text:
# Undefined control sequence \Hy@MakeCurrentHrefAuto when using tex4ht

I'm producing a small encyclopedia with the memoir class which relies fairly heavily on \nameref.

If it's relevant, I have my project directory set up so that I have a folder called articles/ which contains a bunch of .tex files, each beginning with a \section{} and then containing the article. I then have a build script which scans through all the files in the directory, adds chapters for each initial letter, and places these and \input{} statements in a tex file in the compile/ directory (adding "top" and "bottom" files around them), which is then compiled by pdflatex. (See the input file below if that doesn't make sense.) As I say, this works perfectly for pdflatex.

Now I want to produce an html version as well. latex2html, which I've used before, does not seem to support \nameref, so I went looking around and came upon tex4ht. I ran htlatex compile.tex, but it gets stuck when it reaches the first subsection:

/home/soren/current/maudiverse/./articles/history_abandonment.tex:4: Undefined
control sequence.
<argument> \Hy@MakeCurrentHrefAuto
{section*}\setlength {\Hy@SectionHShift }...
l.4 \subsection{Departure}

(I tried a couple of other commands that I found around the Web, since there seem to be a lot of different ways of calling tex4ht; they all gave the same error.)

MWE:

\documentclass[twocolumn]{memoir}
\usepackage[utf8x]{inputenc}
\usepackage{hyperref}

%\copypagestyle{maudcyclo}{plain}
%\createmark{section}{both}{shownumber}{\sectionname}{}

\begin{document}

% the dot in the middle of some paths is a funky consequence of how the build
% script combines paths; it does the same thing with it removed
\chapter{C}
\input{articles/communications.tex}
% ...and so on
\end{document}

When I uncomment the headers lines (which I use in the document), a somewhat different error occurs on the first section:

./compile.tex:11: Undefined control sequence.
<argument> \sectionname
\@nameuse {thesection}
l.11 \section{Section}

At some earlier point, though, before I had pruned it down to this little code, it was giving the same error as the subsection.

It looks like there's some problem with hyperref -- any idea what's making it unhappy? (Hopefully the solution would continue working with pdflatex as well.)

If useful, here's the full output before the error message I showed earlier (if other log files would be useful, let me know).

soren@Emily:~/current/maudiverse/compile\$ htlatex compile.tex
This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian)
restricted \write18 enabled.
entering extended mode
LaTeX2e <2011/06/27>
Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, lo
(./compile.tex (/usr/share/texlive/texmf-dist/tex/latex/memoir/memoir.cls
Document Class: memoir 2011/03/06 v3.6j configurable book, report, article docu
ment class
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty)
(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/etex-pkg/etex.sty)
(/usr/share/texlive/texmf-dist/tex/latex/memoir/mem10.clo)
(/usr/share/texlive/texmf-dist/tex/latex/memoir/mempatch.sty))
(/usr/share/texmf/tex/generic/tex4ht/tex4ht.sty)
(/usr/share/texmf/tex/generic/tex4ht/usepackage.4ht)
(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty
(/usr/share/texlive/texmf-dist/tex/latex/ucs/utf8x.def))
(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucs.sty
(/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-global.def))
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty))
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty)
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def)
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/url/url.sty)

Package hyperref Message: Stopped early.

) (/usr/share/texlive/texmf-dist/tex/latex/memoir/memhfixc.sty)

Package hyperref Message: Driver: htex4ht.

(/usr/share/texlive/texmf-dist/tex/latex/hyperref/htex4ht.def)
(/usr/share/texmf/tex/generic/tex4ht/tex4ht.4ht
::::::::::::::::::::::::::::::::::::::::::
TeX4ht info is available in the log file
::::::::::::::::::::::::::::::::::::::::::
) (/usr/share/texmf/tex/generic/tex4ht/tex4ht.sty
(/usr/share/texlive/texmf-dist/tex/latex/graphics/color.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/graphics/dvips.def)
(/usr/share/texlive/texmf-dist/tex/latex/graphics/dvipsnam.def))
--- needs --- tex4ht compile ---
(./compile.tmp) (./compile.xref) (/usr/share/texmf/tex/generic/tex4ht/html4.4ht
) (/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht)
(/usr/share/texmf/tex/generic/tex4ht/latex.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/fontmath.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/memoir.4ht
(/usr/share/texmf/tex/generic/tex4ht/book.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/verse.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/mempatch.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/inputenc.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/utf8x.4ht)
(/usr/share/texmf/tex/generic/tex4ht/ucs.4ht)
(/usr/share/texmf/tex/generic/tex4ht/hyperref.4ht
(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty))
Redoing nameref's sectioning
Redoing nameref's label
(/usr/share/texmf/tex/generic/tex4ht/nameref.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/pd1enc.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/url.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/color.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/dvips.4ht
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/dvipsnam.4ht
(/usr/share/texlive/texmf-dist/tex/latex/graphics/dvipsnam.def)
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht))
(/usr/share/texmf/tex/generic/tex4ht/html4.4ht)
(/usr/share/texmf/tex/generic/tex4ht/html4-math.4ht)) (./compile.aux)
(/usr/share/texlive/texmf-dist/tex/latex/ucs/ucsencs.def)
(/usr/share/texmf/tex/generic/tex4ht/utf8x.4ht) [1]
l.68 --- TeX4ht warning --- \halign translated into linear text ---
[2] [3] (./compile.4ct) [4]
(/home/soren/current/maudiverse/articles/communications.tex
/home/soren/current/maudiverse/articles/communications.tex:1: Undefined control
sequence.
<argument> \Hy@MakeCurrentHrefAuto
{section*}\setlength {\Hy@SectionHShift }...
l.1 \section{Communications}

?

-
could you post here also sample of included article? simple test file with just one \section and \subsection compiled fine for me –  michal.h21 Dec 11 '13 at 10:08
That's odd, the following test file (named a_test.tex) triggers it for me: \section{Test File} This is a test file that causes the problem. –  Soren Bjornstad Dec 11 '13 at 14:06
no, it is still OK. which TeX distribution do you use? –  michal.h21 Dec 11 '13 at 14:24
From my distro's package manager (Ubuntu/Mint), TeX Live 2012.20120611.5. Tex4HT 20090611-1.1build1. –  Soren Bjornstad Dec 11 '13 at 14:29


text:
## Pandemic blog 34: teaching on the screen

A small proportion of UW-Madison courses were being given in person, until last week, that is, but not mine. I’m teaching two graduate courses, introduction to algebra (which I’ve taught several times before) and introduction to algebraic number theory, which I’ve taught before but not for quite a few years. And I’m teaching them sitting in my chair at home. So I thought I’d write down a bit about what that’s like, since depending on who you ask, we’ll never do it again (in which case it’s good to record the memory) or this is the way we’ll all teach in the future (in which case it’s good to record my first impression.)

First of all, it’s tiring. Just as tiring as teaching in the classroom, even though I don’t have to leave my chair. This surprised me! But, introspecting, I think I actually draw energy from the state of being in a room with people, talking at the board, walking around, interacting. I usually leave class feeling less tired than when I walked in.

