SageMath简易入门手册
Sage 产品说明书
Standardize patient hygieneSageUrine management/bathing/incontinence care/meatal cleansingWhat are the challenges to providing the best care?Inconsistent applicationThe dosage and delivery process often varies greatly between nurses, units, and facilities.Multiple-step products require more time and aren’t always available orpart of the workflow. Potential spills and clean-up also add time to the process.Lack of aneffective alternativeFollowing guidelines and protocols regarding catheter use is difficult when patients need urinary management assistance.Standardize your patient hygiene programOur products can help you address the patient cleansing challenges of CAUTI & IAD. 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Washcloths stay warm throughout the bath when warmed in our commercial-grade warmer.Basins were completely eliminated fromtwo medical/surgical units and replaced with Comfort Bath. CAUTI rates were reduced to zero within one month and the rates remained at zero for five months .9On an 18-bed SICU, female patients were identified for early removal of indwelling urinary catheters during daily rounds. PrimaFit was initiated for female patients who remained incontinent after catheter removal.11A 2015 two-phase evaluation of 86 patients at high risk for developing IAD and HAPI found that, in those who received anintervention that standardized incontinence cleanup with a Barrier Cream Clothfollowing each incontinent episode, none developed IAD or a HAPI.10Here’s the proof:*Removing basins reduces CAUTI risk factorsThe impact of using PrimaFit in an effort to address CAUTI prevalenceBarrier Cream Cloth helps prevent IAD and addresses risk factors of hospital-acquired pressure injuries (HAPI)72-year-old patient with severely denuded, blistered skin and extreme pain from incontinence.After using Comfort Shield Barrier Cream Cloths, patient’sskin vastly improved; no discomfort.CAUTIs for5 months 0%IAD orHAPI See thedifference!12CAUTI incidence reduction—73%*Results based on individual hospital and product use. Data provided by facility.Day 1Day 4Product orderingIncontinence Clean-up Cloths (8) Cloths in peel and reseal package8" x 8"30 packages/case Reorder #7505Comfort Shield Barrier Station with removable adhesive strips for wall-mounting near the bedside 24 stations/case Reorder #7599Comfort ShieldBarrier Cream Cloths (3) H eavyweight cloths in easy-tear package8.5" x 8.5"90 packages/case Reorder #7503Medicare ReimbursementHCPCS Code #A6250Comfort ShieldBarrier Cream Cloths (3) H eavyweight cloths in easy-tear package8.5" x 5.5"100 packages/case Reorder #7502Medicare Reimbursement HCPCS Code #A6250Comfort ShieldBarrier Cream Cloths (8) H eavyweight cloths in peel and reseal package8.5" x 9"48 packages/case Reorder #7905Medicare Reimbursement HCPCS Code #A6250Essential Bath ®(8) Medium weight washcloths/package8” x 8”60 packages/case Reorder #7800Comfort Bath Fragrance-free (5) Premium heavyweightwashcloths/package8” x 8”48 packages/case Reorder #7956Comfort Bath ®(8) Premium heavyweightwashcloths/package8” x 8”44 packages/case Reorder #7900Comfort Bath Fragrance-free (8) Premium heavyweightwashcloths/package8” x 8”44 packages/case Reorder #7903Essential Bath Fragrance-free (8) Medium weight washcloths/package8” x 8”60 packages/case Reorder #7803Essential Bath Fragrance-free (5) Medium weight washcloths/package8” x 8”84 packages/case Reorder #7856Baby Comfort Bath Fragrance-free (4) Premium heavyweightwashcloths/package6” x 8”110 packages/case Reorder #7907Clean-up Cloths and Sage PrimaFit External Urine Management System for the Female Anatomy(1) Package of (3) medium weight clean-up washcloths(1) PrimaFit, adult size/package 40 systems/caseReorder #5452Sage PrimaFit External Urine Management for the Female Anatomy (1) PrimaFit, adult size/package 40 devices/case Reorder #5400Sage PrimoFitExternal Urine Management for the Male Anatomy(1) PrimoFit, adult size/package 40 devices/caseReorder #5404HardwareCart31.71" (shelf L) 17.71" (shelf D) 34.63" (cart H)1 cart/case Reorder #793212-Count Warmer 16.89" (H) 14.69" (W)15.24" (D)1 warmer/case Reorder #793728-Count Warmer 18.39" (H) 27.56" (W) 15.39" (D)1 warmer/case Reorder #7939Rinse-Free Shampoo Cap (1) Cap/package 40 packages/case Reorder #7909M-Care ® Meatal Cleansing Cloths (2) Cloths/package5.5” x 8”168 packages/case Reorder #7953Bath Cloths Fragrance-free (8) Standard weight washcloths/package8” x 8”88 packages/case Reorder #7989Bath Cloths Fragrance-free (5) Standard weight washcloths/package8” x 8”78 packages/case Reorder #7959Clean-up Cloths (3) Medium weight washcloths/package6” x 8.5”100 packages/caseReorder #7957Bath Cloths(8) Standard weight washcloths/package8” x 8”88 packages/case Reorder #7982Bath Cloths Fragrance-free (8) Standard weight washcloths/package8” x 8”40 packages/caseReorder #7991Impreva ® Bath Fragrance-free (8) Standard weight washcloths/package8” x 8”88 packages/caseReorder #7988Impreva ® Bath Fragrance-free (5) Standard weight washcloths/package8” x 8”78 packages/caseReorder #7987Return on investmentCost analysisBenchmark and outcome reportS a m p l e r e p o r t000Sample reportOur commitment to youWe believe building partnerships can deliver better outcomes. Our goal is to provide you with the products, training, education, and support you need to provide the best possible care for your patients.Available resources include:Ongoing product and process in-servicing and educationDedicated Medical Science Liaison to discuss evidence-based information with you and your teamPre- and post-intervention assessmentsFocusRN — a clinical education program that includes speaker programs, online learning, and CE modulesEducation through the FocusRN program from clinical thought leadersProtect your pipesThe Traptex ® Plumbing Protection Systemcan help change flushing behavior to stop wipes and non-flushables from entering and clogging your pipes. The result is fewer maintenance calls for clogs, equipment failures, and plumbing disasters.Incontinence Bathing26181F © 2022 Stryker | For use in USASage Products LLC | 3909 Three Oaks Road | Cary, IL 60013 | | 800 323 2220R eferences: 1. Centers for Disease and Control and Prevention (CDC) Urinary Tract Infection (Catheter-Associated Urinary Tract Infection (CAUTI) and Non-Catheter Urinary Tract Infection (UTI) and Other Urinary System Infection (USI) Events. Device-associated Module UTI, 7-1–7-20. January 2020. 