month. Evaluating Functions Worksheet Name: Evaluate the following expressions given the functions below: g(x) = −3x +1 7f (x) = x2 + x h x 12. For example, here is a function called "avg" that returns the average of its two parameters. Create free worksheets for evaluating expressions with variables (pre-algebra / algebra 1) or grades 6-9. Determine the domain, range, and horizontal asymptote of the function. Given f(x) 3 4x. Expand the following logarithmic expressions completely so that it is in a form where there is not a logarithm of a product, quotient, or power: a. Created Date: 10/9/2013 2:06:12 PM. f(x) 2 x= − from 0 x 5≤ <. Warning! This web page may contain links to one or more websites outside the PWCS network, which are not PWCS venues and may not reflect the views or opinions of PWCS. Easy Steps To Success: A Graphing Calculator Guide For The TI-84 Plus, TI-83, TI-83 Plus, and TI-82 Graphing Calculators gives step-by-step keystrokes and instructions for these calculators, along with examples using these keystrokes to solve problems. In the moderate level, the x-values are decimals or fractions. MAT 0024 Ch 13 Factoring Review Worksheet Instructor: C. 00 up to and including ½ mile, 0. Find x if f(x) = 23 2. Prepare sixth graders for higher level math with in-depth, comprehensive, and fun worksheets that cover the four basic operations as well as algebraic equations, number theory, fractions, decimals, geometry, probability, critical thinking, and much more. Worksheet Piecewise Functions Name: Part I. cannot be determined 3. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In order to extend the definitions of the six trigonometric functions to general angles, we shall make use of the following ideas: In a Cartesian coordinate system, an angle α is said to be in standard position if its vertex is at the origin O and its initial side. Consider the following function de ned by its graph:-x y 6 5 4 3 2 1 0 1 2 3 4 5 4 3 2 1 0 1 2 3 u e e e. What's a Function (Intro to Domain and Range) Function Notation Function Notation 1. The questions cover a wide range of concepts related to functions such as definition, domain, range , evaluation , composition and transformations of the graphs of functions. You can select different variables to customize these Exponents and Radicals Worksheets for your needs. To differentiate between linear and exponential functions, let’s consider two companies, A and B. Denis Page 1 of 4 Strategy for factoring polynomials: Step 1. and Rational Functions Graphs, real zeros, and end behavior. f(-3) Evaluate the following for EOIknkfJi Pn Si8t dexlABlsg geWbZr 9aYW2m. Grid (Graph) Paper - Printable grid paper in all sizes. PrathapaTCOM2. Carefully graph each of the following. (The preceding quote from the Alban Institute is an example. distance (miles) time (minutes) 0 15 30 10 20 1. 18) Find the intercepts for the following graph: 19) Find the zero(s) of the following functions. The range of y = arcsec x. As you can see from the questions, they are quick assessments to check for student understanding of identifying functions, evaluating functions, and finding domain and range. 3-4-Worksheet by Kuta Software LLC Answers to Evaluating Functions :-) 1) −1 2) −3 3) −20 4) 16. Explain how you know if a graph is a function or not: Concept # _____. Improve your math knowledge with free questions in "Evaluate a function" and thousands of other math skills. The corresponding acute angle. Evaluating Expressions - Post-assessment (10 questions) Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:. Math Worksheets Listed By Specific Topic and Skill Area. The symbol = means “is equal to”, so the last sentence actually says, “It follows that f(x) is is equal to 2x. Which of the following graphs represent functions? Circle your answers. Algebra 2 YL 4. Evaluating Expressions and Simple Equations Assessment Short Constructed Response Show all of your math work in the space provided. com, where unknowns are common and variables are the norm. Now you have one unknown in your equation, and you can solve it!. Graphical Transformations of Functions In this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. tv Limits Evaluating Functions Graphically I Worksheet 1 Evaluating Limits Graphically I Use the graph below to evaluate the following limits:. I evaluate the functions for 200 (200 mb) and show how the one function gives a unreasonable cost. Jan 223:47 PM Using Exponential Functions 8. 5 23 Simplify. For example, here is a function called "avg" that returns the average of its two parameters. Lesson 2 - Functions and Function Operations Mini-Lesson Page 63 Functions can be presented in multiple ways including: equations, data sets, graphs, and applications. Evaluating Functions Worksheets - Math Worksheets Land Mathworksheetsland. Piecewise and Step Functions Worksheet. Algebra Function Worksheets (pdfs) with answer keys on domain/range, 1 to 1, evaluating, composition of functions and more. B V 1M la 2d Xe4 aw ui Mt0h I NIVnRffi an li XtVeb 5AWljg cekb2r 4aG w2Q. , find the domain and range of its inverse. Additionally,. Functions • Identify relations between two variables and determine if they are functions • Use function notation and evaluate functions • Determine the domain of a function • Model problems with functions Today's lesson and objectives. Evaluate Your Study Places. 1) Without a calculator evaluate find log 10 and log 100. Example: Write p x+ 1 as a composition f(g(x)). Evaluate each of the following when 16 9 3 1, 4 3 x= y= and z=. Download the PDF and sketch the graph of the functions. Group participation and presentation evaluation, collect worksheet to include as part of evaluation. The answers can be found below. Write Algebraic Expressions. Graph each of the following piecewise functions. Topic : Composition of Functions - Worksheet 5 ANSWERS 1. Which of the following would find the temperature at 10 hours? f(x) = 10 f(10) f(h) f(30) iv. For example, suppose you need to evaluate the following. Excel IF Function The most common and powerful of the logical functions in Excel is the IF function This function is particularly powerful because it can test for a particular condition in the worksheet and: do a calculation if the condition is TRUE; or another calculation if the condition is FALSE Excel IF Function. Free Algebra 2 worksheets created with Infinite Algebra 2. Nonlinear Functions. If, for any reason, another copy should be needed, the students is responsible for either (a) printing a new copy or (2) viewing the worksheet and completing the work on a separate sheet of paper. Improve your DBT skills with strategies and worksheets for emotional regulation. all real numbers. If it is a function, state the domain and range. What's a Function (Intro to Domain and Range) Function Notation Function Notation 1. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. 00 up to and including ½ mile,0. In doing so, we get a solution that looks like this. SECTIO N 7-1 Completing T-Tables A T-tabU is a table used to determine values for x and y that will make an equation true. #9 - 13 Hw pg. y Y UALl3ld drkiCg3hTtSsP wrDefsYeor9vmeidv. 1) tan θ x y 60 ° 3 2) sin θ x y 225 ° − 2 2 3) sin θ x y 90 ° 1 4) cos θ x y 150 ° − 3 2 5) cos θ x y 90 ° 0 6) tan θ x y 240 ° 3 7) cos θ x y 135 ° − 2 2 8) tan θ x y 150 ° − 3 3-1-. Finding limits of a piecewise defined function Calculus I Tutorial, by Dave Collins I. Complete the synthetic substitution shown at the right. Write the particular equation expressing cost (c) in terms of distance (d). Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. 2 y x x= − +2 1 Domain: Domain: Range: Range:. " To evaluate, substitute 4 for s in the rule f(s) 8s 15. ESL Worksheets for Teaching English to Children - Print these ESL PDF. Function? Yes or No. Honors Pre-Calculus Limits Worksheet #5 Name_____ May 2014 Use the graph to estimate the limits and function values, or explain why the limits do not exist or the function values. Graph the piecewise function and evaluate it at the given values. Sign of f(c) fwill determine sign of within interval. (Limits of Constant and Identity Functions) If c is a con-stant, the following limits are true: (i) lim x→a c = c (ii) lim x→a x = a The limit laws can be used to evaluate limits for many algebraic func-tions. I h qARlHlB OrXiQg1h Gtjs P RrSe 7ske4r0v Uekda. Assess student understanding of algebra, geometry, statistics, and trigonometry concepts with these math worksheets for high school students. You may use your calculators to help you graph, but you must sketch it carefully on the grid! 1. Worksheets are Evaluating piecewise functions work pdf, Piecewise functions date period, Work homework piecewise functions name, 7 functionswork, Work piecewise functions, Evaluating functions date period, Piecewise functions, Concept 22 evaluating functions. Algebra 1 Name:_____ Function Notation Worksheet #2 Use the functions below to evaluate at the given value. ©4 pK5u3tja m YSXoafntswsaGrtef lL WL3CP. The following sources were used in preparing this worksheet – Calculus, 2nd Ed. Determine the domain, range, and horizontal asymptote of the function. ©2 h2N0b1 82X Kou VtTan 1S Zo Rf6tew3a6rIeU GLsLUCo. Contribute and share any resources you may have yourself. "I'm Tara, I create resources and write blog posts for TeacherVision. Permission to copy: You are free to copy this worksheet to any number of students for their mathematics work. Does this seem reasonable? Explain. Evaluating piecewise functions worksheet pdf All Manuals Evaluating piecewise functions worksheet pdf. Displaying Worksheet - Piecewise Functions Answer Key. Evaluate the following limits. Plus model. Take a quiz. Worksheet – Piecewise Functions Evaluate the following for 3. free pdf worksheets for grade 1. 1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. Graph each of the following piecewise functions. Find the number of libraries in the United States in 1996. Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations. and obtain other teacher resources. the graph is NOT a function 3. Store the value 2 as X: 2 STO‚ X,T,Ө,n ENTER 2. Find the values of the other 5 trigonometric functions of x, if 13 sec 5 x. Round your answer to the nearest thousandth. Free Pre-Algebra worksheets created with Infinite Pre-Algebra. This booklet contains the worksheets for Math 1A, U. Use a calculator to find an approximation to the nearest ten-thousandth. Easy and quick to print PDF math practice worksheets. All other requirements must support the Business Requirements. My primary objective of this lesson is for students to understand when to find x and when to find f(x) when evaluating functions. For Grades 4, 5 and 6 worksheets,answers are provided. Some of the worksheets displayed are Evaluating functions date period, Concept 22 evaluating functions, Ws69 name, Evaluating expressions date period, , Work logarithmic function, Algebra i name k3 9 function notation work, Name date ms. Worksheet Piecewise Functions Name: Part I. Describe each step of the process. F Worksheet by Kuta Software LLC. Five worked-out examples demonstrating the basics of evaluating functions at a given value. Function Evaluation. The pedigrees below trace the. To clear decimals, multiply both sides of the equation (distributing to all terms) by the lowest power of 10 that will make all decimals whole numbers. Algebra 2 YL 4. i g AMa3dRea Rw iLt Ih g oI 1nif UiBnEibt1e9 TAVlpgLeDb5ria V J2v. NOTE: Limit your money worksheets to a certain value, ie: Each problem not to exceed $1. cos 1 1 2 §· ¨¸ ©¹ 3. The inverse relations. Permission to copy: You are free to copy this worksheet to any number of students for their mathematics work. Piecewise Functions Worksheet #2 Part I. A simple way to know differentiate between the two is to look at the output values when plugging in a number for an unknown variable. Group grade taken. Functions are written using function notation. The equal sign functions as a verb. Algebra 1 Name:_____ Function Notation Worksheet #2 Use the functions below to evaluate at the given value. The answers can be found below. About This Quiz & Worksheet. These worksheets are printable PDF exercises of the highest quality. Checking: d dx sin(x2) = cos(x2) d dx x2 = 2xcos(x2), so Z 2xcos(x2)dx = sin(x2)+ C. Both in theory and practice there. Paraphrasing practice college interview sample. n Worksheet by Kuta Software LLC. Click here for a review of inverse functions. docx Author: Ellen O'Brien Created Date: 5/24/2012 12:29:59 AM. After all, as explained by John Walkenbach in Excel VBA Programming for Dummies:. 