On the screen, no. I teach lectures at 10 and 11 and at noon when both are done I’m wiped out.

My rig, settled on after other setups kept glitching out: Notability open on iPad, I write notes as if on blackboard with the Apple Pencil, iPad connected by physical cable to laptop, screensharing to a window on the laptop which window I am sharing in Microsoft Teams to the class while the laptop camera and mic capture my face and voice.

What I have not done:

• Gotten a pro-quality microphone
• Set up a curated “lecture space” from which to broadcast
• Recorded lecture videos in advance so I can use the lecture hour for discussion
• Used breakout rooms in Teams to let the students discuss among themselves

All of these seem like good ideas.

So far (but I am still in the part of both courses where the material isn’t too hard) the students and I seem to find this… OK. My handwriting is somewhat worse on the tablet than it is on the blackboard and it’s not great on the blackboard. The only student who has told me they prefer online is one who reports being too shy to speak in class, sometimes too shy even to attend, and who feels more able to participate by typing in the chat window with the camera turned off. That makes sense!

I have it easy — these courses have only thirty students each, so the logistical work of handling student questions, homework, etc. isn’t overwhelming. Teaching big undergraduate courses presents its own problems. What happens with calculus quizzes? In the spring it was reported that cheating was universal (there are lots of websites that will compute integrals for you in another window!) So we now have a system called Honorlock which inhabits the student’s browser, watches IP traffic for visits to cheating sites, and commandeers the student’s webcam (!) to check whether their eye motions indicate cheating (!!) This sounds awful and frankly kind of creepy and not worth it. And the students, unsurprisingly, hate it. But then how does assessment work? The obvious answer is to give exams which are open book and which measure something more contentful about the material than can be tested by a usual quiz. I can think of two problems:

• Fluency with the basic manipulations (of both algebra and calculus) is actually one of the skills the class is meant to impart: yes, there are things a computer can do it’s good to be able to do mentally. (I don’t think I place a complicated trig substitution in this category, but knowing that the integral of x^n is on order x^{n+1}, yes.
• Tests that measured understanding would be different from and a lot harder than what students are used to! And this is a crappy time to be an undergraduate. I don’t think it’s a great idea for their calculus course to become, without warning, much more difficult than the one they signed up for.
Tagged , , ,

## Knuth, big-O calculus, implicit definitions (difficulty of)

Don Knuth says we should teach calculus without limits.

I would define the derivative by first defining what might be called a “strong derivative”: The function $f$ has a strong derivative $f'(x)$ at point $x$ if

$f(x+\epsilon)=f(x)+f'(x)\epsilon+O(\epsilon^2)$

I think this underestimates the difficulty for novices of implicit definitions.  We’re quite used to them:  “f'(x) is the number such that bla bla, if such a number exists, and, by the way, if such a number exists it is unique.” Students are used to definitions that say, simply, “f'(x) is bla.”

Now I will admit that the usual limit definition has hidden within it an implicit definition of the above kind; but I think the notion of limit is “physical” enough that the implicitness is hidden from the eyes of the student who is willing to understand the derivative as “the number the slope of the chord approaches as the chord gets shorter and shorter.”

Another view — for many if not most calculus students, the definition of the derivative is a collection of formal rules, one for each type of “primitive” function (polynomials, trigonometric, exponential) together with a collection of combination rules (product rule, chain rule) which allow differentiation of arbitrary closed-form functions.  For these students, there is perhaps little difference between setting up “h goes to 0” foundations and “O(eps)” foundations.  Either set of foundations will be quickly forgotten.

The fact that implicit definitions are hard doesn’t mean we shouldn’t teach them to first-year college students, of course!  Knuth is right that the Landau notation is more likely to mesh with other things a calculus student is likely to encounter, simultaneously with calculus or in later years.  But Knuth seems to say that big-O calculus would be self-evidently easier and more intuitive, and I don’t think that’s evident at all.

Maybe we could get students over the hump of implicit definitions by means of Frost:

Home is the place where, when you have to go there,

They have to take you in.

(Though it’s not clear the implied uniqueness in this definition is fully justified.)

If I were going to change one thing about the standard calculus sequence, by the way, it would be to do much more Fourier series and much less Taylor series.

Tagged , , ,

format: plain


text:
# The average weight of 5 packets is 24 kgs and the average weight of another 10 packets is 12 kgs, then average weight of 15 packets is ……………….

29 views

closed

The average weight of 5 packets is 24 kgs and the average weight of another 10 packets is 12 kgs, then average weight of 15 packets is ……………….

A) 6 Kgs

B) 16 Kgs

C) 10 Kgs

D) 36 Kgs

+1 vote
by (56.9k points)
selected by

Correct option is (B) 16 Kgs

Average weight of 15 packets $=\frac{5\times24+10\times12}{15}$

$=\frac{120+120}{15}$

$=\frac{240}{15}$ = 16 kg

+1 vote
by (42.4k points)