2. Toolkit for Reducing Catheter-Associated Urinary Tract Infections in Hospital Units: Implementation Guide, Agency for Healthcare Research and Quality (AHRQ), Rockville, MD. October 2015. 3. Marchaim D, et al., Hospital bath basins are frequently contaminated with multi-drug resistant human pathogens. American Journal of Infection Control 40 (2012) 562-4. 4. Anaisse EJ, Penzak SR, Dignani C, Arch Intern Med. 8 Jul 2002; 162 (13):1483-92. 5. Gray M, Giuliano K, Incontinence-Associated Dermatitis, Characteristics and Relationship to Pressure Injury: A Multisite Epidemiologic Analysis, Journal of Wound Ostomy Continence Nursing, Jan/Feb 2018;45(1):63-67. 6. Health Research & Educational Trust (2017, April). Hospital Acquired Pressure Ulcers/Injuries (HAPU/I): 2017. Chicago, IL: Health Research & Educational Trust. 7. Sage Products LLC. Data on file. Customer Testimonials Home Care. Terms of use available at: https:///store/pg/152-Terms-of-use. Accessed July 29, 2020. 8. Multi-Hospital Sage Products CustomerOne Sponsored Bath Survey June 2019. Accessed June 18, 2019. 9. Stone S, et al., Removal of bath basins to reduce catheter-associated urinary tract infections. Poster presented at APIC 2010, New Orleans, LA, July 2010. 10. Hall, K. and Clark, R. (2015 Jul.). A Prospective, Descriptive, Quality Improvement Study to Decrease Incontinence-Associated Dermatitis and Hospital-Acquired Pressure Ulcers Ostomy Wound Mgmt, 61:(7); 26-30. 11. Beeson T, Davis C, Vollmann KM, Chasing Zero Catheter Associated Urinary Tract Infections (CAUTIs) through Implementing a Novel Female External Urine Collection Device in a Tertiary Academic Surgical Intensive Care Unit (SICU), Oral Abstract, American Journal of Infection Control, 2018:(46);S2-S15. 12. Sluser S, Consistency the key for treating perineal dermatitis due to incontinence. Poster presented at Clinical Symposium on Advances in Skin and Wound Care (SAWC), Las Vegas, NV , Oct 23-26, 2005.Simple interventions.Extraordinary outcomes.We are your partner for proven prevention. Ourmarket-leading products solve real healthcare problems and are backed by clinical evidence. Our products allow you to deliver essential patient care with confidence by addressing risk factors that can lead to infections, skin injury, and caregiver injuries.We are driven to solve real problems and make healthcare better for you and your patients.Find our nurse trusted products at or call 800 490 6493。
sage使用手册
sage使用手册Sage是一个开源的数学软件系统，提供了许多数学计算和算法实现的功能。
以下是Sage使用手册的简要介绍：1. 安装和配置：首先，您需要下载和安装Sage软件。
您可以从Sage的官方网站上下载适用于您的操作系统的安装程序。
在安装过程中，请遵循屏幕上的指示进行操作。
安装完成后，您需要配置Sage的环境变量和路径。
2. 启动和主界面：启动Sage后，您将看到一个类似于命令行的界面。
Sage的主界面包括一个命令行提示符和一个文本编辑器，您可以在这里输入Sage命令和数学表达式。
3. 基础操作：在Sage中，您可以使用基本的数学操作符（如加、减、乘、除）进行计算。
您还可以使用Sage的内置函数和模块进行更复杂的计算。
例如，使用`factor(n)`函数可以分解一个数字的质因数，使用`plot()`函数可以绘制函数的图像。
4. 变量和表达式：在Sage中，您可以使用变量存储数值或表达式。
例如，您可以使用`x = symbols('x')`定义一个符号变量`x`，然后使用`x^2 + 3x + 2`表示一个表达式。
5. 模块和库：Sage提供了许多数学模块和库，包括代数、数论、几何、离散数学等领域。
您可以使用`import`语句导入所需的模块或库，然后使用其中的函数和类进行计算和操作。
6. 文件和输出：在Sage中，您可以创建、打开和保存文件，以及将输出导出到文件或打印机。
例如，您可以使用`open()`函数创建一个文本文件，然后使用`write()`函数将内容写入文件。
7. 帮助和文档：Sage提供了丰富的帮助和文档资源，可以帮助您了解软件的功能和使用方法。
您可以使用`help()`函数获取有关函数、模块或库的详细信息，并参考Sage的官方文档和教程。
总之，Sage是一个功能强大的数学软件系统，通过学习和实践，您可以利用Sage进行各种数学计算和算法实现。
sagemath扩展欧几里得算法求x和y
sagemath扩展欧几里得算法求x和y全文共四篇示例，供读者参考第一篇示例：Sagemath是一个开源的数学软件，它可以用于代数计算、几何、数论、统计学等领域的求解。
在数论中，扩展欧几里得算法是一个用于求解给定两个整数a和b的最大公约数以及满足ax+by=gcd(a,b)的整数解x和y的算法。
在本文中，我们将介绍如何使用Sagemath来实现扩展欧几里得算法，求得整数a和b的最大公约数以及对应的整数解x和y。
Step 1：初始化我们需要将a和b初始化为要求解的两个整数，同时设置初始值x0=1，y0=0，x1=0，y1=1，以及r0=a，r1=b。
Step 2：迭代计算然后，我们可以通过迭代计算的方式来更新r、x和y的值，直到r 的值为0为止。
具体的迭代过程如下：1. 计算商和余数：q=r0//r1，r=r0%r1。
2. 更新x和y的值：x=x0-q*x1，y=y0-q*y1。
3. 更新r、x和y的索引：r0=r1，r1=r，x0=x1，x1=x，y0=y1，y1=y。
Step 3：返回结果最终，当r的值为0时，就可以得到整数a和b的最大公约数为r0，同时满足ax+by=r0的整数解x为x0，y为y0。
在Sagemath中，我们可以使用内置的函数来实现扩展欧几里得算法。
下面是一个示例代码：```pythondef extended_euclidean_algorithm(a, b):x0, y0, x1, y1 = 1, 0, 0, 1r0, r1 = a, bwhile r1 != 0:q = r0 // r1r = r0 % r1x = x0 - q * x1y = y0 - q * y1x0, y0, x1, y1 = x1, y1, x, yr0, r1 = r1, rreturn r0, x0, y0a, b = 35, 15gcd, x, y = extended_euclidean_algorithm(a, b)通过上面的示例代码，我们可以求得整数35和15的最大公约数为5，同时满足35x+15y=5的整数解x为2，y为-5。
SageMath简易入门手册
SageMath简易入门指导中国矿业大学（北京）理学院2014级创新小组编组长：孙裕道组员：孟坤，尹娟，董光林，李欢，王思高导师: 刘兰冬前言一些数学商业软件如Matlab、Maple、Mathematica需要下载到电脑上，而且这些软件在电脑中需要占用很大的内存，单说Matlab 在电脑中就会占用6.5G的内存左右，从官网下载该软件也会要下载半天，非常不方便。
互联网时代，在云端进行操作和存储事物已经成为一种趋势，SageMath软件就是顺应这种趋势的发展。
SageMath是网上免费的开源数学软件，注册一个SageMath的账号在云端就可以进行相关的操作，非常方便，所以我们创新小组决定学习SageMath.SageMath的功能强大，可以求积分，求极限，求导等一些列高等数学的运算，并且可以对一些复杂问题进行SagaMath编程求解。
我们创新小组在刘兰冬老师的指导下，系统地学习SageMath软件的相关知识，使大家对SageMath的这门语言的一些基础语法和用法有了初步的了解，可以对一些数学问题进行编程求解。
希望我们小组的这个SageMath简易入门指导可以对这门语言感兴趣的人，想学习这门语言的人有入门指导的帮助。