3) Graph it or make a table. Discuss openly with a view to taking corrective action: 1. P Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Evaluating Functions Date_____ Period____ Evaluate each function. In this laboratory we will be exploring how user-defined functions are defined and what happens when they are called. n biological theories of personality attempt to explain differences in behaviour in terms of differences in physiology, particularly brain function; n research in behavioural genetics has permitted the examination of both genetic and environmental factors in. executive function) (schizophrenia) • Non-significant correlations with a measure of functional outcome (Routine Task Inventory), thus lacking ecological validity (schizophrenia) • Poor predictive validity of FIM self-care scores upon discharge from acute care, and adequate predictive validity of FIM cognitive scores (Chinese. Use the following function rule to find f(40). We will look at the deﬁnition of a function, the domain and range of a function, what we mean by specifying the domain of a function and absolute value function. EXAMPLE 2 Evaluate by direct substitution Use direct substitution to evaluatef(x) 5 2x4 2 5x3 2 4x 1 8 whenx 5 3. Links to bonus online materials! Give students the tools they need to. What is The Reference Angle Theorem? The Reference Angle Theorem states that. UNIT 6 WORKSHEET 15 EVALUATING TRIG FUNCTIONS OF ANY ANGLE Find the exact value of the six trigonometric functions of an angle θ, in standard position, given the following information. 2 9600 9400 9200 0 4 8 12 1620-1 Years since 1980 a. Describe the graph of a constant function. bigideaslearning. 1 Scope and purpose of this document This document is a user manual for the XLConnect R package. Y Worksheet by Kuta Software LLC Grade 11 Enriched Mathematics Date_____ ©P 92N0s1M3J qKMuNt6aa 5Sco8f Jt Zw RajrUex dL mLaC1. Using the order of ooperations. Evaluating Polynomials Worksheet We Want Answers! Evaluate each polynomial at the given value(s) of the variable(s). Sketch the graph of the function WITHOUT the graphing calculator. Evaluating Functions. The graph of an exponential or logarithmic function can be used to determine when the average rate of change is the least or greatest. 10 ft 5 ft 7 ft 6 ft (NO CALCULATOR). f(x) x 6, g(x) x 6. Find x if h(x) = –2 j. Describe each step of the process. Fun math games, worksheets, PowerPoints, and teacher resources of more than 800 files. Identify Functions Worksheet. Competencies Required. 1) tan 2) cot Find the measure of each angle indicated. Find the exact value of each trigonometric function. Relations and Functions. Use this checklist in your team to evaluate its health. the graph is a function 2. stitz-zeager. 10 ft 5 ft 7 ft 6 ft (NO CALCULATOR). Solving Exponential and Logarithmic Functions Worksheet In 1‐9, solve each exponential equation. (1) log 5 25 = y (2) log 3 1 = y (3) log 16 4 = y (4) log. Be sure to pay attention to the last example, which is a. Ex: lim x→−1 x2 − 1 x+ 1 16) Give two values of awhere the limit cannot be solved using direct evaluation. Functions are written using function notation. Evaluation should consider presence of major bank failures along the entire reach under evaluation, including uprooted trees on banks, banks falling into channel, formation of islands in channel as they widen, exposed soil, active zones of erosion, etc. Analyze a Photograph. f(-3) Evaluate the following for EOIknkfJi Pn Si8t dexlABlsg geWbZr 9aYW2m. Almost all of the functions you are familiar with are continuous at every number in their domain. pdf is a generic function that accepts either a distribution by its name 'name' or a probability distribution object pd. Evaluate the following limits. Assess your comprehension of the smallpox virus by using this quiz and worksheet combo. 6 I rA ylBlk SrUing9hGtts l crce as oe QrmvLe sdm. To see the integrand is an odd function, compute (−y)5 (−y)2 +1 = −y5 y2 +1 = − y5 y2 +1. (1) log 5 25 = y (2) log 3 1 = y (3) log 16 4 = y (4) log. Since children learn best by doing and since children get bored very easily, giving them well-designed, illustrated worksheets to do makes it easier and more fun for them to learn. Data can be analyzed by the presentation of the data in table format (data table), or the processing of that data through graphical manipulation to visually discern the differences in the variables tested. You've reached your free access limit. Which of the following graphs represent functions? Circle your answers. Read/Download: Evaluating piecewise functions worksheet pdf PIECEWISE FUNCTIONS WITH QUADRATICS WORKSHEET. by Smith & Minton, Calculus, 4th Ed. Working with integers and exponents. 1) tan 2) cot Find the measure of each angle indicated. Find the exact value of the six trigonometric functions of the given x. Each question corresponds to a matching answer that gets colored in to form a symmetrical. Contribute and share any resources you may have yourself. Let x be an acute angle of a right triangle. Free worksheet(pdf) and answer key on Evaluating Functions--25 scaffolded questions that start easy and conclude with some real challenges Evaluating Functions Worksheet and Answer Key. f(x) 3 x= from − ≤ <2 x 2 4) Sketch the graph of. 927x 2 x 4. The process of judging whether or not a project should be accepted is called project evaluation. ABSTRACT This paper describes a design exercise that was conducted to investigate what, if any, correlation exists between the functional complexity of a given artifact and its associated physical complexity as defined by design for manufacturing. Resetting Calculator to Factory Setting: • when the user have used the calculator in various ways and it is difficult to go back to the original. Free Pre-Algebra worksheets created with Infinite Pre-Algebra. Synonyms of fluffed baby. Welcome to the Algebra worksheets page at Math-Drills. What is The Reference Angle Theorem? The Reference Angle Theorem states that. excellent, very good, … poor, unacceptable, no show) with associated criteria. The new sheet will be named with the change value and will also show that text value in cell A1. relation is a function and different ways a function can be represented. 0 sin lim 1. com has thousands of digital resources. (eBook) Connecting the NCTM Process Standards & the CCSSM Practices (PDF) Connecting the Standards, Improving Mathematical Instruction By connecting the CCSSM to previous standards and practices, the book serves as a valuable guide for teachers and administrators in implementing the CCSSM to make mathematics education the best and most effective for all students. Explain how you found your answer. Example: Find R1 0 x2 dx using the evaluation theorem. Identify whether or not he graph is a function. Find the number of libraries in the United States in 1996. by Smith & Minton, Calculus, 4th Ed. Opening – The teacher will define a piecewise function, and go over Key Idea p. Worksheet Level 4: Goals: Identify functions from a graph, table, or diagram. Then, evaluate the graph at the specified domain values. Find the area of the given figure. • A piecewise-defined function applies different rules, usually as formulas, to disjoint (non-overlapping) subsets of its domain (subdomains). K u kMDapd 1eB kwNiRtDh7 EIan NfyionXi7t3ed NA5lpgLe Obnr 9ak O1P. Working with integers and exponents. Use a calculator to find an approximation to the nearest ten-thousandth. A w 7AulJlr lrfitguh7twsQ Ir 2e6sFe0rDvBevd2. Example: Write p x+ 1 as a composition f(g(x)). You can also do this the long way. Real World Application of Step Functions: Prior to September, 2000, taxi fares from Washington DC to Maryland were described as follows:$2. Company A has 100 stores and expands by opening 50 new stores a year, so its growth can be represented by the function $A\left(x\right)=100+50x$. These include:   Business Requirements: those high level features, functions, capabilities and conditions that must be present in project deliverables so that they can be used to deliver the Business Value that is the goal of the project. T HE ANGLES in theoretical work will be in radian measure. To evaluate a function, what we want is to substitute every instance of x in the expression and then simplify. Z i 2AYlXlD 4r SiSgZh itqse 1rre hs 8esr1vvendh. Absolute Value Expressions (Simplifying) Worksheet 5 - Here is a 15 problem worksheet where you will asked to simplify expressions that contain absolute values while you execute the correct order of operations. Do not distribute on websites, books, or any such material without permission. I can write and graph piecewise-definied functions. ) + 3 as inner function g(x) = x. RFC ASSESSMENT IS FOR: CLAIMANT: NUMBERHOLDER (IF CDB CLAIM): PRIMARY DIAGNOSIS: SECONDARY DIAGNOSIS: OTHER ALLEGED IMPAIRMENTS: Page 1 Insured: PRIVACY ACT NOTICE: The information requested on this form is authorized by Section 223 and Section 1633 of the Social Security Act. The best source for free patterns worksheets and free function machine worksheets. Preparation. Functions are written using function notation. Y Worksheet by Kuta Software LLC Grade 11 Enriched Mathematics Date_____ ©P 92N0s1M3J qKMuNt6aa 5Sco8f Jt Zw RajrUex dL mLaC1. 8 Functions - Inverse Trigonometric Functions Objective: Solve for missing angles of a right triangle using inverse trigonometry. Performance Based Learning and Assessment Task. Let's start by stating some (hopefully) obvious limits: Since each of the above functions is continuous at x = 0, the value of the limit at x = 0 is the value of the function at x = 0; this follows from the definition of. Now with a calculator evaluate log 90. The function below determines how many people have swine where t = time in days and S = the number of people in thousands. To distinguish among diff erent functions, it is possible to use diff erent names. Functions can be classified in two different categories: linear or nonlinear. The main theorem cos (−θ) and sin (−θ) Polar coördinates Proof of the main theorem H OW SHALL WE EVALUATE tan 118°, for example? We will see that we will be referred back to an acute angle. College Algebra Combining Functions 1. Links to bonus online materials! Give students the tools they need to. Write a function to represent the distance C remaining atfter you pay n games. Free worksheet(pdf) and answer key on Evaluating Functions--25 scaffolded questions that start easy and conclude with some real challenges Evaluating Functions Worksheet and Answer Key. EXAMPLE 2: Find the values of all trigonometric functions of the angle. 3 Worksheet by Kuta Software LLC Algebra 2 Name_____ Notation and Skills: Practice Evaluating Functions Date_____ Evaluate each function for the given input. The range of y = arccos x. If you're seeing this message, it means we're having trouble loading external resources on our website. Evaluating Functions - Independent Practice Worksheet Complete all the problems. Classroom Strategies Blackline Master Page 131 V - 1 Solving Equations Square Puzzle Cut out the squares above. Worksheet - Piecewise Functions Answer Key. f(x) = bx and g(x) = log b x are inverse functions. THE EVALUATION THEOREM 11 1. 2x2 4y;x = 1;y = 3. Use the graph of the function f(x) to answer each question. Show all work!!! For each of the following situations, write an exponential model of the form y =a(b)x 1. Showing top 8 worksheets in the category - Evaluating Functions. Relations and Functions. Sample multiple choice questions on Functions. This document is only meant to be a very quick reminder. log 2 a2b c § ©¨ · ¹¸ = log 2 a 2b – log 2 c Use the Quotient Rule for Logarithms. Then, evaluate the graph at any specified domain value. f(x) x= from − ≤ <4 x 4 3) Sketch the graph of. Read/Download: Evaluating piecewise functions worksheet pdf PIECEWISE FUNCTIONS WITH QUADRATICS WORKSHEET. How much money is being spent in 2011? Round to the nearest tenth. 7 = b) 2 5 = c) 3π = d) − =6. For example, if we look at the function h(x) = (2x – 1) 2. If you're seeing this message, it means we're having trouble loading external resources on our website. 3 Limits of Functions (PDF). docx Author: Ellen O'Brien Created Date: 5/24/2012 12:29:59 AM. 4 INVERSE FUNCTIONS Inverse Relations Find the inverse for each relation. Maybe you came via internet search engine, then you locate this web site as well as determined to see this internet site, many thanks for that. evaluate group function 2. pdf math worksheets for grade 1 Lesson plans and student worksheets engaging classroom poster. Sketch the following piecewise functions. Graph the function. Evaluating functions Function operations. In doing so, we get a solution that looks like this. We used a special function, one of the trig functions, to take an angle of a triangle. Invoking feval with a function handle is equivalent to invoking the function handle directly. Now you have one unknown in your equation, and you can solve it!. A) 3 Given sin the angle lies in quadrant II. 00 up to and including ½ mile, \$0. the greatest integer function to express C, the delivery cost, as a function of x, the number of miles from the store. Input and output prealgebra tables and functions. If it is a function, state the domain and range. all real numbers. If it is a function, give the domain. Worksheets are Evaluating piecewise functions work pdf, Piecewise functions date period, Work homework piecewise functions name, 7 functionswork, Work piecewise functions, Evaluating functions date period, Piecewise functions, Concept 22 evaluating functions.