Correct option is  B) 16 Kgs


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A proof is an argument from hypotheses (assumptions) to a conclusion. Download Logic Calculator for free. In Example 1, the tilde is at the beginning of the statement, but it is followed immediately by a capital A, so the scope of the tilde is only the A, and the statement is not fundamentally a negation. I coded it to allow users of propositional logic to perform operations with the same ease as that offered by a mathematical calculator. Even if you are using just a fraction of the functionalities, the iphone-ish, easy-to-use interface makes life much easier. For many students translating is one of the hardest parts of learning how to do symbolic logic. calculator for a specific kind of modal logic, modal propositional logic, . Sympy : Symbolic Mathematics in Python — Scipy. Consider the statement to the right. Gödel also made (1931) the surprising discovery that number theory cannot be complete, i. (2) a and b are both in front of c; moreover, both are smaller than it. Type letters to represent variables. Thank you! [3] 2021/01/29 17:45 30 years old level / High-school/ University/ Grad student / Very /. An image is created in the tables and columns to show, How to generate truth table changes with true. Modernizing the sentential and predicate logic programs, Bertie and Twootie, by cleaning up the code, rewritting the code to conform to the standard Pascal defination, and developing a graphical user interface for both X and MS Windows. , an electronic health record) may open the web address of the ACS NSQIP surgical risk calculator in a new browser window. Includes some logic lessons and puzzles. Symbolic logic definition is - a science of developing and representing logical principles by means of a formalized system consisting of primitive symbols, combinations of these symbols, axioms, and rules of inference. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations. In logic, a disjunction is a compound sentence formed using the word or to join two simple sentences. The modern development begin with George Boole in the 19th century. It is simply the name given to the Morden treatment of deductive logic. Now let's put those skills to use by solving a symbolic logic statement. 5ReferenceManual:SymbolicLogic,Release9. Indirect proof is based on the classical notion that any given sentence, such as the conclusion, must be either true or false. The use of symbolic logic also makes reasoning formal and mechanical, contributing to the simplification of the reasoning and making it less prone to errors. 24K subscribers in the logic community. Online Calculator is a simple web application that lets you perform advanced calculations, plot 2D and 3D graphs, and make symbolic calculations such as differentiation. In the event that you seek guidance with algebra and in particular with symbolic equation solving online or negative exponents come pay a visit to us at Polymathlove. Use symbolic logic and logic algebra. Symbolic logic can be extended to involve concepts of number, and modalities such as knowledge and possibility. 'formula in propositional logic', in short: formulas. necessarily, if its premises are true, its conclusion is true), and to identify other important properties of arguments. Note carefully: it is understood here that if a formula replaces a given letter in one place, then the formula replaces the letter in every place. In this lesson, we will learn how to determine the truth values of a compound statement with the logical connectors ~, , and. Get the free "logic calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. It is a version of sentential logic, because the basic units of the language will represent entire sentences. Typical topics covered include: techniques of symbolization, truth tables, validity and soundness, and techniques of natural deduction. As a meta-language specifying the system, a logic programming language, namely, Prolog is adopted. The "turnstile" symbol, used in the context Γ⊢φ, means that, relative to the proof system we are working with, there is a derivation of the . We covered the basics of symbolic logic in the last post. Primitive Rule application using do statements. This tool generates truth tables for propositional logic formulas. If you are looking to learn a subject similar to Logic, tap into the nation's largest community of private tutors. A Selection from symbolic logic. Learn more about symbolic logic by exploring the basics of logic, truth tables, logical operators, and. The symbolic form of mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction. The symbolic form of mathematical logic is, '~' for negation '^' for conjunction and ' v ' for disjunction. The laws are named after Augustus De Morgan (1806-1871), who introduced a formal version of the laws to classical propositional logic. The key to solving this problem is to break it down into it's…. To generate a truth table for the statement " P → Q ," you would type a "P," then type a greater-than symbol (>), then type a "Q. integration) with symbolic expressions. Build a truth table for the formulas entered. Symbolic Logic The starting point for appreciating symbolic logic is the appreciation of the difference between simple statements and compound statements. Enter functions in standard mathematical notation, using x as independent variable. Find more Mathematics widgets in Wolfram|Alpha. Please let me know if anything should be added, something doesn't function properly, or text should be worded differently. 22 Symbolic Logic Study Guide: Class Notes 1. The Boolean expression for the AND logic gate is A ⋅ B = . Free Logical Sets calculator - calculate boolean algebra, truth tables and set theory step-by-step. Visual tool used to illustrate the relationship between two. Natural deduction proof editor and checker. Cookies are small text files stored by your web browser when you use websites. Propositional Logic Truth Table Calculator. In symbolic logic, one introduces symbols like p and q to stand for statements (or “propositions”) like “this is an interesting essay”. Think about logic as a generic way of writing rules: proving formulas and answering questions is a way of detecting what follows from the rules we wrote. Such API groups in a single module all the functions to construct formulae, to check the satisfiability and to retrieve Solver instances. Any list of three English sentences could be translated by three proposition symbols: p, q, r. For iPhone, iPod Touch and iPad. Even if you are using just a fraction of the functionalities, the iphone-ish, easy-to-use. What is Symbolic Logic Calculator. In Polish notation the logical operators are placed before the statement letters rather than between them. If you enter a modal formula, you will see a choice of how the accessibility relation should be constrained. Philosophy 254: Symbolic Logic is an introduction to reasoning in formal symbolic logic. Logical connectives, such as disjunction (symbolized ∨ . The only limitation for this calculator is that you have only three atomic propositions to choose from: p,qand r. Table of Logical Equivalences Commutative p^q ()q ^p p_q ()q _p Associative (p^q)^r ()p^(q ^r) (p_q)_r ()p_(q _r) Distributive p^(q _r) ()(p^q)_(p^r) p_(q ^r) ()(p_q. ; Conjunction is a truth-functional connective similar to "and" in English and is represented in symbolic logic with the dot " ". Index Terms: Boolean functions, symbolic manipulation, binary decision diagrams, logic design verification 1. As evident from the examples on this page, arguments to helper functions must be enclosed. The premier professional organization of logicians. There is NO calculator that can do it on the internet it seems. Logic Calculator Symbolic. A standard of a correct translation A (not the) logical symbolization of an English sentence is correct iff both are logically equivalent. Organic chemistry is the most difficult science course at the college only if it's GPA course is lower than that of genetics. 5 • PaulScurek(2013-08-12) sage. Obtained symbolic formula can be used with calculators Precision series, and with Graphing Calculator 2D Numeric, Graphing Calculator 2D Parametric, and Graphing Calculator 2D. When symbolizing English sentences in propositional logic, it is often helpful to work backwards, reversing the order in which well-formed formulas (WFFs) are constructed. ) and Windows (desktops, laptops, tablets, xbox ones) platforms. The specific system used here is the one found in forall x: Calgary. About Calculator Symbolic Logic. The Hex Calculator is used to perform addition, subtraction, multiplication and division on two hexadecimal numbers. Truth tables exhibit all the truth-values that it is possible for a given statement or set of statements to have. It follows that genetics is the most difficult science course at C-SC. For sure, this proof is completely . In economic crisis has never to. The facts and the question are written in predicate logic, with the question posed as a negation, from which gkc derives contradiction. Klaus Dethloff who taught this stuff and much more. Oh, well yes, using a dot instead of writing an ampersand or the word "AND" and using a triple bar instead of writing out "if and only if" must be time saving, although in math I was taught to use "iff" as the shorthand to "if and only if," but even then drawing three straight lines should be shorter than making at least 4. How does a calculator add two numbers together? · Representing numbers in binary · Converting decimal to binary · Using logic gates with binary. Symbolic Logic and the Logic of Symbolism. Each step of the argument follows the laws of logic. Look: Symbolic Logic II, Lecture 3. Your first 5 questions are on us!. 98 Symbolic Logic Study Guide: Practice Tests and Quizzes Problem 3. In the second form, images can be renamed to a different symbolic name, (a="NAME=img. This is an image tool that is used to. This method makes it possible to manipulate ideas mathematically in much the same way that numbers are manipulated. CL was originally invented as a continuation of the reduction of the set of logical constants to a singleton set in classical first-order logic (FOL). Place brackets in expressions, given the priority of operations. Logic and the Study of Arguments. There's a magma calculator online here, but your programs are limited to 60 seconds which should be sufficient for most things. If you are facing problems with symbolic equation solving online, why don’t you try Algebrator. [Use 'Falsum' for the '⊥' symbol] [Acceptable individual constants are: 'a', 'b', 'c', 'd', . Symbolic logic proof solver Please wait. We will give two facts: john is a father of pete and pete is a father of mark. Logic is the study of consequence. The thing solves algebra, and basic symbolic logic uses, well, I don't want to say the same sort of symbol manipulation because the overlap is imperfect, but both proofs and algebra work by manipulating symbols via a set of well-defined rules. The novel dramatizes the capacity of symbolic logic to redeem representation by locating positive value—aesthetic, social, and even spiritual—in the systematicity of formal interrelationships. Type in any function derivative to get the solution, steps and graph. Rather than trying to identify