2014年11月1日目录1 SageMath的登陆方法 (4)1.1进入官网 (4)1.2 界面登陆 (5)1.3创建账号 (5)1.4创建工程 (6)1.5工程搜索 (7)1.6新建文件 (8)1.7新建工作簿 (8)1.8编辑界面 (9)1.9进行操作 (9)2.SageMath的基本语法 (12)2.1基本命令语 (9)2.1.1 加法 (10)2.1.2 减法 (10)2.1.3 乘法 (10)2.1.4 除法 (10)2.1.5 乘方 (10)2.1.6 开方 (10)2.2判断语句 (10)2.2.1 if语句的用法 (10)2.3循环语句 (11)2.3.1 For循环语句 (11)2.3.2 While循环语句 (11)2.4 画图 (12)2.4.1 plot语句 (12)2.4.2 show语句 (12)3.SageMath中的数学函数 (13)3.1高等数学中的Sage命令 (13)3.1.1函数表示 (13)3.1.2复合函数 (13)3.1.3微分 (14)3.1.4Talor公式 (15)3.1.6求极限 (16)3.1.8数论素数分解 (16)3.2线性方程组中常用命令 (16)3.2.1矩阵运算 (16)3.2.2逆矩阵 (17)3.2.3求解方程组 (17)4.Sage中的编程 (19)4.1插值多项式 (19)参考文献 (20)SageMath简介SageMath 是一个免费的、开源的数学软件系统，采用GPL协议。
SAGE Coursepacks - Blackboard LMS 用户指南说明书
Frequently Asked Questions: Blackboard1) What are Coursepacks?2) Which systems support Coursepacks?3) Are Coursepacks compatible with my LMS?4) What is available in the Coursepacks?5) How do I access my Coursepacks file?6) How do I import Coursepacks into the Blackboard LMS?7) How do my students access the interactive eBook?8) How do I make a test available to my students?9) How long do I have access to this content?10) My web browser prevents me from viewing a video or other content. What do I do?11) Whom do I contact if I have trouble using my LMS?12) Whom do I contact for support with content in Coursepacks?13) Where are the SAGE premium videos located?14) Where are the quizzes that go with the SAGE premium videos, and how do they work?15) What is the Media Guide (also known as Video Guide) and how do I use it?16) What if my Coursepack file un-Zips automatically after I download it?17) Why are my tests out of order when I go to deploy them?18) When I edit a question in a test or a pool, are my updates saved everywhere?1) What are Coursepacks?SAGE Coursepacks p rovide easy to import, highly customizable, and high-quality instructor and student content for your school’s learning management system (LMS). Intuitive and simple to use, S AGE Coursepacks are collections of book-specific instructor/student resources, as well as assessments, that allow you to focus on what really matters: customizing course content to meet your students’ needs.Key Features:✓Delivers SAGE content d irectly into your LMS.✓The intuitive and simple-to-use format allows for easy course integration with minimal effort.✓Pedagogically robust assessment tools f oster review, practice, and critical thinking, and offer a better, more complete way to measure student engagement. Tools include but are not limited to: o Diagnostic chapter Pre-Tests and Post-Testso Test banks built on Bloom’s Taxonomy2) Which systems support Coursepacks?The following table summarizes compatibility* of Coursepacks with various systems and browsers.Operating SystemWindows ✔Macintosh ✔BrowserWe support current versions of browsers andone version back unless otherwise noted.Chrome ✔Firefox ✔Internet Explorer ✔Safari ✔* If you have questions regarding mobile compatibility or other LMS features, please contact your school's LMS administrator.3) Are Coursepacks compatible with my LMS?Coursepacks work with the most recent versions of popular learning management systems including Blackboard, Moodle, D2L (Desire2Learn), and Canvas. The learning management administrator/ instructional technologist at your school can confirm the version of the LMS you’re using.LMS CompatibleBlackboard Learn 9.1 ✔Canvas ✔D2L 9.2 and above ✔Moodle 2.8 and above ✔4) What is available in the Coursepacks?The answer to this question depends on the SAGE title being utilized. For example, one title may include SAGE Data Maps with assessments attached to them, while another title may include educational videos provided by the author of the text. The core materials within Coursepacks are:●Textbook Information: This page provides basic information including a description of the book,a link to purchase the eBook, and SAGE technical support information.●Student Resources: These materials are provided for the student to enrich their learning of thesubject being taught.●Instructor Resources: These materials are only visible to the instructor and are provided to helpwith the teaching of the class.●Assessments: The assessments are available for instructors and students and can only bedeployed/published by the instructor.5) How do I access my Coursepacks file?Navigate to h ttps:// and search for the title of your textbook.Click on the title of your textbook.Click the R esources t ab.Next, scroll down and click I nstructor Resource site.Log in with your SAGE credentials. If you have not signed up yet, you can do so by clicking the N ew User?button.Click I nstructor Resources a nd then the S AGE coursepacks link on the left.Next, at the bottom of the page, click the D ownload SAGE coursepack link to begin downloading the file for Blackboard 9.6) How do I import Coursepacks into the Blackboard LMS?For a detailed step-by-step guide, click on the following link:https:///system/files/How%20to%20Import%20a%20SAGE%20Coursepack%20into%2 0Blackboard.pdf7) How do my students access the interactive eBook?Students can navigate to the Textbook Information section where they will find a link and instructions for how to access the eBook through the VitalSource website. Students may either purchase access to the book, or, if already purchased, redeem an access code. Each chapter of Student Resources also has a corresponding link to that chapter in the eBook. Once students have purchased the eBook and/or redeemed their access code, they are able to access the eBook through your LMS.8) How do I make a test available to my students?In Blackboard, you must deploy a link to the test in a content area. Click the A ssessments d rop-down menu and select T est.Select the