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Contents

# Technical overview

To set up the workflow, you still have to have some technical expertise. Once it’s set up, non-technical editorial team members with a couple of hours training (taught or self-taught) can add and edit books in it.

The technical team members who run the workflow need to be familiar with:

• HTML and CSS: the fundamental building blocks of almost all digital content.
• Markdown: a simple, plain-text shortcut for creating HTML. (The original Markdown syntax reference is the easiest intro to basic markdown. We use a markdown variant called kramdown. It lets us use attributes like classes, has a stricter syntax, and allows adding of IDs to elements.
• Sass: a way to create complex CSS from simple rules.
• Git: software for tracking a team’s changes and syncing them with a remote server. We like to use GitHub.

## Dependencies

To use the workflow on your own machine, you must have the following software installed:

• Ruby: the software that reads and runs Ruby code. (We highly recommend installing Ruby with a Ruby version manager like Chocolatey in Windows or Homebrew on Mac.)
• Bundler: software that manages which version of Jekyll (and other Ruby gems) to apply to a project.
• Jekyll: software that turns markdown and Sass into HTML and CSS. (To learn about Jekyll, start here. If you’re installing it on Windows, you’ll also need this guide.) From version 0.4.0, our template requires at least Jekyll 3.2.
• Node.js, which we use for doing things like converting images and optimising Javascript.
• PhantomJS: a headless browser that we use for rendering MathJax in PDF and for generating search indexes.
• PrinceXML: software for creating PDFs from HTML and CSS (Prince is the only proprietary tool you’ll need).
• GraphicsMagick: the software we use for optimising images.
• Git: the software we use for version control.

You can see guidelines for installing Jekyll on Windows here, and a guide to setting up on Mac here.

## Key structural concepts

Here are some of the main technical features of the template and how they work.

### Folder (repo) structure

A workflow folder (often tracked in Git as a repo) usually contains a set of related books. Its folders and files follow the standard Jekyll structure. We then put each book’s content in its own folder. In the template, the first book folder is simply called book.

### Using the template

The Electric Book repo (folder) is ready to use for a set of one or more books. In short, to get up and running, see the Quick Start guide.

Now, let’s get into some more detail about how it all works. There are several folders and files in the Electric Book template’s root directory.

Folders:

• _app: template files for app output. You shouldn’t ever have to change these.
• _configs: a folder of configuration settings for different outputs. You’ll rarely have to change these, though you might occasionally need to customise outputs here.
• _data: a folder of data to use in your books (including project metadata).
• _docs: this documentation on how to use the template.
• _epub: template files for epub output. You shouldn’t ever have to change these.
• _includes: HTML templates that Jekyll uses to build your books. You will rarely change anything here. You may need to add new templates here for custom book features.
• _layouts: templates that Jekyll uses to structure pages. You shouldn’t ever have to change these.
• _output: the folder where our output scripts will save your PDFs and epubs.
• _sass: a folder that stores the default styles for your books. You shouldn’t ever have to change these unless you’re heavily modifying designs for a series.
• _site: where Jekyll and our output scritps will generate the web and app versions of your books.
• _tools: utilities required for output. You shouldn’t have to change these.
• assets: a folder of Javascript, font files and images that your whole project might use.
• book: a folder for a book’s content, stored in markdown files. You might add more similarly strcutured folders for further books in your project.
• samples: a sample book for demo and testing purposes. You can safely delete it (if you do, you should also remove its metadata in _data/meta.yml).

Files:

• _config.yml: a file for setting configuration options for Jekyll, which will compile your book for output. There are several other smaller config files you can ignore. They are for changing specific config settings on output.
• _prose.yml: configuration settings for using prose.io for online book editing (generally, you won’t have to edit this file) and for excluding files from view in the Electric Book Manager.
• index.md: the home page of your project when served as a website.
• .bat, .command and .sh scripts for quickly generating books in different formats on various operating systems.

There are other files in the root directory that are important to the template. Leave them as is, unless you really know what they are and what you’re doing.

### Creating a new book

The process of setting up a new book is covered briefly in our quick-start section. Here is more detail.

To create a new book in a new project:

1. The repo (or project folder) can hold one book or many, like a series of books that share similar metadata or features (e.g. they’re all by the same author). Make a copy of the folder and, if you like, rename it for your project. E.g. my-sci-fi.
2. Inside my-sci-fi, open and edit these three files:
• _config.yml: Edit the values there for your Jekyll setup. The comments will guide you.
• index.md: Replace our template text with your own. Usually, a link to each book is useful, e.g. [Space Potatoes](space-potatoes).
• README.md: Replace our template text with any notes your collaborators might need to know about your project. (The README file is usually only read in the context of editing the files in your folder/repo.)
3. Optionally, rename the book folder with a one-word, lowercase version of your book’s title (e.g. space-potatoes). Use only lowercase letters and no spaces. If you’re creating more than one book, make a folder for each book.
4. In _data, edit the meta.yml file, filling in your project info and info about at least your first book.
5. Inside a book’s text folder, add a markdown file for each piece of your book, e.g. one file per chapter. Our template contains files we consider minimum requirements for most books: a cover, a title page, a copyright page, a contents page, and a chapter.
6. Inside each book’s folder, store images in the images folder. Add a cover.jpg image of your book’s front cover there, too.
7. In each book’s styles folder, edit the values in print-pdf.scss, screen-pdf.scss, web.scss and epub.scss.

### Creating book content

Each markdown file in space-potatoes is a part of a book, such as a table of contents or a chapter. Each file must start with:

---
---

And between those ---s, we can and should specify some information about that part. This information is called YAML frontmatter.

In each file’s YAML frontmatter (the info between ---s at the top) we specify the book-part’s title and (sometimes) the book-part’s style to use for that part. The style specifies what kind of book-part it is, such as a title-page or chapter.