the simplest components of the sentence and build up from them, first try to determine whether the sentence as a whole is a negation, a conjunction, a disjunction. Symbolic logic is an expression of logic by using symbols in the place of natural language. Anyone who has attended Mathematics particularly Algebra and Probability, must have a good understanding of this diagram. The following is a list of characters that can be used. This is a versatile truth-table calculator for propositional logic. It's completely free and does not collect any information from its users. So we need precise de nitions of 'sentence' and 'follows from. Simple to use Truth Table Generator for any given logical formula. To enter logic symbols, use the buttons above the text field, . The only limitation for this calculator is that . Well-formed Formulas (WFFs) of Propositional Logic. Symbolic Logic, 66:3 (2001), 1121-1126. Association for Symbolic Logic. Here we'll survey the simplest variety of formal logic: sentential logic. Read from here about the differences between algorithms. It is to Kant that we owe the insight to not treat “existence” as a predicate, and of course Aristotlean logic did dominate Western philosophy for two thousand years –until modern symbolic logic was developed by people like Frege,Russell and Wittgenstein. Before you start: Be sure to study the Logic handout, and in particular familiarize yourself with the various English phrases expressing logical statements. Like any language, this symbolic language has rules of syntax—grammatical rules for putting symbols together in the right way. " Then you would hit the "Generate Truth Table" button. Basic Mathematical logics are a negation, conjunction, and disjunction. Verbal/logic thinkers — Verbal/logic thinkers tend to be good at learning languages, and have an affinity for words, literature, and speech. Denote missing numeric or date/time values with the missing value symbol * enclosed in single quotation marks ('*'). It has three modes: (1) Evaluation of logic formulae: In this mode we have the basic boolean operations (negation, conjunction, disjunction, conditional and biconditional) so the user can insert the logic formula and the Logic Calculator. The Propositional Logic Calculator. The following truth table gives the truth value of p ∨ q depending on the truth values of p and q. Translate the following English sentences into the formal language of the Tarski's World (50 points). It provides mental shorthand which permits one to say much in a small piece. The statement does not begin with a tilde, but with a bracket. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. It is also known as mathematical logic. A logical statement is a mathematical . Apparently the calculator was "hardly a part of application of symbolic logic", but Berkeley found a parallelism between the Complex Number Calculator and IBM punch card machine used in Prudential, and he learned the detail of Shannon's 1938 paper, that is, the relationship between Boolean. Solve polynomial and transcendental equations. In the rules of inference, it's understood that symbols like "P" and "Q" may be replaced by any statements, including compound statements. These symbolic representations can make it much easier to see whether a certain argument is valid (i. But if the original sentences had some common structure, showing . Yavuz Oruç and JavaScript, computes the truth value of a logic expression comprising up to four variables, w,x,y,z, two constants, 0,1 and sixty symbols ( . A Calculator to perform logical operations. The Propositional Logic Calculator The Propositional Logic Calculator finds all the models of a given propositional formula. Use the buttons below (or your keyboard) to enter a proposition, then gently touch the duck to have it. In this project we will study the basics of propositional and predicate logic based on the original historical source Principia Mathematica [13] by Russell . An introduction to formal deductive logic, covering propositional logic (truth-functional logic) and first-order predicate logic (quantification theory). Propositional logic uses a symbolic "language" to represent the logical structure, or form, of a compound proposition. DEFINITION OF SYMBOLIC LOGIC: This is a method of reasoning by employing symbols and other special symbols. A disjunction is true if either one or both of the statements in it is true. The logic module for SymPy allows to form and manipulate logic expressions using symbolic and Boolean values. Free Logical Sets calculator - calculate boolean algebra, truth tables and set theory step-by-step This website uses cookies to ensure you get the best experience. Ulti-mately, then, although its best-known legacy is the Boolean algebra that. Most people are already familiar with the use of letters and other symbols to represent both numbers and concepts. Evaluate expressions with arbitrary precision. A proposition In categorical logic, an A proposition is a universal affirmative proposition. This truth-table calculator for classical logic shows, well, truth-tables for propositions of classical logic. Primary connective (P ∧ Q) ∧ (Q ∨ R) T F F F F T T. Introduction to Symbolic Logic. This is a really trivial example. The laws are named after Augustus De Morgan (1806–1871), who introduced a formal version of the laws to classical propositional logic. For example, in an application of conditional elimination with citation "j,k →E", line j must be the conditional, and line k must be its antecedent, even if line k actually precedes line j in the proof. Apparently the calculator was “hardly a part of application of symbolic logic”, but Berkeley found a parallelism between the Complex Number Calculator and IBM punch card machine used in Prudential, and he learned the detail of Shannon’s 1938 paper, that is, the relationship between Boolean. For example, if I told you that a particular real-valued function was continuous on the interval $$[0,1]\text{,}$$ and $$f(0) = -1$$ and $$f(1) = 5\text{,}$$ can we conclude that there is some point between $$[0,1]$$ where the. Many statements can be combined with logical connections to form new statements. mathematics, HP-48SX (Calculator), Logic, Symbolic and mathematical, Symbolic and mathematical Logic HP 48SX engineering mathematics library | Open Library Read Book Hp 48sx Engineering Mathematics Library An Introduction To Symbolic And Complex Computation With Applications astonishing points. You can enter multiple formulas separated by commas to include more than one formula in a single table (e. Click the "Reference" tab for information on what logical symbols to use . It would be really helpful for quickly visualizing test cases for people like me who fumble a bit somewhere on longer inputs. Use the graphing calculator with logic symbols (boolean logic). Find Normal Forms of Boolean Expression: Conjunctive normal form (CNF), including perfect. We carry a good deal of quality reference materials on matters varying from graphs to square roots. Symbolic logic, however, does not aim at giving such insight" (Andrew Bachhuber, Introduction to Logic (New York: Appleton-Century Crofts, 1957), p. Grammar: What's a sentence? What are the rules that determine whether a string of symbols is a sentence, and when it is not?. Symbolic logic is the branch of mathematics that makes use of symbols to express logical ideas. Rather than trying to identify the simplest components of the sentence and build up from them, first try to determine whether the sentence as a. Go to Daemon Proof Checkeror Quick Help Index. In this paper we propose a Logic Calculator with three op- eration modes: evaluation of logical formulae; logical entailment and conversion of a formula to . If you don't understand what you read, then you will have a difficult time representing. Symbolic logic, and its notation, originated in the works of George Boole (1815-1864), of which Boole (1854) is the best known. You can select and try out several solver algorithms: the "DPLL better" is the best solver amongst the options. You can use and, or, not, then, equals , xor as well as symbols like -> for then etc. You can enter logical operators in several different formats. But it is more likely that the calculator logic will be pushing numbers down onto the stack every time a pair of brackets is opened or is implied by the. Atanasoff and graduate student Clifford Berry, of Iowa State College complete a prototype 16-bit adder. Symbolic Logic is a calculator that will enable you to build a logical statement using specific symbolic statements and once it is created you can evaluate its possible truth values that are. 2 How to determine the truth value of a sentence? (1) If the truth-values of component sentences of a compound sentence are given: From inside to outside! (when you determine the truth value of a sentence based on a Tarski’s World). The definition starts by stating that every atomic proposition is of that type, i. (3) But there is a third reason for the popularity of symbolic logic among philosophers, which is more substantial, for it involves a very important difference in philosophical belief. A little writeup by Piotr Bania. New features: Bugfix: disabled infinite branch detection, known to be using a defective algorithm which gives the wrong results in some cases, except for the straightforward detection of infinite branches due to applications of the modal. [+] Rules for Sentential Logic NOTE: the order in which rule lines are cited is important for multi-line rules. This calculator calculates derivative functions of high orders in symbolic and numeric forms. We honour the ancestry, heritage, and gifts of the Indigenous Peoples and give thanks to them. A Logic Calculator a web application that decides statements in symbolic logic including modal logic, propositional logic and unary predicate logic ⇚Home English|Español A Logic Calculator DecideDepictTruth TableExampleCounterexampleTree ProofCancel Quick Reference Information: What is this?. Barton, later wrote that he developed reverse Polish notation independently of Hamblin sometime in 1958 after reading a 1954 textbook on symbolic logic by . Athabasca University respectfully acknowledges that we live and work on the traditional lands of the Indigenous Peoples of Canada (First Nations, Inuit, Métis). 