test you’d like to deploy.Review the the test options, then click “Submit”.If you are unfamiliar with the testing tools in Blackboard, please contact y our school's LMS support team.9) How long do I have access to this content?Access to SAGE digital content embedded in or linked to from Coursepacks will be available for the life of the edition of the textbook. All other information will remain available inside the course in which Coursepacks are imported.Please be aware that SAGE does not have control over third-party multimedia links. Over time, links may become inactive, so it is recommended that before you begin teaching your course you review media links to ensure they are working.10) My web browser prevents me from viewing a video or other content. What do I do?Although unlikely, it is possible that web browsers may block media that they interpret are coming from an unverified source. In most cases, it will be fine to allow the web browser to load the content by selecting the appropriate option in your browser when prompted.If you encounter problems accessing external links or media, contact the SAGE support team.●Call us at 1 (800) 818-7243 ext. 7080 [toll free] / 1 (805) 410-7080 [direct]●Email us at t*******************************In addition, it is recommended that you turn off your browser’s pop-up blocker. Links to some external sites or media may open in a pop-up window, so any blockers should be disabled. For help with managing your browser’s pop-up blocker or other features, contact your university’s IT department. 11) Whom do I contact if I have trouble using my LMS?For help using, navigating within, or managing your Blackboard courses, contact your institution’s instructional technology department or LMS administrator.For additional support, you may consult the instructor support website for Blackboard Learn 9+: https:///Learn/Instructor12) Whom do I contact for support with content in Coursepacks?For support questions about the materials in Coursepacks or other SAGE digital products,visit w /support.●Call us at 1 (800) 818-7243 ext. 7080 [toll free] / 1 (805) 410-7080 [direct]●Email us at t*******************************13) Where are the SAGE premium videos located?For many titles that have an interactive eBook, all SAGE premium videos are available exclusively within that eBook. Your students will need to purchase access (and/or redeem their access code) for the eBook in order to view the videos.14) Where are the quizzes that go with the SAGE premium videos, and how do they work?If your Coursepack has SAGE premium videos, then any quizzes that align with those videos are located in your Coursepack. They may be found in the “Tests, Surveys, and Pools” section of your course after you’ve imported the Coursepack into Blackboard. For some Coursepacks, videos are located directly within the quizzes. However, for many Coursepacks, the videos are located separately, within the interactive eBook.If, for your Coursepack, the SAGE premium videos are located in the interactive eBook, here is how the quizzes work:●Within each quiz, each question contains a link that takes the student to the video in theinteractive eBook. Clicking the link will open up VitalSource Bookshelf in a new browser tab. The student will need to log in to Bookshelf if that hasn’t yet been done.●Once logged in, the student will be brought directly to the eBook page in which the video islocated. Students should follow the directions contained in the quiz question: click the link toaccess the video in the eBook, watch the video, then return to the test and answer the question.15) What is the Media Guide (also known as Video Guide) and how do I use it?The Media Guide (or Video Guide) provides an overview of every media asset offered to complement the textbook. The Guide organizes all media by chapter and learning objective, and also lists all quiz questions that align with the media (e.g., SAGE premium video quizzes). Once you’ve imported your Coursepack, quiz questions can be found in "Tests, Surveys, and Pools" for testing purposes.In some Coursepacks, the Media Guide is in two different file formats rather than one (or more) Word document:1. A customizable/filterable Excel spreadsheet that organizes all media by chapter and learningobjective2. A Word document that lists the questions for the SAGE premium videosYou may use the Media Guide as a quick reference to help you review and select media assets and assessments for use in your course.16) What if my Coursepack file un-Zips automatically after I download it?On Macs, Zip files will automatically un-Zip upon download. Be sure that the file you import into Blackboard is the correct format. It should be a Zip file, so this may mean you will need to re-Zip the file prior to importing.17) Why are my tests out of order when I go to deploy them?Due to a limitation in Blackboard, tests are not shown in alphanumerical order when they’re being deployed. Unfortunately you’ll have to search the list of tests to find the ones you’d like to deploy. You may try using Ctrl+F (PC) or [open apple]+F (Mac) to search for the test you need.18) When I edit a question in a test or a pool, are my updates saved everywhere?If questions in a pool are linked to the corresponding questions in a test, any edits you make to a question in one location will automatically be made to the question in the other location. For example, if you edit question #1 in the Chapter 3 Pre-Test in “Pools”, and those questions are linked to the corresponding questions in the Chapter 3 Pre-Test in “Tests”, then your edits to question #1 will automatically be made in “Tests” as well. If questions are not linked, then you will need to edit the question in both “Tests” and “Pools” in order for the changes to be reflected in both places.。