Technical note: the style YAML sets the class attribute of the output HTML’s <body> element. Themes use that class to control CSS and page structure.

When you create your book, we recommend following these conventions for file naming and YAML frontmatter style settings:

Book section Sample file Style in YAML
Front cover (for the ebook) 0-0-cover.md cover
Title page 0-1-titlepage.md title-page
Copyright page 0-2-copyright.md copyright-page
Table of contents 0-3-contents.md contents-page
Acknowledgements 0-4-acknowledgements.md frontmatter
A first chapter 1.md chapter
A second chapter 2.md chapter

If you don’t set the style, the page will default to style: chapter. So you actually don’t need to ever set style: chapter in a YAML header. For most chapters in a book, then, your YAML frontmatter will simply include a chapter title:

---
title: "Chapter One: What are Space Potatoes?"
---

Page styles we’ve designed for in the Classic theme include:

• index for the home page of a collection
• cover for a front cover, which will appear in ebook editions
• halftitle-page for a book’s halftitle page
• previous-publications-page for a book’s list of the author’s previous publications
• title-page for a book’s title page
• copyright-page for the copyright or imprint page
• contents-page for the book’s table of contents
• dedication-page for a dedication page
• epigraph-page for an epigraph page
• frontispiece-page for a frontispiece page
• frontmatter for other prelim pages not accounted for otherwise
• chapter for a book’s default chapter page (and the global default)

You can also invent your own page styles, and use them in your custom CSS instead of these, though you may get unexpected results if you’ve been relying on a theme for existing styles like chapter.

#### Set ‘page number one’

Many books have two ‘page ones’:

1. the half-title or title page and,
2. if the prelims have roman-numeral page numbers, the first chapter.

You should specify those pages so that Prince knows where to start numbering when creating PDFs.

Why? Well, for example, in print output if you use frontmatter on a book-part, by default it will have roman-numeral page numbers. When the first chapter starts, it will have decimal page numbers. However, the page numbering will be consecutive from roman through decimal. That is, it will run ‘ix, x, 11, 12’. You reset the numbering to 1 at the start of the first chapter to avoid this.

You reset page numbering by adding the class page-1 to the first block-level element on the relevant page.

You can do this in two ways:

1. If a markdown document starts at ‘page one’, add the class to the style YAML header. E.g.

---
title: Half-title page
style: halftitle-page page-1
---

And at the first chapter:

---
title: Chapter One
style: chapter page-1
---

Remember that chapter is the default, so you normally don’t have to specify it. But if you want to add a class in addition to chapter, you must specify both classes. This is because, if you were to use style: page-1 in a YAML header, the class page-1 would override the default style: chapter, not add to it.

2. Alternatively, add the page-1 class to the first block-level element in the chapter by adding the tag {:.page-1} in the line immediately after it. But for this to work, the element must not have a CSS float applied to it. So often this doesn’t work as well as specifying page-1 in YAML frontmatter.

#### File naming

Name each book’s markdown files in perfectly alphabetical order. We recommend using a numbering system, where prelims (frontmatter) files start with a 0, e.g. 0-1-titlepage.md, 0-2-copyright.md, and chapter files are numbered for their chapter number, e.g. 01.md, 02.md, and so on. The alphabetical order makes it easy to see the documents in the right order at all times, and it makes ordering outputted HTML files easy when dropping them into Prince for PDF output.

Note: We recommend using leading zeros in file-name numbers – that is, 02.md rather than 2.md – because that sorts correctly in most file browsers. Otherwise, some file browsers will sort 10.md before 2.md. In the rare event that you have over 99 chapters, use two leading zeros: 001.md.

### The images folder

Alongside the content files in a book’s folder is an images folder, for images that belong to that book only.

A book’s folder should only ever need to contain markdown files and images. If you’re embedding other kinds of media you could add folders for that alongside images. We don’t recommend sharing images or media between books, in case you want to move a book from one project to another later. (So, for example, copy the publisher logo into each book’s images folder separately.)

If your project home page requires images, keep those in /assets/images, so that you can link to them from any page.

format: plain


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Home > Error Rate > Bit-error Probability Of Qpsk With Noisy Phase Reference

Bit-error Probability Of Qpsk With Noisy Phase Reference

Contents

You should multiply factor of 1/sqrt(2) to the noise term which you have defined. Related posts: Symbol Error Rate (SER) for 16-QAM Symbol Error Rate for 16PSK Symbol Error Rate (SER) for 4-PAM Comparing 16PSK vs 16QAM for symbol error rate Tagged as: AWGN, PSK, Symmetric Differential Quadrature Phase Shift Keying (SDQPSK) is like DQPSK, but encoding is symmetric, using phase shift values of −135°, −45°, +45° and +135°. I will appreciate if you reply me soon. check my blog

moyeen Reply Krishna Sankar May 24, 2011 at 5:32 am @moyeen: You can refer to the post on BER for 16QAM with Gray coding http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/ Reply Moyeen May 5, 2011 The modulated signal is shown below for a short segment of a random binary data-stream. Reply Krishna Sankar July 24, 2012 at 5:40 am @candy: To convert to a distance, one needs to know - Transmit power, Path loss, Receive noise power The SNR, dB at Here, the odd-numbered bits have been assigned to the in-phase component and the even-numbered bits to the quadrature component (taking the first bit as number 1).

Qpsk Bit Error Rate

The first PLL used in the system employs a voltage-controlled crystal oscillator (VCXO) to eliminate the input jitter whereas the second PLL provides wide bandwidth. I will try to answer to the best of my knowledge. Hope the post on thermal noise and awgn gives additional pointers http://www.dsplog.com/2012/03/25/thermal-noise-awgn/ Reply Ravinder February 5, 2013 at 1:35 pm Thank you very much for your reply Krishna. Matlab Code For Ber Vs Snr For Qpsk Changing the BPSK in OFDM to QPSK in OFDM case should have been reasonably straightforward.

Difference of the phase between QPSK and OQPSK Taking four values of the phase (two bits) at a time to construct a QPSK symbol can allow the phase of the signal Bit Error Rate For Qpsk Matlab Code Here is my code: clear b = 10000; % number of bits or symbols %----------- Transmitter--------- %Message signal ip = rand(1,b)>0.5; % generating 0,1 with equal probability %generating m-sequence polynomial=[6 1 This shows the two separate constellations with identical Gray coding but rotated by 45° with respect to each other. If third party material is incorporated into such work, the user must ensure that permission from the owner of such third party material has been obtained for its incorporation and for

You can try the two constellation mapping approaches and obtain the BER. Qpsk Ber Equation Pls, you are indeed a very good teacher, help me out Thanks, you are really very helpful, you must really reap the fruit of your efforts. The BER curve for this example is compared to ordinary BPSK on the right. What do you think?

Bit Error Rate For Qpsk Matlab Code

can u send it to me plzzz Reply Krishna Sankar July 21, 2010 at 6:00 am @prashant: I referred the text book Digital Communication by Proakis Reply Ayesha313 July 18, The error-rates quoted here are those in additive white Gaussian noise (AWGN). Qpsk Bit Error Rate Secondly if now i am given a symbol like P which when converted to binary is equal 011. Symbol Error Rate And Bit Error Rate Receiver structure for QPSK.

Any replies are accepted. Do they mean the same thing? The alphabet size, M, must be at least 4. Can see good agreement between the simulated and theoretical plots for 4-QAM modulation 2. Ber Of Qpsk In Awgn Channel Matlab Code

In other, the base is 10. In the absence of noise, the phase of this is ϕ k − ϕ k − 1 {\displaystyle \phi _{k}-\phi _{k-1}} , the phase-shift between the two received signals which can Reply Krishna Sankar February 1, 2013 at 5:25 am @ruby: wont be able to help directly, but can point you to the following wikipedia links: http://en.wikipedia.org/wiki/Doppler_effect http://en.wikipedia.org/wiki/Rayleigh_fading Reply Ozgeee December news This gives maximum phase-separation between adjacent points and thus the best immunity to corruption.

Do I need to do anything to compansate the phase errors? Qpsk Ber Curve Using DPSK avoids the need for possibly complex carrier-recovery schemes to provide an accurate phase estimate and can be an attractive alternative to ordinary PSK. Reply Abrar May 20, 2011 at 4:37 am Hi for QPSK on fading channel can this equation if ok for theoretical expression?

or there is other things that i should to change ?

How is that related to SNR parameter? May i contact you by mail to send you my table?. thanks! Qam Symbol Error Rate Reply mak_m August 29, 2009 at 4:35 am thanks very much krishna i have changed my code rate … actually i was jus following the matlab Communications Toolbox User’s Guide”

With thanks. At the k th {\displaystyle k^{\textrm {th}}} time-slot call the bit to be modulated b k {\displaystyle b_{k}} , the differentially encoded bit e k {\displaystyle e_{k}} and the resulting modulated The two signal components with their bit assignments are shown the top and the total, combined signal at the bottom. What I mean is, the symbol error rate that you obtained versus Es/No would it be the same as saying Symbol error rate vs SNR?

M must be no greater than 64 for 'noncoherent'.ber = berawgn(EbNo,'fsk',2,coherence,rho) returns the BER for binary nonorthogonal FSK over an uncoded AWGN channel, where rho is the complex correlation coefficient. Reply Krishna Sankar April 4, 2010 at 3:17 am @Rebecca: Though I have not discussed BER for QPSK case, I have a post on BER for 16QAM @ http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/ Hope this Identify a block code from Table 6.4 and show the coding gain for this code by plotting the Error performance before and after the code.You are to do a Matlab of If EbNo is a vector, the output ber is a vector of the same size, whose elements correspond to the different Eb/N0 levels.

I thought the bandwidth for BPSK is fc-1/2T to fc+1/2T.


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# Operations that Produce Equivalent Equations

We can see quite a few operations that produce equivalent equations. In this part, we’ll look at these two: addition & subtraction.

Here we talk about Adding identical quantities to both sides of equations.