19 June 2020: Added a new dropdown box for all basic/normal modal logic variants - selecting an item in the dropdown sets the appropriate toggles of reflexivity, symmetry, transitivity, extendability, Euclidean and S5. Example 1 : Translate the following sentence into symbolic form : The earth is a planet. They don't belong to any symbolic logic that I know of. Symbolic logic is used in argumentation, hardware and software development and many different disciplines. Numerical values (and mathematical operator symbols) can be added to the expression directlly. Greek philosopher, Aristotle, was the pioneer of logical reasoning. Modal logic has its diamond and box inference rules, but from what I've seen of it used in Fitch's Symbolic Logic they have introduction and elimination rules as well. , that no matter what axioms are. SYMBOLIC LOGIC, for instance, shows the mind of Charles Lutwidge Dodgson rather than the whimsical Lewis Carroll. Symbolic logic has been extended to a description and analysis of the foundations of mathematics, particularly number theory. The syllogism and many other more complicated arguments. Items in the dropdown are prefixed by a number - equivalent modal logic. About Logic Symbolic Calculator. Grammar: What’s a sentence? What are the rules that determine whether a string of symbols is a sentence, and when it is not?. Venn Diagram Shading Calculator - Venn Diagram - The Definition and the Uses of Venn Diagram Venn Diagram Shading Calculator - You have most likely been exposed to or encountered the Venn diagram prior to. Since atomic propositions are the . I just started following your blog. The conditional operator ( → ) can be inserted if you press the shift key and the > key at the same time. This free app allows users of propositional logic to perform operations with the same ease as that offered by a mathematical calculator. It is dedicated to the memory of Dr. KEYBOARD MODELS COUNTERMODELS p q r p q r p q r p q r UNSAT TAUT CONTG ILL-FD Instructions. Chapter 7 focuses on simply translating regular English statements into a new symbolic language. This page contains a JavaScript program which will generate a truth table given a well-formed formula of truth-functional logic. Free derivative calculator - differentiate functions with all the steps. Example 2 : Translate the following sentence into symbolic form : David is not a soccer player. We apply certain logic in Mathematics. The purple box lists the keyboard symbols and the operations they represent. For example, if I told you that a particular real-valued function was continuous on the interval [0,1], [ 0, 1], and f(0)= −1 f ( 0) = − 1 and f(1)= 5, f ( 1) = 5, can. This may be achieved by parsing the bracketed expression before carrying out the calculation. The symbolic form of mathematical logic is, . Makoto Tsukada describes a proof checking program using Prolog. Boolean Algebra Calculator. Truth Table Calculator Use seven basic logic gates: AND, OR, XOR, NOT, NAND, NOR, and XNOR, as shown below with it,s Name, Boolean Equation, Symbol & Truth Table. So we need precise de nitions of ‘sentence’ and ‘follows from. Logic Symbolic Calculator. The bracket does not encompass the entire statement, so we could skip any connective within the brackets, but we will consider them, just for the sake of example. Rules of Inference and Logic Proofs. If either Hume did not invent truth tables or Wittgenstein wrote the Tractatus. ProofTools: a symbolic logic proof tree generator. We will cover the syntax and semantics of classical sentential and . In Propositional Logic, atomic propositions correspond to simple sentences in the object language. What is a proposition? paradox? open sentence? with Examples #1-9; What is Symbolic Logic? What are common connectives? Negate each statement (Examples . The calculator will give you an average over the percentage you have completed so far. Anyone who has studied Mathematics in particular Algebra and Probability, must have a good understanding of the Venn diagram. INTRODUCTION In the present chapter, we discuss how to translate a variety of English state-ments into the language of sentential logic. The propositional logic statements can only be true or false. All in one boolean expression calculator. Note that the lowercase "v" represents the "or" operations, so lowercase "v" cannot be used as a variable. Become a Symbolic Logic Homework Answers freelance writer with us! If you are an experienced, knowledgeable writer, do apply for work at our service! We offer beneficial working conditions and do our best for you to do your job most effectively. Truth Functionality: In order to know the truth value of the proposition which results from applying an operator to propositions, all that need be known is the definition of the operator and the truth value of the propositions used. I haven't started using your product, but I would like to get familiar with it. 146 Hardegree, Symbolic Logic Definition: If F is a formula of sentential logic, then a substitution instance of F is any formula F* obtained from F by substituting formulas for letters in F. To generate a truth table for the statement " P → Q ," you would type a "P," then type a greater-than symbol (>), then type. for certain strings of symbols to count as well-formed formulas, or. Alright, so now let's see if we can determine if an argument is valid or invalid using our logic rules. Mathematics is such a diverse subject, that it sometimes becomes tedious to understand every part with equal ease. The symbol for this is $$ν$$. Getting a contradiction shows us that it is. , the classic syllogism: All men are mortal. A toolkit for proving first order predicate logic formulas, answering questions and converting between different syntaxes for logic. 18 Symbolic Logic Study Guide: Class Notes 3. To use the app, enter a boolean logic expression below. · We use · One reason for having two symbols . Symbolic logic can be thought of as a simple and flexible shorthand: Consider the symbols: [ (p q) (q r)] (p r). Abbreviated Truth Table In constructing a reverse truth table, assume that all the premises are true and the conclusion is false, then consistently assign truth values to the components in an attempt to show that your assumption is correct. For example, (a -> b) & a becomes true if and only if both a and b are assigned true. Translating Sentences into Symbolic Form - Examples. Tool/Calculator to simplify or minify Boolean expressions (Boolean algebra) containing logical expressions with AND, OR, NOT, XOR. The three building options "truth table", "clause normal form" and a "parse tree" are simple, useful utilities: The truth table prints a full truth table of a formula up to 1024 rows: nice for checking out small propositional formulas. Mathematical Logic, truth tables, logical equivalence calculator - Prepare the truth table for Expression : p and (q or r)=(p and q) or (p and r), p nand q, p nor q, p xor q, Examine the logical validity of the argument Hypothesis = p if q;q if r and Conclusion = p if r, step-by-step online. The language this tool uses is a kind of symbolic logic. Download Logic Calculator Free - Latest version 4. There would be little logic in offering here the entire text of SYMBOLIC LOGIC. About Symbolic Calculator Logic. Giuseppe Castagna and Andrew D. What that means is that whether we know, for any given statement, that it is true or false does not get in the way of us knowing some other things about it in relation to certain other statements. Below is a ProB-based logic calculator. Symbolic logic is the simplest form of logic. Any expression that obeys the syntactic rules of propositional logic is called a well-formed. Symbolic logic calculator. Propositional Argument Validity Calculator. Rule do Application Explanation; Wedge Introduction: do X 3 vI L: X is the disjunct to be introduced, 3 is the line number to which Wedge Introduction needs to be applied and L denotes - introduce the argument X on left side. In mathematics, a statement is not accepted as valid or correct unless it is accompanied by a proof. Hi everyone, here's a validity calculator I made within Desmos. (Although based on forall x: an Introduction to Formal Logic, the proof system. The calculator will generate the truth table for the given logic formula/expression. Developed by George Boole, symbolic logic's main advantage is that it allows operations -- similar to algebra -- to work on the truth values of its propositions. Input values are different variables and symbols (commonly known as logic gates). Symbolic Logic Calculator ) and Windows (desktops, laptops, tablets, xbox ones) platforms. Set Notation Venn Diagram Calculator - Venn Diagram - The Definition and the Uses of Venn Diagram Set Notation Venn Diagram Calculator - Most likely, you've been exposed to or encountered a Venn diagram before. The rules of mathematical logic specify methods of reasoning mathematical statements. The converse of this statement is the related statement if Q, then P. Venn Diagram Shading Calculator. Truth-Functional Propositional Logic. We will ask whether from these two facts we can derive that john is a father of pete: obviously we can. There are many valid argument forms, however, that cannot be analyzed by truth-functional methods, e. A Logic Calculator a web application that decides statements in symbolic logic including modal logic, propositional logic and unary predicate logic ⇚Home English|Español A Logic Calculator DecideDepictTruth TableExampleCounterexampleTree ProofCancel Quick Reference Information: What is this? Instructions The Language The Algorithm Updates Contact. Operates the logical connectives (and, or, xor) of a pair of numbers expressed in Decimal, Hexadecimal, Octal , Senary or Binary form. 4 Sentential Logic This chapter introduces a logical language called SL. Featuring a purple munster and a duck, and optionally showing intermediate results, it is one of the better instances of its kind. Example 1: Given: p: 72 = 49 true q: A rectangle does not have 4. For the biconditional you may use any of the symbols: . Symbolic logic and set theory are intertwined and lie at the foundations of . Logic Calculator This simple calculator, the courtesy of A. (whenever you see $$ν$$ read 'or') When two simple sentences, p and q, are joined in a disjunction statement, the disjunction is expressed symbolically as p $$ν$$ q. What are the basic logic gates? · 1: Logic symbol of AND gate (Source: wikimedia. Calculational propositional logic is a product of researchers in the field of the formal development of algorithms. For modal predicate logic, constant domains and rigid terms are assumed. In Example 2, the tilde is followed by a parenthesis, and the entire rest of the statement is contained by the parentheses, so the statement is a negation, and the tilde is the main operator. linux x86 32-bit, GTK2 linux x86 32-bit, Qt linux x86 64-bit, GTK2 linux x86 64-bit, Qt5 win32 win64 mac osx x86. Russell’s paradox was very bad news to Frege (and not only to him!). Solving a classical propositional formula means looking for such values of variables that the formula becomes true. Raster Calculator (Spatial Analyst)—ArcGIS Pro. Mathematical Logic, truth tables, logical equivalence calculator - Prepare the truth table for Expression : p and (q or r)=(p and q) or (p and r), p nand q, . Calculator Symbolic Logic. The reasoning may be a legal opinion or mathematical confirmation. Here is the abstract: A proof system for propositional and predicate logic is discussed. About Logic Calculator Symbolic. Input two bits x;y and output two bits representing the absolute value of x−y 3. In symbolic logic, the disjunction of p and q is written p ∨ q. First, we will translate the argument into symbolic form and then determine if it matches one of our rules. Additionally, it helps prevent logical confusion. A conjunction is a compound statement formed by combining two statements using the word and. An online truth table calculator will provide the truth table values for the given propositional logic formulas. The calculate this better by the second of, and relationships between the way can i am an answer?. Full paths to data or data existing in the specified current . Logic NEW by: Anonymous Either organic chemistry or genetics is the most difficult science at culver Stockton college.