geomagic学习教程汇总
点云数据分类：1、根椐扫描设备来分类 2、根椐扫描质量来分类 3、操作中产生的多余的 点
扫描设备 扫描质量
有序点云 无序点云
杂点
在行列方向上有恒定的密度进行排列 不定的密度在空间的任一位置存在（这样的例子很多） 杂点就是测量错误的点（不是噪声），是无效的点，放 大后就看得出、很明显地离开零件表面，孤立的点
测后作出调整。
Boundaries > Create Curve Object Curves > Curves to Boundaries 边界与曲线的转换
第六章曲面的命令 ——感谢虚拟样机技术论坛提供，无维论坛TomLee整理
作者：sea_heart 关键词：Geomagic8.0,逆向,曲面 来源：无维网（）
1、Patches > Shuffle > Panels，选择所要编辑的面板，即在所要编辑的面板内任点一点，动 作在 Define（定义）上类型在 Grid（网格）上
3、观察面板各边面片的数量，如下图所圈 12 与 16 是需要编辑的
1．Geomagic 曲面片(Patches)的划分 Geomagic 中曲面片(patch)的划分是做好曲面的关键，它要以曲面分析为
The grid, in turn, contributes to the precision of the ultimate NURBS surface. Therefore, the density of the grid and the size of the patch contribute to the precision of the NURBS surface.
Sage 操作手册 概述
操作手册概述制作人：张世军更新时间：二〇〇九年九月二十九日一、 登录1、双击图标进入2、输入用户名和密码，按ENTER键进入。
（图1）图1二、操作界面1、功能模块区会列出所有可以使用的功能模块（图2）2、你也可以把经常使用的某一功能或功能组通过鼠标右键加入收藏区图23、浏览区通常是列出你所使用的功能的内容（图3）4、点击添加到收藏可以把当前的功能模块收藏（图3）5、可以随时通过单击收藏列表与功能列表调用图2的内容（图2、图3）6、可以通过导航路径知道你正在使用的是哪个功能模块（图3）7、创建按钮是用来实现当前功能模块的创建（图3）图37、单击选择所有行按钮将选择所有列表的内容（图4）8、点击最大化按钮将把列表全屏，在同一屏幕内显示更多的内容（图4）9、最大化后可以按ESC链退出全屏状态。
图410、在列表内单击鼠标右键后，可以将列表的内容导出到Excel中。
（图5）图511、导出时会弹出导出窗口，单击导出完成导出操作。
（图6）12、导出EXCEL时并没有生成文件，需要保存后内容才会被保存。
图613、在浏览区的列标题处单击鼠标右键会弹出菜单（图7），并单击快速选择，可以输入你要过滤的信息（图8），其中过滤信息*号表示任何字符并不计位数，？号表示任何字符且只表示一位。
例：输入在产品列过滤时输入0*，表示列出所有以0开前的内容。
图7图8三、热键1、ENTER键（回车）。
在正常输入信息或修改信息时，按ENTER键后会默认为保存或新建。
但象图5那种操作界面按ENTER只是表示完成当前行的操作。
2、ESC键（取消）。
此键通常在是行操作时取消当前行的操作，或取消最大化行窗口的操作。
3、Ctrl+C和Ctrl+V分别为复制与粘贴，在大多数输入操作时如同其它软件的复制与粘贴操作。
4、F1键。
此键为帮助键，可以在操作时按F1后弹出前功能的相关帮助，但此部分帮助内容还没有中文版，并需要我们进一步将其完善，因此还没有可以显示的内容。
Matlab最新入门教程(超级简单实用)
4
ans = 5 512 》A.\B↙ ans = 5.0000 Inf 1.5000 (Inf 表示正无穷) 2.6667 2.2500 Inf 》B.\A↙ （与A./B的结果相同） ans = 0.2000 0 0.6667 0.3750 0.4444 0 应注意上述运算中两个矩阵的维数应该相同。至于标量与矩阵进行上述运算的含义，请看 》2.^A↙ （标量2相当于元素全为2的与A同维数的矩阵） ans = 2 1 4 8 16 1 》A.^2↙ ans = 1 0 4 9 16 0 1.6 行向量的特殊输入方式 行向量与一维数组是一样的数据对象，除了作为矩阵的特例像1×n矩阵一样地输入外，常采用―： ‖ 和函数linspace、logspace两种输入方式，它们的用法可以从下面的例子知道。 》a=1:5↙ （从1到5公差为1（可缺省）的等差数组） a= 1 2 3 4 5 》b=1:2:7↙ （从1到7公差为2的等差数组，如果输入b=1:2:8,得到同样结果） b= 1 3 5 7 》c=6:-3:-6↙ （从6到-6公差为-3的等差数组） c= 6 3 0 –3 -6 》b=[0:2:8,ones(1,3)] ↙ （等差数组和行向量拼接） b= 0 2 4 6 8 1 1 1 》linspace(0,1,9) ↙ （从0到1共9个数值的等差数组） ans= 0 0.1250 0.2500 0.3750 0.5000 0.6250 0.7500 0.87500 1.0000 即 linspace(a,b,n) 生成从a到b共n个数值的等差数组，公差不必给出。与它相仿的是 logspace(a,b,n) 生成从10a到10b共n个数值的等比数组。 4等分π（MA TLAB中π的符号是pi）的数组可以用这两种方式输入： 》x=0:pi/4:pi↙ x= 0 0.7854 1.5708 2.3562 3.1416 》x=linspace(0,pi,5) ↙ 输出同上。 请特别注意―:‖的用法，其实矩阵的裁剪中用到的―:‖的含义与此是完全相同的。如 》G(1:2:end,4:-1:2) ↙ （与G([1 3],[4 3 2]) 等价） ans = 0 0 3 1 9 6561 1 （与B./A的结果相同）
{六西格玛管理}SIGMA使用说明书
{六西格玛管理}SIGMA使用说明书SIGMAPC-15使用说明书28页?1.21.区域指示?区域指示告诉你目前所处于3个训练区域中的哪一个2.时间格式?在12小时格式下你可以看到时间处于Am或是Pm3.跑人图案?在训练指导功能开启後，跑人图案会显示在屏幕上4.闹钟?闹钟功能启动后，闹钟图案会显示在屏幕上5.菜单指针?菜单指针指示你目前所处于哪一个手表功能上6.秒表?秒表功能启动后，秒表图案会显示在屏幕上29页?1.3按键位置（Keyallocation）1.功能键1（FunctionKey1）--此键指示的功能可以在屏幕上看到。
如果屏幕上没有显示此键所处功能，代表正处于“退出”功能。
2.减键（Minus）--向后翻滚菜单，或减少数值3.功能键2（FunctionKey2）--此键指示的功能可以在屏幕上看到。
4.训练指导键（T-ManagerKey）--此键可以直接将你代入训练指导的菜单中5.加键（Plus）--向前翻滚菜单，或增加数值6.灯光键（Lighting）--同时按下加键（Plus）和减键（Minus）功能简述（Functionoverview）时间菜单（TIME，【timemenu】）●∙ ∙∙ ∙∙ ∙∙ ∙时钟（Clock）●∙ ∙∙ ∙∙ ∙∙ ∙保健区（HealthZone）●∙ ∙∙ ∙∙ ∙∙ ∙健身区（FitnessZone）●∙ ∙∙ ∙∙ ∙∙ ∙力量区（PowerZone）●∙ ∙∙ ∙∙ ∙∙ ∙秒表（StopWatch）●∙ ∙∙ ∙∙ ∙∙ ∙全程时间（TotalTime）●∙ ∙∙ ∙∙ ∙∙ ∙闹钟（Alarm）设置（SET，【input】）●∙ ∙∙ ∙∙ ∙∙ ∙语言（Language）●∙ ∙∙ ∙∙ ∙∙ ∙心率区（HeartRatezones）●∙ ∙∙ ∙∙ ∙∙ ∙时钟（Clock）●∙ ∙∙ ∙∙ ∙∙ ∙日期（Date）●∙ ∙∙ ∙∙ ∙∙ ∙闹钟（alarm）●∙ ∙∙ ∙∙ ∙∙ ∙钟声（Beep）●∙ ∙∙ ∙∙ ∙∙ ∙主人姓名（“Myname”）心脏（HEATR【Pulsemenu】）●∙ ∙∙ ∙∙ ∙∙ ∙训练时间（Trainingtime）●∙ ∙∙ ∙∙ ∙∙ ∙心率平均值（Averageheartrate【HR】）●∙ ∙∙ ∙∙ ∙∙ ∙最快心率（MaximumHR）●∙ ∙∙ ∙∙ ∙∙ ∙千卡热量消耗（Kcalconsumption）●∙ ∙∙ ∙∙ ∙∙ ∙全部热量消耗（Totalcalorieconsumption【totalkcal】）训练指导（MANAGER）●∙ ∙∙ ∙∙ ∙∙ ∙训练指导（TrainingManager）圈数统计（LAPCOUNTER）●∙ ∙∙ ∙∙ ∙∙ ∙圈数统计（Lapcounter）●∙ ∙∙ ∙∙ ∙∙ ∙记忆（Memory）30页?1.41.你的PC15有5个主菜单，下图手表边框的红点和表面文字提示显示你目前所处的功能。
sagemath求解同余方程
sagemath求解同余方程同余方程是数论中的重要问题，它涉及到整数之间的关系和等价性。
在数论中，同余方程是指形如$ax \equiv b \pmod{m}$的方程，其中$a$是未知数，$b$和$m$是已知数，$\pmod{m}$表示对$m$取模。
为了求解同余方程，我们可以利用SageMath这一强大的数学软件。
SageMath是基于Python编程语言的开源数学软件，它集成了多个数学库和算法，可以用于解决各种数学问题，包括求解同余方程。
下面我们来看一些具体的例子，以帮助理解如何用SageMath求解同余方程。
例子一：求解$4x \equiv 3 \pmod{7}$。
为了求解这个同余方程，我们可以使用SageMath中的solve_mod函数。
具体操作如下：```pythonx = var('x')solve_mod(4*x == 3, 7)```运行上述代码后，我们可以得到方程的解为$x \equiv 6 \pmod{7}$。
例子二：求解$12x \equiv 5 \pmod{17}$。
同样地，我们可以使用SageMath中的solve_mod函数求解这个同余方程。
具体操作如下：```pythonx = var('x')solve_mod(12*x == 5, 17)```运行上述代码后，我们可以得到方程的解为$x \equiv 2 \pmod{17}$。
通过上述例子，我们可以看出SageMath能够轻松地求解同余方程。
除了solve_mod函数外，SageMath还提供了其他求解同余方程的函数，如solve_mod_linear、solve_mod_congruence等，可以根据不同的需求灵活选择。
需要注意的是，SageMath对于大数的运算具有很强的能力，可以处理高阶同余方程以及复杂的数学问题。
因此，在实际应用中，可以放心地使用SageMath来求解同余方程。
RSA bleeding edge patent sagemath pdf说明书