### The “All-in-One” GED Prep

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1. Solve $$x + 5 = 12\: for \: x$$.
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Question 1 of 2

2. Solve $$y -8 = 11\: for \: y$$.
A.
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Question 2 of 2

This lesson is provided by Onsego GED Prep.

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### Video Transcription

If we add the same quantities to both the left and the right sides of a given equation, the solution set will not be changed. Let’s see:

If a = b, and we’ll add c to both sides of this equation, we’ll have an equivalent equation.
a + c = b + c.

Let’s take a look if this really works.

We recommend the Online GED Classes from Onsego.  Simple, Fast & Easy. Onsego Provides Everything You Need to Pass Your GED.
Get Started.

Consider the equation x −4 = 3

We can see that the number 7 (seven) is the only solution here in our equation.

So, let’s, for example, add 4 (four) to both sides of our equation and see if the equation that’s the result is equivalent to the original x−4 = 3.

x −4 = 3 is our given equation.
x − 4 + 4 = 3 + 4 (we’ve added 4 to both sides of our equation.
x = 7 ( just simplify both sides of our equation).

Well, 7 is the solution (and the only one) of our equation x = 7. Therefore: the equation x = 7 is the equivalency of the original equation x − 4 = 3 (they both have identical solutions).

This is an important point. If we add the same amount to both the left and the right sides of an equation, its solution won’t change.

It is a fact as well that if we subtract the same quantity from both equation sides, an equivalent equation will be the result.

Subtracting the same quantities from both equation sides.

Again, if we subtract the same quantities from both equation sides, our solution set won’t change.

So let’s see:

If a = b, and we subtract c from both sides of our equation, we’ll have the equivalent equation:
a − c = b − c.

Let’s see if this also works as stated:

Consider this equation: x + 4 = 9.

By inspection, the number 5 is this equation’s only solution.

Now, let’s subtract 4 (four) from both sides of our equation and check if the resulting equation still is equivalent to our original x+ 4 = 9.

x + 4 = 9 is our given equation.
x + 4 − 4 = 9 − 4 (we subtract 4 (four) from both sides of our equation.
x = 5 (just simplify both sides of our equation.

The number 5 is actually the only solution to our equation, so x = 5. Therefore, the equation x = 5 is the equivalency of our initial equation x + 4 = 9 (both equations have the same solution).

The important point is that if we subtract the same amount from both the left side and the right side of an equation, its solutions will not change.

Last Updated on June 13, 2022.


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Home > Bit Error > Bit Error Rate Modem

# Bit Error Rate Modem

## Contents

Good connection? Isn't it presumptuous to say "On good connections the BER should be below 10-9."? A walk-through of the source code follows. // modem_ber_example.c : simulate modem bit error rate // http://liquidsdr.org/ #include #include #include #include #include int main() { // Generated Sun, 02 Oct 2016 05:05:17 GMT by s_hv972 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection Logged MediacomTim Guest Re: Degraded Internet Connections « Reply #19 on: May 24, 2012, 09:47:51 PM » If it goes down again, we'll schedule a tech to come out. have a peek at these guys

Please do not modify it. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. If the BER is higher than typically expected for the system, it may indicate that a slower data rate would actually improve overall transmission time for a given amount of transmitted Most people expect modem connections to be error free, which is technically impossible to measure.

## Acceptable Bit Error Rate

I think we'll try a new modem if there is one available locally. These are synonymous terms. Any three bit errors (BER of 3 x 10-6 or 3E-6) can be easily fixed by the RS decoder. It would never get anywhere near 0% at the rate it was doing this.

It's one of those things where it's surprising it worked before. i'm looking at my cable modem diag page, and it shows downstream snr at 39, signal strength 4.6dbmv, both of which are good, but the bit error rate is hovering at and so is my system. Bit Error Rate Calculator BTW, I've seen it go much higher, about 900%, if I recall.

Any thoughts on if it's the modem, the lines, or maybe even both? Figure [constellations]. For example, it's usually only necessary to observe a certain number of bit errors rather than a total number of bits. Gaeddert ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection to 0.0.0.8 failed.

The "Started Unicast Maintenance Ranging - No Response received" messages still appear very frequently whether working poorly or working well. Bit Error Rate Tester Software It might be best to get a tech back out. Subsequent comments should be made in a new section on the talk page. Logged drt Newbie Posts: 17 Re: Degraded Internet Connections « Reply #18 on: May 24, 2012, 09:46:05 PM » As of 9:00pm here it's working well again, with about 10 minutes

## Bit Error Rate Measurement

Be the first to submit a comment Leave your comment Guest Sunday, 02 October 2016 Subscribe to updates (Please fill in your email address to subscribe to blog updates.) About UsNewsCareersContact They use the BER to calculate what the SNR would need to be in order to produce that BER using formulas based upon the Shannon formulas. Acceptable Bit Error Rate It's happened a few times (% higher than 2 digits). Bit Error Rate Pdf If it is dropping to 24, it is rare a modem replacement can fix that.

After a simple power cycle, BER would be at 0% and remain there.So I think you're on to something. · actions · 2009-Mar-29 10:40 pm ·

the error rate is fluctuating, but staying around 0.65-0.67. · actions · 2009-Mar-24 10:15 pm · TurbocpePremium Memberjoin:2001-12-22IA

Turbocpe to K Patterson Premium Member 2009-Mar-24 11:57 pm to K PattersonBased on just curious. · actions · 2009-Mar-24 7:48 pm · [email protected] NSA_CIA Anon 2009-Mar-24 9:01 pm It's indicative of intermittent interference that occasionally crosses into the downstream data channel.What frequency is the So lets fast forward to the real world. check my blog SchuminWeb (Talk) 05:05, 30 December 2009 (UTC) Bit error ratio → Bit error rate — Bit error rate is a 3.3 times as common than Bit error rate according to books.google.com,

Normal practice is to express results as the ratio, but use of the term 'bit error rate' is a habit hard to kill despite deprecation in international standards for at least Bit Error Rate Testing By Steve Day on - Apr 26 in Solutions Comments No comments made yet. When I check my modem, I look for a high SNR (high SNR means that the signal is much stronger than the noise), and good TX and RX levels.

## That is, linear modems demodulate by finding the closest of $$M$$ symbols in the set $$\mathcal{S}_M$$ to the received symbol $$r$$ , viz  \hat{s}_k = \underset{s_k \in \mathcal{S}_M}{\arg\min} \bigl\{ \|

My plan is to replace the runs into the house with RG6. Welcome, Guest. Then bit error rates begin to climb and the connection degrades. Bit Error Rate Tester Agilent comcast loses another area to another isp [ComcastXFINITY] by bbscript257.

do your own homework. 128.128.98.46 (talk) 17:28, 30 January 2009 (UTC) Bit error ratio vs. Cheetah does both MER and CER. Washington mall attacker illegally voted in at least 3 elections [InTheNews] by Krisnatharok357. news Up on 25 MHz is normal...

I have not seen any connection or signal problems without the router. Mar 13, 2010 at 1:22 AM #4 OrbitzXT New Member Joined: Mar 22, 2007 Messages: 1,969 (0.57/day) Thanks Received: 59 Location: New York City System Specs System Name: AX-01 Processor: Intel Figure [modem_ber_example]. Before You Begin...

Logged drt Newbie Posts: 17 Re: Degraded Internet Connections « Reply #7 on: May 19, 2012, 08:17:37 PM » It has not been working well this evening, as I have seen You wouldn't be able to have a connection.can you cut and paste the error rate? · actions · 2009-Mar-24 9:06 pm · [email protected] bats Anon 2009-Mar-24 10:15 pm the bit error


text:
• Corpus ID: 220347398

# Balanced squeezed Complexes

@article{JuhnkeKubitzke2020BalancedSC,
title={Balanced squeezed Complexes},
author={Martina Juhnke-Kubitzke and Uwe Nagel},
journal={arXiv: Combinatorics},
year={2020}
}
• Published 3 July 2020
• Mathematics
• arXiv: Combinatorics
Given any order ideal $U$ consisting of color-squarefree monomials involving variables with $d$ colors, we associate to it a balanced $(d-1)$-dimensional simplicial complex $\Delta_{\mathrm{bal}}(U)$ that we call a balanced squeezed complex. In fact, these complexes have properties similar to squeezed balls as introduced by Kalai and the more general squeezed complexes, introduced by the authors. We show that any balanced squeezed complex is vertex-decomposable and that its flag $h$-vector can…

## References

SHOWING 1-10 OF 30 REFERENCES
A generalized lower bound theorem for balanced manifolds
• Mathematics
• 2016
A simplicial complex of dimension $$d-1$$d-1 is said to be balanced if its graph is d-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced
Squeezed complexes
• Mathematics
Journal of the London Mathematical Society
• 2019
Given a shifted order ideal U , we associate to it a family of simplicial complexes (Δt(U))t⩾0 that we call squeezed complexes. In a special case, our construction gives squeezed balls that were
Balanced complexes and complexes without large missing faces
• Mathematics
• 2009
The face numbers of simplicial complexes without missing faces of dimension larger than i are studied. It is shown that among all such (d−1)-dimensional complexes with non-vanishing top homology, a
Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra
• Mathematics
Math. Oper. Res.
• 1980
It is shown that several cases in which the Hirsch conjecture has been verified can be handled by these methods, which also give the shellability of a number of simplicial complexes of combinatorial interest.
Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals
Abstract In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will give an example of a nonpure
Balanced generalized lower bound inequality for simplicial polytopes
• Mathematics
• 2015
A remarkable and important property of face numbers of simplicial polytopes is the generalized lower bound inequality, which says that the h-numbers of any simplicial polytope are unimodal. Recently,
Many triangulated spheres
• G. Kalai
• Mathematics
Discret. Comput. Geom.
• 1988
A construction of Billera and Lee is extended to obtain a large family of triangulated spheres and it is proved that logs(n) =20.69424n(1+o(1)).