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The conductivity of a pure semiconductor is roughly proportional to
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The conductivity of a pure semiconductor is roughly proportional to $\mathrm{T}^{3 / 2} \mathrm{e}^{-\Delta \mathrm{E} / 2 \mathrm{kT}}$ where $\Delta \mathrm{E}_{\text {is }}$ the band gap. The band gap for germanium is $0.74 \mathrm{eV}$ at $4 \mathrm{k}$ and $0.67 \mathrm{eV}$ at $300 \mathrm{k}$. By what factor does the conductivity of pure germanium increase as the temperature is raised from $4 \mathrm{~K}$ to $300 \mathrm{~K}$ ?

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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

An algebraic expression consists of numbers and/or variables, often with operating signs and grouping symbols. An equation consists of two expressions separated by an equal sign. The equal sign tells us that the expressions on both sides of the equation have equal value. Therefore, $45=a-1$ is an equation, because its components are separated by an equal sign.


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# In what way is the Riemann curvature tensor related to 'radius of curvature'?

In Misner, Thorne & Wheeler, they say, in their delightful 'word equations' that

$$\left(\frac{\mathrm{radius\,\, of \,\,curvature}}{\mathrm{of\,\, spacetime}}\right) = \left(\frac{\mathrm{typical\,\, component\,\, of\,\, Riemann\,\, tensor}}{\mathrm{as\,\, measured\,\, in \,\,a \,\,local \,\,Lorentz\,\, frame}}\right)^{-\frac{1}{2}}.$$

My question is: does this definition of radius of curvature (and others like it - where tensor are described in words) depend on the valence of the Riemann curvature tensor?

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You link to a definition of curvature radius that is appropriate for "extrinsic" curvature – the curvature of a line/submanifold embedded into a higher-dimensional space. The Riemann tensor measures all the components of the intrinsic curvature so they're not exactly the same. However, they're of the same order and the MTW equation you mention is meant to be only an order-of-magnitude estimate, too. Of course, by the typical component, they mean roughly speaking the largest components. If some of them are zero, they're not typical.