®Version 1.0 March 2001Technical SpecificationsHigh-precision stereo 2-way/mono 3-way crossover with subwoofer outputCX2310SUPER-X®PRO s Professional, high-precision stereo 2-way/mono 3-way crossover with separate subwoofer outputs World-class performance 24 dB per octave Linkwitz-Riley filterss Absolutely flat summed amplitude response, zero phase differences Separate subwoofer section with independent frequency controls Individual output level controls for all bandss Individual output mutes for easy band adjustments Individual phase reverse switches for instant phase corrections Switchable 25 Hz subsonic filter on each input for low-frequency driver protections Servo-balanced, gold-plated XLR connectors for all inputs and outputss Ultra-high precision ALPS potentiometers for ultimate accuracy and repeatabilitys Ultra low-noise audio operational 4580 amplifiers for outstanding sound performances Illuminated switches for secure operation in dark stage environmentss High-quality components and exceptionally rugged construction for long life and reliabilitys Shielded toroidal mains transformer for minimal noise interferences Manufactured under ISO9000 certified management system2SPECIFICATIONSINPUTSConnectors XLRType Electronically servo-balanced, HF filteredImpedance balanced >50 kOhm, unbalanced >25 kOhmMax. Input level+22 dBu typical, balanced or unbalancedCMRR>40 dB, typical >55 dB at 1 kHzOUTPUTSConnectors XLRType Electronically servo-balanced, HF filteredImpedance balanced 60 Ohm, unbalanced 30 OhmMax. Output level+20 dBm balanced/unbalancedPERFORMANCEBandwidth20 Hz to 20 kHz, +0/-0.5 dBFrequency response<5 Hz to >60 kHz, +0/-3 dBSignal to noise Ref.: +4 dBu, 20 Hz to 20 kHz, unweightedStereo-Mode:Mono-Mode:Low output>93 dB>93 dBMid output>95 dBHigh output>91 dB>91 dBInterchannel crosstalk High to Low:<93 dBHigh to Mid:<94 dBMid to Low:<95 dBCROSSOVERFilter-Type Linkwitz-Riley, 24 dB/octave, state-variableMono Mode Frequencies x1x10Low/High44 to 930 Hz440 Hz to 9.3 kHzLow/Mid44 to 930 Hz440 Hz to 9.3 kHzMid/High440 Hz to 9.3 kHzStereo Mode Frequencies x1x10Low/High44 to 930 Hz440 Hz to 9.3 kHzPOWER SUPPLYMains voltage USA/Canada120 V ~, 60 HzU.K./Australia240 V ~, 50 HzEurope230 V ~, 50 HzGeneral Export Model100 - 120 V ~, 200 - 240 V ~, 50 - 60 Hz Power consumption<17 WFuse UL100 -120 V ~: T 630 mA HEurope200 - 240 V ~: T 315 mA HJP90 - 110 V ~: T 630 mA HMains connection Standard IEC receptaclePHYSICAL/WEIGHTDimensions approx. 1 ¾" (44.5 mm) * 19" (482.6 mm) * 8 ½" (217 mm)Weight approx. 3 kgBEHRINGER is constantly striving to maintain the highest professional standards. As a result of these efforts, modifications may be made from time to time to existing products without prior notice. Specifications and appearance may differ from those listed or illustrated.3The information contained in this manual is subject to change without notice. No part of this manual may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording of any kind, for any purpose, without the express written permission of BEHRINGER Spezielle Studiotechnik GmbH.BEHRINGER and SUPER-X are registered trademarks. ALL RIGHTS RESERVED.© 2001 BEHRINGER Spezielle Studiotechnik GmbH.BEHRINGER Spezielle Studiotechnik GmbH, Hanns-Martin-Schleyer-Str. 36-38, 47877 Willich-Münchheide II, GermanyTel. +49 (0) 21 54 / 92 06-0, Fax +49 (0) 21 54 / 92 06-304。
sage CRT运算
将整数转化为二进制列表sage: 10.bits()解方程solve 函数用于解方程。
要使用它，先要指定变量，然后将方程（或方程组）以及要求解的变量作为参数传给 solve。
1 2 3 4 5 6 7 8 910111213 sage: var('x y p q')sage: eq1 = p+q==9sage: eq2 = q*y+p*x==-6sage: eq3 = q*yˆ2+p*xˆ2==24sage: solve([eq1,eq2,eq3,p==1],p,q,x,y)[[p == 1, q == 8, x == -4/3*sqrt(10) - 2/3, y ==1/6*sqrt(2)*sqrt(5) - 2/3], [p == 1, q == 8, x == 4/3*sqrt(10) - 2/3, y == -1/6*sqrt(2)*sqrt(5) - 2/3]]要求解的近似值，可以这样：sage: solns = solve([eq1,eq2,eq3,p==1],p,q,x,y, solutiondict=True)sage: [[s[p].n(30), s[q].n(30), s[x].n(30), s[y].n(30)] for s in solns][[1.0000000, 8.0000000, -4.8830369, -0.13962039], [1.0000000, 8.0000000, 3.5497035, -1.1937129]]求解方程的数值解用 find root 在区间 0 < ϕ< π/2 上寻找上述方程的解。
• 整数环 {…,−1,0,1,2,…}, Sage 中叫 ZZ;•有理数环 ，即整数构成的分数，Sage 中叫 QQ;• 实数环，Sage 中叫 RR;• 复数环，Sage 中叫 CC ；sage: ratpoly.<t> = PolynomialRing(QQ)ratpoly 是集合的名字，自己定义.<t>是变量的名字，自己定义PolynomialRing()是环QQ 是有理数环有限域还有，GF(2)、GF(2^8,modulus=[1,0,0,1,1,1,0,0,1]) …… 使用方法 solve right. 执行 A.solve right(Y) 返回一个矩阵（或向量）X 满 足 AX = Y:类似的，使用 A.solve left(Y) 求解满足 XA = Y 的 X.矩阵所在的环影响它的性质。
Sage 护理用品保护系统说明书
Protect your pipesStop wipes and non-flushablesfrom clogging pipesSageTraptex ® Plumbing Protection SystemMunicipal finesSanitationWipes in the pipes: a problem that costsFlushing of inappropriate items is awidespread problem in healthcare, resulting in clogs, burst pipes, and flooding, and is a huge drain on hospital resources and revenue.Just because an item leaves the toilet bowl doesn’t mean it’s flushable.Even products labeled “flushable anddispersible” cause problems because they A nationwide survey of US hospitals found that:1• Approximately 57% of plumbing clogs werecaused by a variety of flushed disposable, nonwoven wipe products.• The cost to fix a minor clog ranged between$15 - $2,000 per clog , with an average of over $300.• The number of maintenance calls due to plumbingclogs ranged from 45 - 2,200 per month.• Approximately 50% of hospitals reported coststo repair clogs ranging from tens of thousands of dollars to over $1 million per year.Hospital plumbing clogs are a growing problemTraptex system changes behaviorThe Traptex Plumbing Protection System helps change flushing behavior with innovative devices, education, and monitoring to help prevent non-flushable items from entering the pipes. The result is fewer maintenance calls for clogs, equipment failures, and plumbing disasters.The Traptex Plumbing Protection System includes:P rofessional, on-site sizingCustom-made Traptex toilet guard and hopper guard devicesP rofessional installation2-year device warranty No Wipes in the Pipes ® education program Traptex Wipe RetrieversOngoing monitoring and measurementLearn more and see Traptex in action/us/en/sage/products /sage-traptex.htmlGuidelines support the useof cloth-based products Professional guidelines and studies recommend the use of cloth-based products to address various risk factors for surgical site infections, incontinence-associated dermatitis, and urinary tract infections. Don’t let potential or past plumbing