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Methodology for the use of proportional counters in pulsed fast neutron yield measurements

# Methodology for the use of proportional counters in pulsed fast neutron yield measurements

Ariel Tarifeño-Saldivia111Corresponding author: atarifeno@cchen.cl, atarisal@gmail.com, Roberto E. Mayer, Cristian Pavez,
and Leopoldo Soto
a) Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile.
b) Center for Research and Applications in Plasma Physics and Pulsed Power, , Chile.
c) Comisión Nacional de Energía Atómica, Univ. N. de Cuyo, Argentina.
###### Abstract

This paper introduces in full detail a methodology for the measurement of neutron yields and the necessary efficiency calibration, to be applied to the intensity measurement of neutron bursts where individual neutrons are not resolved in time, for any given moderated neutron proportional counter array. The method allows efficiency calibration employing the detection neutrons arising from an isotopic neutron source. Full statistical study of the procedure is descripted, taking into account contributions arising from counting statistics, piling-up statistics of real detector pulse-height spectra and background fluctuations. The useful information is extracted from the net waveform area of the signal arising from the electric charge accumulated inside the detector tube. Improvement of detection limit is gained, therefore this detection system can be used in detection of low emission neutron pulsed sources with pulses of duration from nanoseconds to up. The application of the methodology to detection systems to be applied for fusion neutrons from plasma focus devices is described. The present work is also of interest to the nuclear community working on fusion by magnetic confinement and lasers, and working on neutron production by accelerators or similar devices.

Keywords: Fast pulsed neutrons; neutron detectors; proportional counters ; piling-up statistics ; plasma focus diagnostics.

## 1 Introduction

Foil activation is usually used as a standard technique for neutron yield measurements in pulsed fusion sources. From the early plasma focus (PF) research [1, 2], activation of Silver and Indium foils have been used [3, 4, 5], although the so called silver activated Geiger counter is the most known detector from both. In PF devices [6], depending on the filling gas, neutrons from reactions or reactions are produced with typical energies of and respectively. For fast neutrons, activation detectors usually require neutron moderation to thermal energies. Notwithstanding, when neutron intensity is high enough, typically higher than per source pulse, activation by fast neutrons could be used as in the case of the Indium or Beryllium counters. [5, 7, 8]. Detectors based on activation by thermal neutrons have usually detection limits higher than per source pulse [3, 5, 9].

In recent years, several groups around the world have started research programs on small scale low energy plasma focus devices, especially in the sub-kiloJoule energy range [10, 11, 12, 13, 14, 15, 16, 17, 18, 19] and in the sub-hundredJoule energy range [20, 6, 21, 22, 23, 24]. As a consequence, requirements on detector sensitivity were increased in order to characterize such devices. For the low emission regime ( per source pulse) it is possible to use moderated gas proportional counters based on or filled tubes [25]. In these detectors thermal neutron capture occurs with cross sections one order of magnitude higher than Indium or Silver activation cross section. Therefore, detection limits in neutron proportional counters should be at least one order of magnitude lower. The disadvantage of these detectors for pulsed sources is the pulse piling-up produced during high instantaneous count rates due to the burst of fast neutrons, which make it impossible to count single neutron pulses by standard nuclear electronics. To deal with this problem two schemes of use have been proposed:

• Use of high counting rate electronics and controlling of the instantaneous count rate by detector-source separation. This technique has been reported to be successful in resolving yields higher than per source burst [26].

• Cross calibration on the accumulated charge (preamplifier output signal) generated in the counter tube by the neutron burst using as neutron reference a foil activation detector [27, 16]. The comparison of the response of a reference detector with the proportional counter allows to obtain a calibration factor in the high emission regime. Thus, by means of extrapolation, it is possible to detect yields of the order of in the low emission regime using the moderated proportional counters. Due to the fact that detection limits are transferred by the calibration process from the reference detector, the uncertainties in single measurements are of the order of the yield or greater. Thus, no improvement in measurement uncertainties is obtained for the low emission regime despite the high efficiency of neutron proportional counters tubes in comparison with foil activation detectors. However, for bursts of the order of , it is still possible to measure the pulsed neutron emission rate with an accuracy of the order of by taking averages on large samples of shots [21].

The current state of the art in the use of proportional counters for pulsed fast neutrons lacks a calibration technique to allow reducing detection limits below per source burst in single shot measurements. To overcome this deficiency, in the following, a methodology is proposed for the analysis of the detector output signal to find the number of piled-up individual detected events per burst and its uncertainties, while allowing for detector efficiency to be established through the measurement of neutrons arising from an isotopic neutron source. Thus, it is possible to obtain the real neutron yield. The detailed study of the pulse piling-up statistics and other sources that influence the measurement process, namely counting statistics and background, are described in what follows.

## 2 Working principles for fast neutron counting through a moderated proportional counter tube

In the so called continuous regime, as depicted in fig. 1, detection system consists of a moderated counter tube connected to a charge preamplifier and an amplifier, and finally connected to a counting system. As a consequence from the detection process in the counter tube, charge is produced and collected at the input terminal of the preamplifier. The output of the preamplifier is a signal whose pulse height is proportional to the integrated charge provided at the input. Decay of the preamplifier output is characterized by an exponential fall and time constant. Once in the amplifier, typically a linear amplifier, the signal is shaped and amplified in order to make it suitable for counting systems. To allow proper counting, the count rate should in general satisfy . In fig. 1 it is also shown the output in the so called pulsed regime. In this case the preamplifier output is directly connected to a digital oscilloscope. When the detection system is irradiated by an extremely short pulse of fast neutrons (), the pulse is spread over tens of microseconds as a result of neutron moderation to thermal energies. When fluence is high enough to make the instantaneous count rate to be , single neutron signals will be piled-up thus smoothing the output signal and making it impossible to count individual detected events by standard nuclear electronics. In contrast for lower fluence, when , signal shape is not smooth and eventually it is possible to distinguish single neutron pulses from the output signal. In both cases notwithstanding, the total number of detected events should be proportional to the output signal area. Even in the case of pulse piling-up, the number of detected events could be always obtained only from the net signal area, provided that space charge accumulation in the detector tube does not impair linearity.

When detection system is set up for pulsed regime (“charge integration mode”), there are three sources of fluctuations that influence the measurement process:

1. Counting statistics: Fluctuations arise from the detection process and are well described by the Poisson distribution.

2. Pulse piling-up statistics: Arise from the “wall effect” taking place inside the counter tube, which results in a very asymmetrical distribution. Therefore, when pulse piling-up happens, the sum of two or more single random detected events generate overlapping distributions which give rise to differences between the true and the expected number of detected events.

3. Background: The extracted signal from the detection system corresponds to the total charge generated in the tube, which is equivalent to the integral of the waveform acquired by the oscilloscope. Thus, electrical noise acts as background. Besides electrical noise, natural background is always present although in some cases it could be negligible.

## 3 Detection system and experimental setup

Detection systems available in our facilities were reported previously by Moreno et al [27]. They are based on a paraffin wax moderator () and a He tube (model LND 2523) sheathed by a thick lead sheet to stop x-rays and prevent their subsequent detection. The moderator is surrounded by an external cadmium sheet to absorb thermal neutrons. The tube is connected to a preamplifier (CANBERRA 2006) and the high voltage feed is set to . In order improve the signal-to-noise ratio, the preamplifier is adjusted with a conversion gain of which produces a voltage output factor scale [28]. The time constant is set to , this is the fall time for individual pulses when the input pulse risetime is less than hundred nanoseconds. When used for the pulsed regime, signal output from the preamplifier is recorded by a digital oscilloscope (Tektronix model TDS 684) at input impedance, AC coupling, and bandwidth. Horizontal scale is set in accordance with moderator decay time (governing neutron feeding into the He tube), in the case of our detectors time scale is set to . Direct measurements of the total signal area are obtained using the internal integration oscilloscope function on a time window, which starts close to the trigger point. The oscilloscope is triggered by the electromagnetic pulse generated from the electrical discharge.

Detector efficiency or calibration factor () for fast neutrons was obtained operating in the continuous regime by comparing neutron intensity from a standard isotopic source, used as neutron reference, and the registered net counting rate. The last is valid in the approximation that after many neutron scatters in the moderator the result is highly independent of the neutron input spectra; that is, the standard source spectra or that originated at the Plasma Focus. To satisfy this approximation the fast neutron reference should have a neutron energy spectra as similar to the fusion spectra as possible. Although reaction at low incident energies produces neutrons, observed fusion spectra around and extending from to have been reported in the literature [29, 5]. To fulfill this requirement a certified Cf isotopic source was used. This source is characterized by a mean energy between and its spectrum extends from . Source neutron emision at the time of experiments was . Measurements of count rate were carried out at different positions from to . For this purpose, the preamplifier output was connected to a Tennelec TC-244 amplifier and then to a multichannel analyzer Camberra Multiport II controlled by the interface GENIE2K. The gross counting was corrected by discounting natural background and air attenuation according to that reported by Eisenhauer et al. [30]. To account for solid angle, the neutron intensity was corrected by the source anisotropy factors [31], which were previously characterized [32], and thus the number of neutrons arriving to the detector front face was calculated using the formula provided by Gotoh et al. for a rectangular slit [33, 34]. These same measurements of count rate provided the pulse height spectrum of each proportional counter. In the following sections results are referred to one of our detection systems which is called He-206 system.