To see that the estimate is right, just calculate the Riemann tensor for a sphere of radius $a$. You will get the Ricci scalar equal to something like $2/a^2$. The only thing you need to fix in your equation is the power. The typical component of the Riemann tensor goes like $a^{-2}$ where $a$ is the curvature radius. The power may be calculated by dimensional analysis. I guess that you – or they? – just forgot the power.

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Thanks for the reply. Your comment on the difference between in/extrinsic curvature is helpful (note that the links were added by Qmechanic). Also, very insightful is the comment on the word 'typical', +1 for those. Yes, I forgot the power, I'll edit that. Although, one thing I'm still not clear on is how the valence of the Riemann tensor affects its physical meaning, or does it not? E.g. does it matter if in the above equation we use $R^{a}_{bcd}$ or $R_{abcd}$? – user12345 Feb 16 '13 at 14:04
Thanks for your understanding. It shouldn't matter whether you raise/lower indices because you should be expressing the components in a local frame where the metric tensor is essentially the identity matrix, perhaps up to the signs (signatures), so the raising/lowering of indices just changes some signs. This form of the coordinates in which the metric tensor is this simple is imposed by the condition "local Lorentz frame" on the right hand side. Note that the signs of the Riemann tensor components must be ignored although there's a big difference between positive/negative curvature. – Luboš Motl Feb 16 '13 at 14:14
Oh, that's an interesting conclusion! – user12345 Feb 16 '13 at 14:22


text:
To clarify, are you asking the following: If Gurobi finds a feasible solution $$(\hat{x}, \hat{y})$$ to the above problem, is it guaranteed that $$\hat{y}_i = \max\{0, d \hat{x}_i\}$$ for all $$i$$? I'm assuming $$d$$ is a scalar and $$b \geq 0$$ (the latter must hold or the problem is unbounded).

If so, then no. This is only guaranteed at an optimal solution (assuming $$b > 0$$). However, for this specific problem, you can trivially improve a feasible solution by setting $$\hat{y}_i := \max\{0, d \hat{x}_i\}$$ for all $$i$$. Additionally, although the $$y$$ variables are not guaranteed to be tight against their constraints at a feasible solution found by Gurobi, I would be surprised if they weren't for this problem.

Ok , thank you. Yes, you understood the question correctly. Of course $$b \geq 0$$ and yes $$d$$ is a scalar.

For that trivial case, I could indeed use the max function. However, my problem is actually more complicated than this. I was just simplifying to explain the problem more easily. But when even this simple case is not guaranteed to be optimal, my actual case will not be either.

Overall your last sentence explains my observation as well: Mostly, the continuous variables seems to be tight/optimal. However, in some cases this is not true. For those cases, I was not sure if it is due to a bug in my code or due to the fact that the solution is not optimal and therefore my question.

But now it is clear. Thank you again.


text:
## CCC '96 S4 - When in Rome

View as PDF

Points: 10
Time limit: 2.0s
Memory limit: 64M

Problem type
##### 1996 Canadian Computing Competition, Stage 1, Problem D

If the Roman Empire had not fallen, then Rome would surely have discovered electricity and used electronic calculators; however, the Romans used Roman Numerals! Your task is to implement a simple Roman Calculator which accepts two Roman Numerals and outputs the sum in Roman Numerals. You may assume that numbers greater than 1000 will not occur in the input. Output numbers greater than 1000 are illegal and should generate the message CONCORDIA CUM VERITATE (In Harmony with Truth).

The input consists of a number, indicating the number of test cases, followed by this many test cases. Each test case consists of a single line with two numbers in Roman Numerals separated by a + along with an = at the end. There are no separating spaces.

For each test case the output is a copy of the input with the Roman Numeral that represents the sum. Outputs for different test cases are separated by a blank line.

#### Roman Research

The Roman Numerals used by the Romans evolved over many years, and so there are some variations in the way they are written. We will use the following definitions:

1. The following symbols are used: I for 1, V for 5, X for 10, L for 50, C for 100, D for 500, and M for 1000.
2. Numbers are formed by writing symbols from 1. from left to right, as a sum, each time using the symbol for the largest possible value. The symbols M, C, X, or I may be used at most three times in succession. Only if this rule would be violated, you can use the following rule:
• When a single I immediately precedes a V or X, it is subtracted. When a single X immediately precedes an L or C, it is subtracted. When a single C immediately precedes a D or M, it is subtracted. For example: II = 2; IX = 9; CXIII = 113; LIV = 54; XXXVIII = 38; XCIX = 99.

#### Sample Input

3
VII+II=
XXIX+X=
M+I=

#### Sample Output

VII+II=IX
XXIX+X=XXXIX
M+I=CONCORDIA CUM VERITATE

CCC problem statements in large part from the PEG OJ

• Narcariel  commented on Sept. 13, 2019, 12:22 p.m.

I am outputting the right and exact answer and it is giving me a WA? Help pls

• tzak_el  commented on Sept. 13, 2019, 2:46 p.m.

I've tested a few of your recent submissions, and none of them pass the sample input provided. I would recommend running your code through the sample input on your own to figure out what's wrong.

• Narcariel  commented on Sept. 14, 2019, 5:22 p.m.

Lol I lied something wrong withda output.

• Zafirua  commented on March 2, 2019, 3:38 p.m. edit 2

Removed Comment

• Ninjaclasher  commented on June 12, 2017, 9:12 p.m.

For example, if it was IIX, would that be 10, or 12? I find the problem statement about this section a bit confusing.

• Kirito  commented on June 12, 2017, 10:51 p.m.

IIX is not a valid Roman Numeral.

• Dordor1218  commented on March 18, 2018, 10:31 a.m. edited

I'm still kind of confused why it isn't a roman numeral? Update: never mind i found out why

• PaulOlteanu  commented on July 5, 2015, 9:36 p.m. edit 3

DMOJ output is different from my local machine.

Screenshot

Have I hardcoded too much for my submission to be illegitimate?


text: Haier Electronics Group, Forum Of Trajan, History Of C Language Ppt, Golmaal 1 Meme Template, Backus Hospital Phone Number, Space Station Silicon Valley Bug, Where To Sell Stuff In Skyrim,


text:
Increasing notebook magnification pushes output onto a new line

When I increase the notebook magnification beyond a certain level, it pushes the output of a command onto a newline.

It does this normally when you enter something like foo // FullForm, because Out[n]= gets replaced by Out[n]//FullForm=, which is so much wider that it has to start a newline for the output. But it's a shame that once n enters double-digits that at a certain magnification, the usual Out[n]= is just barely too wide, and this behavior occurs. Setting the magnification with

SetOptions[EvaluationNotebook[], Magnification -> 1.65]

is enough to get this behavior, but a magnification of 1.6 is still fine. Is there an easy way to avoid this behavior? Can we slightly increase the size of the margin where In[n]:= and Out[n]= live to avoid this issue?

I'm running Mathematica 11.0 in Linux x86 (64-bit), and apparently this is an issue on OS X too, but not on Windows.