issues keep you from using single-use products as part of your risk reduction strategy.Guideline recommendations: IHI2Provide premoistened, disposable barrier wipes to help cleanse, moisturize, deodorize, and protect patients from perineal dermatitis due to incontinence.WOCN3Combined products can be used to save time and make providing perineal care easier for the caregiver. Combined products include moisturizing cleansers, moisturizerskin protectant creams, and disposable washcloths that incorporate cleansers, moisturizers, and skin protectantsinto a single product.APIC4A rinse-free CHG cloth has been introduced as analternative to CHG showers, and some data suggests easeof use and improved patient compliance as well as reduced rates of SSI.CDC5Eliminate contaminated water or fluidenvironmental reservoirs wherever possible(e.g., in equipment or solutions). Category IBNo Wipes in the Pipes education programWe offer a variety of free materials to educate and remind staff, patients, and families not to flush non-flushable items. Through the use of awareness posters and videos, the ‘No Wipes in the Pipes’ education program reinforces proper flushing behavior.Monitoring and measurementOur dedicated CustomerOne team can assist you in tracking savings from avoided plumbing clogs and provide return on investment (ROI) reports. You’ll be able to see and share results on success in changing flushing behavior. Just providethe raw data, and you will receive customized reports for ongoing measurement.Find these and other nurse trusted products at or call 800 490 649326182B 2021 StrykerSage Products LLC | 3909 Three Oaks Road | Cary, IL 60013 | | 800 323 2220References: 1. Traptex Survey conducted by Sage Products LLC, data on file. 2013 2. Getting started kit: prevent pressure ulcers, how-to guide. Protecting 5 Million Lives from Harm Campaign, Institute for Healthcare Improvement, 2011 Dec. 3. Wound Ostomy and Continence Nurses Society. Guideline for Prevention and Management of Pressure Ulcers; June 2010. 4. Guide to Elimination of Orthopedic Surgical Site Infections. Association for Professionals in Infection Control and Epidemiology (APIC), 2010. 5. Centers for Disease Control and Prevention. Guidelines for environmental infection control in health-care facilities: recommendations of CDC and the Healthcare Infection Control Practices Advisory Committee (HICPAC). MMWR 2003;52 (No. RR-10)5,14.。
SAGE Permissions Log指南说明书
Quick Guide: Completing the SAGE Permissions Log The Permissions Log is used to record the details of any third party content requiring permission or that has license restrictions, as well as the details of any identifiable people appearing in a publication. As licenses, agreements, and releases for a project are obtained (collectively, the Permissions File), any restrictions detailed in these documents should be noted on the log.Included on the Permissions LogAny content that:∙Contains personal rights concerns∙Is being used by permissionIncluding content from another SAGE owned publicationIncluding author created content previously published with another publisher ∙Is being used under any kind of license termsIncluding STMIncluding Creative CommonsDoes not need to be included on the Permissions LogAny content that:∙Is being used under Fair UseUnless it contains personal rights concerns∙Is Public DomainUnless it contains personal rights concerns∙Author created content, created for this publicationIncluding author created content being carried over from previous editionImportant Points∙Each column of the log should be filled out.See the Legend on the log template for detail on each column.∙The items listed on the log should be ordered chronologically as they appear in the book.∙Credit lines are important.If the perm agreement specifies a particular credit line, the log should indicate it EXACTLY.If no specific credit line is required, indicate “Production to create.”▪You must include full source info.∙In the restrictions columns, on ly indicate “No Restrictions” if we have received permission for Worldwide distribution, all languages, all formats, life of the edition, all future editions and versions. Author ConfirmationOnce the log is finalized, it must be sent via email to the author to confirm that all content requiringpermission has been accounted for. The author can respond with an email for the record. Here is asuggested message to the Author:Dear <Author Name>,Attached please find a copy of the final permissions log for your upcoming project. As you know, this document is an importantorganizational tool for documenting the third-party material included in your manuscript requiring permission. Completeness andaccuracy on this log will help streamline development and production, as well as simplify tasks for any future editions.In accordance with your author/editor agreement, you have warranted that you will identify and obtain all required permissionsand/or releases needed for any third-party material contained within the manuscript. In addition, for all photographs you havepersonally taken, you must also obtain a visual likeness release from any identifiable person(s) in the photo.Please review this log to ensure that all third-party material appearing within your work requiring permission is accurately listed, andthat all necessary permission has been obtained. If the log is complete, please email me to confirm. Please also contact us ASAP ifthere are any items missing, so we can address any additional permissions needed as soon as possible.Please let me know if you have any questions.Kindest regards, <Name>03/2017。
sagemath 语法