## 4 Piling-up statistics for proportional counters

Piling-up statistics was studied by means of the acceptance-rejection Monte Carlo method, which was used to numerically construct pulse piling-up distributions. The starting point was to obtain the waveform area spectrum for single events. Due to pulse height at the preamplifier output being proportional to the accumulated charge provided at the input, then for single events waveform area is given by , where is the pulse height and a constant. Thus, the pulse area spectrum could be obtained from the pulse height spectrum through rescaling it by the constant . depends only on the detection system. In order to characterize , let us first consider a typical output signal from the preamp associated to detection of a single event, as shown in fig. 2. This signal can be modeled by the mathematical expression

 S(t)=⎧⎪⎨⎪⎩b, if t≤−t01.Vp(1−e−(t+t01)/τ1)+b, if −t01≤t≤t02.Vpe−(t−t02)/τ2+b, if t02≤t. (1)

Thus the signal area is given by

 Ap=Vp⋅(τ2+τ1(e−(t01+t02)/τ1−1)+t01+t02)

where

 FA=(τ2+τ1(e−(t01+t02)/τ1−1)+t01+t02). (2)

To obtain proper values to calculate , hundreds of waveforms from single neutron events were analyzed using the model of eq. 1 and the non-linear least squares (Levenberg-Marquardt method) routine provided by the function fit of the GNUPLOT package [35]. Results of this analysis are presented in table 1. Using these results it was possible to construct the probability density function (pdf) and the cumulative distribution function for the proportional counter tube as shown in figure 3.

Piling-up statistics was studied by simulating the random detector response in terms of the waveform area and the other statistics associated to the measurement process. Let be the total number of detected events and a random number extracted from the counter tube (fig. 3) by means of the acceptance-rejection Monte Carlo method. When events are detected, the random ideal response of the detection system is given by

 XT(m)=m∑j=1x(). (3)

Thus the probability density function from the pulse piling-up statistics is obtained as a function of by sampling of equation 3.

Samples were generated numerically for . The sample size choice was . Results from the He-206 detection systems are shown in fig. 4. As expected, for the numerical algorithm reproduces the experimental of the counter tube. From numerical results it is observed that when pulse piling-up distribution is highly asymmetrical, for asymmetry is still present at tails of the distributions, finally when tail differences are not apparent from histograms. From the central limit theorem, the pulse piling-up statistic is expected to converge to the normal distribution. This property was evaluated at the significance level by means of Kolmogorov-Smirnov and Jarque-Bera normality test. Convergence of the counter tube (fig. 3) to the normal distribution was found in terms of cumulative probability (K-S test) when , while in terms of asymmetry and peakedness (J-B test) when .

False positive readings are generated in the detection system by two mechanisms:

• Natural background: Corresponds to events from the environment which are characterized by a constant count rate. Natural background count rate in our experimental room is usually found in the range . These measurements were done under the continuous regime. For the pulsed regime the measurement time window is , therefore contribution to the total number of detected events by natural background is negligible.

• Electrical background noise (EBN): In absence of detected events, the electrical noise contributes randomly to the total waveform area (detector reading), thus it behaves as a background reading. When the operative parameters in the detection system are fixed, readings from EBN respond to a normal distribution. The latter is concluded from analysis of EBN samples by the Kolmogorov-Smirnov test at significance level.

These facts imply that the gross detector reading () should be corrected to discount background contributions. Let and respectively be the sample mean and sample standard deviation associated to the EBN. Therefore, the net detector reading is obtained from

 XTnet=XTgross−B. (4)

For a specific time window, the EBN sample statistical parameters depend on oscilloscope horizontal and vertical scale, they are affected by changes in laboratory room temperature and should be monitored in-situ together with neutron measurements for shots with no neutron detection.

## 6 Counting model from the waveform area

To arrive at a counting model as a function of the net waveform area, let us first consider a sequence of random values associated to detected events: . Therefore the following expressions are satisfied

 m′ = a1XT1 m′ = a2XT2 ⋮ m′ = anXTn.

Selecting as a constant, let the following be defined as follows,

 m′1 = a⋅XT1 m′2 = a⋅XT2 ⋮ m′N = a⋅XTn.

By properly choosing , convergence of the distributions ensures that

 E(m′i)=E(a⋅XTi)=a⋅E(XTi)=m′. (5)

Being the mathematical expectation of the variable . This constant was evaluated using samples from the pulse piling-up statistic. Detected number of events was plotted against the sample mean of the waveform area,

 m(E(XTi))=a⋅E(XTi). (6)

Thus, a linear least squares through the origin yields the value of . Results of this analysis are shown in table 2.

Finally the counting model is defined by means of the rounding function, which round the argument to the nearest integer, as follows

 mmc=G(XT)=[a⋅XT], (7)

where corresponds to a predicted value for the number of detected events from the signal waveform area or accumulated charge. Once the counting model has been obtained, it becomes necessary to study the predictive power of the method and the uncertainties. As already stated in section 2, in practical situations fluctuations are due to the counting statistics, which responds to the Poisson distribution, also due to the pulse piling-up statistics whose distribution has been studied in section 4 and to the electrical background noise which is governed by the normal distribution (see section 5).

Predictive power was studied by simulating random measurements as predictions from the counting model. For that purpose pseudo-random numbers from the Poisson and normal distributions where required. Due to its proven mathematical properties although being slower than others, the gsl_rng_ranlux389 pseudo-random number generator provided by the GNU Scientific Library (GSL) was used [36]. The algorithm for simulating random measurements and model predictions is described as follows:

1. Let be the true number of detected events.

2. Let be a pseudo-random integer extracted from the Poisson distribution with expected value .

3. Let be a pseudo-random number extracted from the pulse piling-up statistic associated to detected events.

4. Let be a pseudo-random number extracted from a Gaussian distribution () with . Thus a new variable is defined by . At this point, corresponds to the simulated net detector reading.

5. Finally a prediction from the counting model is obtained by .

Sampling of the above described algorithm allows further calculation of the statistical parameters , , , , and , and comparison of them with the true number of detected events.

Samples were created for the interval with a step size of . Sample size choice was . For each value of , was varied in the interval with steps of when , and when .

Analysis of numerical results to determine predictive power and model uncertainties was done by means of linear models and hypothesis testing. For predictive power, if predictions from the counting model () converge to the true number of detected events (), then these two variables should be related in a plot by the identity function. To evaluate shift of the counting model caused by its definition or by numerical reasons, a general linear model is used: . Thus, the hypothesis to be tested by the F-test is given as follows:

If null hypothesis is accepted for a given significance level , then a high predictive power is concluded for the counting model. Otherwise, the counting model is assumed to be poorly predictive and should be rejected.

For the F-test, the significance level was chosen to be (). Therefore, our sample with degrees of freedom has a F-test critical value of . At the top of figure 5 results are shown of application of the F-test on samples as a function of for the study of counting model predictive power. For each sample, it was verified that the expected value of the counting statistics also converge to the true number of detected events. From figure 5, it is observed that all calculations are less than the critical F-value, thus the counting model defined by equation 7 is concluded to be highly predictive, this is to say

 E(mmc)=m. (8)

The last being valid at least in the interval under study: and .

Once counting model is accepted as predictive, it is necessary to study uncertainties of the model. With this purpose, two cases were considered:

• Case 1: Uncertainties of the counting model due only to counting statistic and pulse piling-up statistic. This case is equivalent to consider sample generation when

 limdB→0Bran⟶0. (9)
• Case 2: Uncertainties of the counting model due to counting statistic, pulse piling-up statistic and electrical background noise.

For case 1 samples in the interval , with and sample size of , were analyzed. As a result, it was found that variance of predictions from the counting model are proportional to the expected value for predictions from the counting model,

 σ2(mmc)=f0⋅E(mmc)=f0⋅m. (10)

Thus, distributions generated by the counting model, neglecting background effects, could be said to be Poisson-like because effects of the counting statistic dominate over pulse piling-up statistic. Last conclusions are supported by numerical results as shown in figure 6 and table 3. On one hand, samples from the counting statistics were analyzed by linear least squares (LLS) using the model . Use of the T-test of hypothesis allowed to conclude for the significance level that , as expected. On the other hand, analysis of sample data by LLS and model results from equation 10 allow to conclude that . Therefore, it is possible to say that pulse piling-up statistical contribution is the contribution from the counting statistic to counting model variance when neglecting background effects.

For case 2 is postulated that counting model variance is given by,

 σ2(mmc)=f0⋅E(mec)+σ2(a⋅Bran)=f0⋅m+a2⋅dB2sample. (11)

To demonstrate the last hypothesis, predictive power of equation 11 was studied. If the right side of equation 11 converges to the left one, then the plot should be given by the identity function. By considering samples with the same characteristics than those set up for the study of counting model predictive power, it was obtained that equation 11 is highly predictive for the sample counting model standard deviation, as it could be verified at bottom of figure 5. It is important to note that to achieve predictability, the sample standard deviation of the background electrical noise should be used.

Summarizing results so far, it has been demonstrated that definition of the counting model by equation 7 ensures and .

## 7 Neutron yield measurements

Let us consider a single shot from the pulsed source, e.g a plasma focus device. Now we deal with the problem of estimating the expected number of detected events and its uncertainties. Let the net detector response (see equation 4). Then, for this single measurement the best estimation of the expected number of detected events comes from the measurement itself [37],

 m=E(mmc)≅G(XTnet)=[a⋅XTnet]. (12)

Thus, the uncertainty associated to the expected number of detected events in a single measurement is calculated from

 σ(m)=√f0⋅m+a2⋅dB2sample≅√f0⋅G(XTnet)+a2⋅dB2sample=√f0⋅[a⋅XTnet]+a2⋅dB2sample (13)

Once obtained an estimation of the number of detected events has been obtained, the neutron yield is easily deduced by using the calibration factor of the detection system (). Consequently, the number of neutrons per solid angle is given by

 Y=jc⋅[a⋅XTnet]⋅⎛⎜⎝1± ⎷(djcjc)2+f0[a⋅XTnet]+a2⋅dB2muestral[a⋅XTnet]2⎞⎟⎠. (14)

Let be the solid angle subtended by the detector at its measurement position, then . Thus under the assumption of isotropic emission, the total neutron emission per pulse is given by

 Y4π=f4π⋅Y. (15)

In order to study detection limits, let us consider table 4 where characteristic values for and of the typical positioning interval in an extremely low energy plasma focus device (PF-50J, [21]) are shown. In addition, from and the standard relative error is then calculated by

 %dY(Y)=100⋅ ⎷(d¯jc¯jc)2+¯f0⋅¯jc⋅¯f4πY4π+(¯a⋅dBsample⋅¯jc⋅¯f4πY4π)2. (16)

Plots from equation 16 are shown as a function of in figure 7. It is observed from this figure that when total neutron emission is higher than , uncertainties are less than . For uncertainties are of the order . Finally, it has to be pointed out that reasonable uncertainties () are still obtained in the range . The last is a direct consequence of the methodology proposed in this work.

## 8 Concluding remarks

The statistics of the signal generated from pulse piling-up (pulse piling-up statistics) in a neutron proportional counter when used in the herein called pulsed regime has been studied. It has been found that pulse piling-up statistics converge to a normal distribution typically when the number of piled-up pulses is higher than a hundred. From the pulsed piling-up statistics, the counting statistical behaviour and background contributions, a measurement methodology for bursts of neutrons has been developed. The method is based on a counting model for the number of detected events based upon the net accumulated charge at the output of the detection system (waveform area). It has been demonstrated that the model, as defined in equations 7 and 10, ensures and , when is the true number of detected events. Then by using equation 14 it is possible to calculate the neutron emission, bearing in mind that the model holds while space charge accumulation in the detector tube does not run so high as to impair linearity. By this methodology, it has been possible to achieve detection limits almost two orders of magnitude lower than those from state of the art techniques. The methodology is quite general and could be reproduced by other groups in order to calibrate neutron detectors based on moderated proportional counters for fast neutrons.

## Acknowledgments

This work was supported by the Chile Bicentenial Program in Science and Technology grant ACT 26, Center for Research and Applications in Plasma Physics and Pulsed Power Technology (P4 Project).

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text:
# rs_exs

## 1296 days ago by zoen

F.<a> = FiniteField(2^2) F.modulus()
 x^2 + x + 1 x^2 + x + 1
F.list()
 [0, a, a^2, a^3, a + 1, a^2 + a, a^3 + a^2, a^3 + a + 1, a^2 + 1, a^3 + a, a^2 + a + 1, a^3 + a^2 + a, a^3 + a^2 + a + 1, a^3 + a^2 + 1, a^3 + 1, 1] [0, a, a^2, a^3, a + 1, a^2 + a, a^3 + a^2, a^3 + a + 1, a^2 + 1, a^3 + a, a^2 + a + 1, a^3 + a^2 + a, a^3 + a^2 + a + 1, a^3 + a^2 + 1, a^3 + 1, 1]
F = GF(11) F.list()
 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
M = GF(5) M.list()
 [0, 1, 2, 3, 4] [0, 1, 2, 3, 4]
Mx.<x>=M[] n, k = 5 , 2 C = codes.GeneralizedReedSolomonCode(M.list()[:n], k) C.list()
 [(0, 0, 0, 0, 0), (1, 1, 1, 1, 1), (2, 2, 2, 2, 2), (3, 3, 3, 3, 3), (4, 4, 4, 4, 4), (0, 1, 2, 3, 4), (1, 2, 3, 4, 0), (2, 3, 4, 0, 1), (3, 4, 0, 1, 2), (4, 0, 1, 2, 3), (0, 2, 4, 1, 3), (1, 3, 0, 2, 4), (2, 4, 1, 3, 0), (3, 0, 2, 4, 1), (4, 1, 3, 0, 2), (0, 3, 1, 4, 2), (1, 4, 2, 0, 3), (2, 0, 3, 1, 4), (3, 1, 4, 2, 0), (4, 2, 0, 3, 1), (0, 4, 3, 2, 1), (1, 0, 4, 3, 2), (2, 1, 0, 4, 3), (3, 2, 1, 0, 4), (4, 3, 2, 1, 0)] [(0, 0, 0, 0, 0), (1, 1, 1, 1, 1), (2, 2, 2, 2, 2), (3, 3, 3, 3, 3), (4, 4, 4, 4, 4), (0, 1, 2, 3, 4), (1, 2, 3, 4, 0), (2, 3, 4, 0, 1), (3, 4, 0, 1, 2), (4, 0, 1, 2, 3), (0, 2, 4, 1, 3), (1, 3, 0, 2, 4), (2, 4, 1, 3, 0), (3, 0, 2, 4, 1), (4, 1, 3, 0, 2), (0, 3, 1, 4, 2), (1, 4, 2, 0, 3), (2, 0, 3, 1, 4), (3, 1, 4, 2, 0), (4, 2, 0, 3, 1), (0, 4, 3, 2, 1), (1, 0, 4, 3, 2), (2, 1, 0, 4, 3), (3, 2, 1, 0, 4), (4, 3, 2, 1, 0)]
Fx.<x> = F[] n, k = 10 , 5 C = codes.GeneralizedReedSolomonCode(F.list()[:n], k) E = C.encoder("EvaluationPolynomial") p = x^2 + 3*x + 10 c = E.encode(p); c
 (10, 3, 9, 6, 5, 6, 9, 3, 10, 8) (10, 3, 9, 6, 5, 6, 9, 3, 10, 8)
G = codes.encoders.GRSEvaluationVectorEncoder(C) G.generator_matrix()
 [1 1 1 1 1 1 1 1 1 1] [0 1 2 3 4 5 6 7 8 9] [0 1 4 9 5 3 3 5 9 4] [0 1 8 5 9 4 7 2 6 3] [0 1 5 4 3 9 9 3 4 5] [1 1 1 1 1 1 1 1 1 1] [0 1 2 3 4 5 6 7 8 9] [0 1 4 9 5 3 3 5 9 4] [0 1 8 5 9 4 7 2 6 3] [0 1 5 4 3 9 9 3 4 5]
m = matrix(F,[[10,3,1,0,0]]); m; m.parent()
 [10 3 1 0 0] Full MatrixSpace of 1 by 5 dense matrices over Finite Field of size 11 [10 3 1 0 0] Full MatrixSpace of 1 by 5 dense matrices over Finite Field of size 11
A = matrix(F,[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 4, 9, 5, 3, 3, 5, 9, 4], [0, 1, 8, 5, 9, 4, 7, 2, 6, 3], [0, 1, 5, 4, 3, 9, 9, 3, 4, 5] ])
m*A
 [10 3 9 6 5 6 9 3 10 8] [10 3 9 6 5 6 9 3 10 8]
C.minimum_distance()
 6 6
C.weight_distribution()
 [1, 0, 0, 0, 0, 0, 2100, 6000, 29250, 61500, 62200] [1, 0, 0, 0, 0, 0, 2100, 6000, 29250, 61500, 62200]
Fx.<x> = F[] n, k = 10 , 5 C = codes.GeneralizedReedSolomonCode(F.list()[:n], k) E = C.encoder("EvaluationPolynomial") p = x^2 + 3*x + 10 c = E.encode(p); c
 (10, 3, 9, 6, 5, 6, 9, 3, 10, 8) (10, 3, 9, 6, 5, 6, 9, 3, 10, 8)
C.decode_to_message(c)
 (10, 3, 1, 0, 0) (10, 3, 1, 0, 0)
C.parity_check_matrix()
 [10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5] [10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5]
H=C.parity_check_matrix()

 [10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5] [10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5]
[H,H]
 [ [10 9 8 7 6 5 4 3 2 1] [10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5], [ 0 9 7 6 7 1 3 9 8 5] ] [ [10 9 8 7 6 5 4 3 2 1] [10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5], [ 0 9 7 6 7 1 3 9 8 5] ]
G=H.augment(H)
 [10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5 0 9 7 6 7 1 3 9 8 5] [10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1] [ 0 9 5 10 2 3 2 10 5 9 0 9 5 10 2 3 2 10 5 9] [ 0 9 10 8 8 4 1 4 7 4 0 9 10 8 8 4 1 4 7 4] [ 0 9 9 2 10 9 6 6 1 3 0 9 9 2 10 9 6 6 1 3] [ 0 9 7 6 7 1 3 9 8 5 0 9 7 6 7 1 3 9 8 5]
G*vector([1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1])
 (0, 0, 0, 0, 0) (0, 0, 0, 0, 0)
F = GF(59) n, k = 40, 12 C = codes.GeneralizedReedSolomonCode(F.list()[:n], k) D = codes.decoders.GRSErrorErasureDecoder(C) c = C.random_element() n_era = randint(0, C.minimum_distance() - 2) Chan = channels.ErrorErasureChannel(C.ambient_space(), D.decoding_radius(n_era), n_era) y = Chan(c) D.connected_encoder().unencode(c) == D.decode_to_message(y)
 Traceback (click to the left of this block for traceback) ... AttributeError: 'module' object has no attribute 'GRSErrorErasureDecoder' Traceback (most recent call last): Chan = channels.ErrorErasureChannel(C.ambient_space(), D.decoding_radius(n_era), n_era) File "", line 1, in File "/tmp/tmpeo1cen/___code___.py", line 6, in D = codes.decoders.GRSErrorErasureDecoder(C) AttributeError: 'module' object has no attribute 'GRSErrorErasureDecoder'
F = GF(59) n, k = 40, 12 C = codes.GeneralizedReedSolomonCode(F.list()[:n], k) D = codes.decoders.GRSErrorErasureDecoder(C)
 Traceback (click to the left of this block for traceback) ... AttributeError: 'module' object has no attribute 'GRSErrorErasureDecoder' Traceback (most recent call last): File "", line 1, in File "_sage_input_12.py", line 10, in exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("RiA9IEdGKDU5KQpuLCBrID0gNDAsIDEyCkMgPSBjb2Rlcy5HZW5lcmFsaXplZFJlZWRTb2xvbW9uQ29kZShGLmxpc3QoKVs6bl0sIGspCkQgPSBjb2Rlcy5kZWNvZGVycy5HUlNFcnJvckVyYXN1cmVEZWNvZGVyKEMp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in File "/tmp/tmpXH6ymo/___code___.py", line 6, in exec compile(u'D = codes.decoders.GRSErrorErasureDecoder(C) File "", line 1, in AttributeError: 'module' object has no attribute 'GRSErrorErasureDecoder'