sagemath 语法
Sagemath 是一个开源的数学软件系统，它支持各种数学操作和符号计算。
以下是Sagemath 的一些基本语法：
1. 赋值语句：使用"=" 符号进行赋值。
例如，`x = symbols('x')` 创建一个符号变量x。
2. 运算符：支持常见的数学运算符，如加法、减法、乘法、除法等。
例如，`x + y` 表示x 和y 的加法。
3. 函数：Sagemath 提供了许多内置函数，可用于执行各种数学操作。
例如，`sin(x)` 表示正弦函数，`exp(x)` 表示自然指数函数。
4. 控制结构：Sagemath 支持基本的控制结构，如if-else、for 循环和while 循环。
例如，`if x > y: print(x)` 表示如果x 大于y，则输出x。
5. 矩阵和向量：使用方括号[] 和逗号分隔元素来创建矩阵或向量。
例如，`[1, 2, 3]` 表示一个包含三个元素的向量，`[[1, 2], [3, 4]]` 表示一个2x2 的矩阵。
6. 注释：使用"#" 符号添加注释。
例如，`# This is a comment`。
这只是Sagemath 语法的一小部分，更多高级功能和详细信息可以查阅Sagemath 的官方文档或教程。
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SageMath简易入门指导中国矿业大学（北京）理学院2014级创新小组编组长：孙裕道组员：孟坤，尹娟，董光林，李欢，王思高导师: 刘兰冬前言一些数学商业软件如Matlab、Maple、Mathematica需要下载到电脑上，而且这些软件在电脑中需要占用很大的内存，单说Matlab 在电脑中就会占用6.5G的内存左右，从官网下载该软件也会要下载半天，非常不方便。
互联网时代，在云端进行操作和存储事物已经成为一种趋势，SageMath软件就是顺应这种趋势的发展。
SageMath是网上免费的开源数学软件，注册一个SageMath的账号在云端就可以进行相关的操作，非常方便，所以我们创新小组决定学习SageMath.SageMath的功能强大，可以求积分，求极限，求导等一些列高等数学的运算，并且可以对一些复杂问题进行SagaMath编程求解。
我们创新小组在刘兰冬老师的指导下，系统地学习SageMath软件的相关知识，使大家对SageMath的这门语言的一些基础语法和用法有了初步的了解，可以对一些数学问题进行编程求解。
希望我们小组的这个SageMath简易入门指导可以对这门语言感兴趣的人，想学习这门语言的人有入门指导的帮助。
2014年11月1日目录1 SageMath的登陆方法 (4)1.1进入官网 (4)1.2 界面登陆 (5)1.3创建账号 (5)1.4创建工程 (6)1.5工程搜索 (7)1.6新建文件 (8)1.7新建工作簿 (8)1.8编辑界面 (9)1.9进行操作 (9)2.SageMath的基本语法 (12)2.1基本命令语 (9)2.1.1 加法 (10)2.1.2 减法 (10)2.1.3 乘法 (10)2.1.4 除法 (10)2.1.5 乘方 (10)2.1.6 开方 (10)2.2判断语句 (10)2.2.1 if语句的用法 (10)2.3循环语句 (11)2.3.1 For循环语句 (11)2.3.2 While循环语句 (11)2.4 画图 (12)2.4.1 plot语句 (12)2.4.2 show语句 (12)3.SageMath中的数学函数 (13)3.1高等数学中的Sage命令 (13)3.1.1函数表示 (13)3.1.2复合函数 (13)3.1.3微分 (14)3.1.4Talor公式 (15)3.1.6求极限 (16)3.1.8数论素数分解 (16)3.2线性方程组中常用命令 (16)3.2.1矩阵运算 (16)3.2.2逆矩阵 (17)3.2.3求解方程组 (17)4.Sage中的编程 (19)4.1插值多项式 (19)参考文献 (20)SageMath简介SageMath 是一个免费的、开源的数学软件系统，采用GPL协议。
它整合了许多开源Python包，采用Python语言编写，但也支持其他语言。
它的目标是创造一个可变的开源软件以替代Magma、Maple、Mathematica和Matlab。
SageMath不仅是一个软件，也是一个编程环境，提供命令行模式、笔记本模式，可以编写编译型程序和解释型程序。
目前SageMath支持Linux、Mac OS X、BSD、Solaris平台。
SageMath采用浏览器作为GUI界面，融入了云计算的思想。
学生不用再为写一次作业而装几Ｇ多的而苦恼了，他们可以不在电脑上面安装 SageMath 而使用它Matlab。
1 SageMath的登陆方法1.1进入官网首先登录 sage的官方网站： 也可以通过搜索引擎通过搜索 sagemath 进行寻找。
1.2 界面登陆using SageMath online 进入SageMath界面，然后你需要创建一个账号，下次登陆时直接登陆就可以了（Sign in）1.3创建账号请大家自己创建自己的账号，下一次用邮箱名登陆即可，邮箱可以任何自己已有的邮箱，QQ邮箱，网易邮箱，新浪邮箱都可以申请，申请完毕后需要在需要在邮箱激活账号。
1.4创建工程登陆成功后进入以下界面，需要你创建自己的工程“Projects”，在Projects 上输入正确的字符字母，下划线，汉字等，但注意不能开头不能是数字输入你的工程项目名，以下以“Step20150907”为例，建立一个新项目“New Project”对新Project的描述，自己根据需要填写，比如你是2015年10月7日做的，即可以写成step_0151007，需要由英文，下划线，字符串组成1.5工程搜索在Projects中找到你要编辑的Project，例如：我要编辑“Exercise20160907”，双击进入即可，就能找到你之前编辑过的SageMath文本1.6新建文件点击New按钮，弹出界面,在Name your file文本框上输入正确的字符，如字母，下划线，汉字等，但注意不能开头不能是数字1.7新建工作簿点击Select the type 下面的按钮“SageMath Worksheet”，然后会弹出下面页面，然后再点击即可1.8编辑界面进入编辑界面，可以在上页面上进行数学运算，上面有一组工具栏，在这些工具栏可以找出各种数学运算的命令。
1.9进行操作在此界面你可以完成你的计算任务例1: 计算2的3次方，可以如下操作，点击Run界面2.Sage的基本语法介绍2.1基本命令语2.1.1 加法如我们想做8+3，在SageMath键入如下即可2.1.2 减法如我们想做6-3，在SageMath键入如下即可2.1.3 乘法如我们想做5*3，在SageMath键入如下即可2.1.4 除法8 ，在SageMath键入如下即可如我们想做42.1.5乘方如我们想做3的3次方，在SageMath键入如下即可2.1.6 开方如我们想做64的1/2次方，在SageMath键入如下即可2.2判断语句2.2.1 if语句的用法编程用if语句判断奇偶性，并且用print语句输出它的奇数和偶数注意事项：需要注意格式if语句要跟变量对齐，否则就会报错2.3循环语句2.3.1 For循环语句用for循环语句，计算7的1/3次方到2015的1/3次方步长为1的加和，并输出结果2.3.2 While循环语句用while循环语句，计算2015到2025之间所有整数的之和2.4 画图2.4.1 plot语句用plot语句来画出心形线，函数为2.4.2 show语句用show语句画出初始值为1到末位值为100之间，步长5的所有半径的圆，如下图3．SageMath 中的数学函数3.1高等数学中的Sage 命令 3.1.1函数表示例1：定义函数及画图。
例如我们想定义函数x x x f -=3)(以及21)(x x g -=，并求)0()2(g f +的值，还要画出)(x f 在[-2，2]上的图像，可如下操作3.1.2复合函数例1：如我们定义了函数53)(+=x x f 以及1)(3+=x x g ，我们想要计算))(()(x g f x h =，如下操作即可。
注意：))(())((x f g x g f ≠，我们这个例子中83))((3+=x x g f ，而126225135271)53())((233+++=++=x x x x x f g3.1.3微分例1： 对xe x x x x x xf +++++=ln arctan 2sin cos )(2求一阶导数例2：求二元函数223),(y xy x y x f ++=的偏导数3.1.4Talor 公式例1： 求)sin()(x x f =的9阶泰勒多项式3.1.5积分例1：对分)1/(3)(22/5x e x x f x +++=求不定积分例2：求区间[0,3]的定积分222)33()(+-=x x x x f例3：求函数 xy y x f =),( 的二重积分例4：求函数x z y x f =),,(3.1.6求极限例1：求极限x x x)11(lim+∞→3.1.7求方程根例1：计算cosx-x=0 在区间(0,2)内的实根，敲入“find_root(cos(x)-x,0,2)”，#表示注释语句，点击Run界面，得到结果“0.7390851332151607”3.1.8数论素数分解例1：计算2015的素数分解，敲入“2015.factor()”，#表示注释语句，点击Run界面，得到结果“5*13*31”3.2线性方程组中常用命令3.2.1矩阵运算例1：计算矩阵⎪⎪⎭⎫⎝⎛4321的平方矩阵，敲入“matrix（[[1，2]，[3，4]]）^（2）”，# #computes the square of a matrix 表示注释语句，点击Run 界面，得到结果 “[ 7 10] [15 22]”3.2.2逆矩阵例：计算矩阵⎪⎪⎭⎫ ⎝⎛4321的逆矩阵，敲入“matrix （[[1，2]，[3，4]]）^（-1）”，# #computes the inverse of a matrix 表示注释语句，点击Run界面，得到结果 [ -2 1][3/2 -1/2]3.2.3求解方程组例1：求解线性方程组Ax=b ，其中⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫⎝⎛=31,4321b A ，求出的解为：⎪⎪⎭⎫⎝⎛=01x ，如下所示：例2： 求解线性方程组Ax=b ，其中⎪⎪⎪⎭⎫ ⎝⎛-=⎪⎪⎪⎭⎫ ⎝⎛--=7514,112811543b A ，求出的解为：⎪⎪⎪⎭⎫⎝⎛=103x ，我们也可采用把矩阵A 约化为单位矩阵的方法，约化后的右端项就是所求解，即()⎪⎪⎪⎭⎫ ⎝⎛→→⎪⎪⎪⎭⎫ ⎝⎛---=1100001030017112581114543, b A Sage 的操作如下所示：例3： 线性方程组无解的情⎪⎪⎪⎭⎫ ⎝⎛=⎪⎪⎪⎭⎫ ⎝⎛=24167,987654321b A 况。
求解线性方程组Ax=b ，其中 ，我们仍可采用把矩阵A 约化为单位矩阵的方法，约化后得到()⎪⎪⎪⎭⎫ ⎝⎛-→→⎪⎪⎪⎭⎫ ⎝⎛=10000210010124987166547321, b A最后一行对应矛盾方程0=1，所以无解，Sage 的操作如下所示：请大家自己练习求解如下方程组，求解线性方程组Ax=b ，其中⎪⎪⎪⎭⎫ ⎝⎛=⎪⎪⎪⎭⎫ ⎝⎛=25167,987654321b A4.Sage中的编程4.1插值多项式def Newton_Interpolation(x):f(x)=1/(1+25*x^2)myPlot=plot(f(x),(x,-1,1),color='black')colors=['orange','green','blue','orange']step=0for n in [4,8,16,32]:points=[(((cos((2*i+1)*pi)/(2*n+2))).n(),f((cos((2*i+1)*pi)/(2*n+2))) .n()) for i in [0,1,..,n]]p(x)=Newton_Interpolation(x)myPlot+=plot(p(x),(x,-1,1),color=colors[step],legend_label="p"+str(n) +"(x)")step=step+1myPlot+=list_plot(points,color='red',size=70)myPlot.show()参考文献.[1] Atkinson.K,Han.W. Elementary Numercial Analysis,3rd edn. Wiley,New York，2003[2] Epperson,J.F. An Introuction to Numercial Mathematics and Analysis,revised edition.Wiley, Hobokoken，2007.[3] Sage Cell Server. /.Retrieved , 2014.[4] Stein W.A. Sage for power users./book/sagebook.pdf, 2012.。