• Possible duplicate of Out labels looks strange after turning on magnification – m_goldberg Feb 26 '17 at 23:24
• @m_goldberg Yeah that's about the same question, but the accepted answer of "just use 150% magnification" is a bit disappointing (sorry). The reason I came across this issue is that I'm preparing a presentation in Mathematica, and for the notebook text to be readable to my whole audience, I think I need the magnification to be in the 180% to 200% range. But then is sucks to lose that much vertical space when every output eats up an extra line. – Mike Pierce Feb 26 '17 at 23:46
• It is surprising to see this bug still exists after almost two years. Thank you for bringing this up, so I have got another solution. – vapor Feb 27 '17 at 7:30

You can increase the CellMargins for the styles "Input" and "Output" in your style sheet to accommodate the increased size of the cell labels. For example, the following setting:

CellMargins -> {{80, 10}, {10, 5}}

fixes the issue for me with a Magnification of 2.

If you don't want to mess around with editing the style sheet, you could evaluate the following instead:

SetOptions[
EvaluationNotebook[],
StyleDefinitions -> Notebook[{
Cell[StyleData[StyleDefinitions->"Default.nb"]],
Cell[StyleData["Input"],CellMargins->{{80,10},{10,5}}],
Cell[StyleData["Output"],CellMargins->{{80,10},{10,5}}]
}]
]

• I'm running SetOptions[EvaluationNotebook[], CellMargins -> {{200, 10}, {10, 5}}] and watching the corresponding option change in the Options Inspector, but there is no visible change in the notebook. :/ – Mike Pierce Feb 27 '17 at 0:06
• That's because you need to change the CellMargins of the "Input" and "Output" cells, not of the notebook. Do this in the style sheet of your notebook. You can test by selecting the Input/Output cell and setting it's CellMargins in the option inspector. – Carl Woll Feb 27 '17 at 0:10
• Ah! I got ya. I've never edited the stylesheet directly, so I was having a hard time figuring it out. But the SetOptions[...] command you posted works perfectly. Thank you. – Mike Pierce Feb 27 '17 at 1:01
• So Magnification doesn't affect Cell margins, right? I thought it magnifies everything... – Alexey Popkov Feb 27 '17 at 3:30


text:
What is the limit of  (sqrt(x^4 - 6x^2)) - x^2 as x goes to infinity?

Oct 19, 2015

${\lim}_{x \rightarrow \infty} \left(\sqrt{{x}^{4} - 6 {x}^{2}} - {x}^{2}\right) = - 3$

Explanation:

${\lim}_{x \rightarrow \infty} \left(\sqrt{{x}^{4} - 6 {x}^{2}} - {x}^{2}\right)$ has indeterminate form $\infty - \infty$.

So we'll do some algebra:

$\sqrt{{x}^{4} - 6 {x}^{2}} - {x}^{2} = \frac{\left(\sqrt{{x}^{4} - 6 {x}^{2}} - {x}^{2}\right)}{1} \cdot \frac{\left(\sqrt{{x}^{4} - 6 {x}^{2}} + {x}^{2}\right)}{\left(\sqrt{{x}^{4} - 6 {x}^{2}} + {x}^{2}\right)}$

$= \frac{\left({x}^{4} - 6 {x}^{2}\right) - {x}^{4}}{\sqrt{{x}^{4} - 6 {x}^{2}} + {x}^{2}}$ $\text{ }$ (has indeterminate form $\frac{\infty}{\infty}$)

$= \frac{- 6 {x}^{2}}{\sqrt{{x}^{4} \left(1 - \frac{6}{x} ^ 2\right)} + {x}^{2}}$ for $x \ne 0$

$= \frac{- 6 {x}^{2}}{\sqrt{{x}^{4}} \sqrt{\left(1 - \frac{6}{x} ^ 2\right)} + {x}^{2}}$ for $x \ne 0$

$= \frac{- 6 {x}^{2}}{{x}^{2} \left(\sqrt{1 - \frac{6}{x} ^ 2} + 1\right)}$ for $x \ne 0$

$= \frac{- 6}{\sqrt{1 - \frac{6}{x} ^ 2} + 1}$ for $x \ne 0$

Now as $x \rightarrow \infty$, we see that the ratio $\rightarrow \frac{- 6}{2}$

So, ${\lim}_{x \rightarrow \infty} \left(\sqrt{{x}^{4} - 6 {x}^{2}} - {x}^{2}\right) = - 3$

Note that because the identity $\sqrt{{x}^{4}} = {x}^{2}$ is true for both positive and negative values of $x$, we also have

${\lim}_{x \rightarrow - \infty} \left(\sqrt{{x}^{4} - 6 {x}^{2}} - {x}^{2}\right) = - 3$


text:
# Is it possible to compile hidden files?

(This question may make sense only in Linux.)

I have the following simple file called .main.tex. Note that it is a "hidden" file because of its name.

\documentclass[]{article}
\begin{document}
sample
\end{document}

I cannot compile it the usual way pdflatex .main.tex because I get this error:

$pdflatex .interpolation.tex This is pdfTeX, Version 3.1415926-2.6-1.40.14 (TeX Live 2014/dev) restricted \write18 enabled. entering extended mode (./.main.tex ... No file .main.aux. pdflatex: Not writing to .main.aux (openout_any = p). ! I can't write on file .main.aux'. \document ...ate \openout \@mainaux \jobname .aux \immediate \write \@mainau... l.4 \begin{document} (Press Enter to retry, or Control-D to exit; default file extension is .tex') Please type another output file name:  Of course if the filename were main.tex it would work. Is there a workaround to compile dot files directly? Or is this another limitation of how TeX detects file extensions (confused by the dots)? Note that other related but different questions where asked before, this is however different: (limitations of extension handling) How to avoid automatic .tex extension in filenames? - ## 1 Answer It depends on how paranoid your settings in texmf.cnf are. Mine (default texlive 2014) says: % Allow TeX \openin, \openout, or \input on filenames starting with .' % (e.g., .rhosts) or outside the current tree (e.g., /etc/passwd)? % a (any) : any file can be opened. % r (restricted) : disallow opening "dotfiles". % p (paranoid) : as r' and disallow going to parent directories, and % restrict absolute paths to be under$TEXMFOUTPUT.
openout_any = p
openin_any = a

So this gives the error you get, tex can read your main file, but is prevented from writing the aux file with a name starting with a dot.

note r prevents opening dotfiles.

-
openout_any = a in my /usr/share/texlive/texmf-dist/web2c/texmf.cnf (line 598) solved it. This also explains why I was never able to compile from a different directory! (It is the first time I see that creating dot files is a security problem.) – alfC Aug 30 '14 at 8:48
@alfC if you leave it as a generally then copying a malicious MWE from a tex web site and running it could trash your system files like .profile .login etc... unless you are totally sure what the macros are doing – David Carlisle Aug 30 '14 at 8:55
Shouldn't you make these changes in /usr/local/texlive/2014/texmf.cnf rather than in texmf-dist/web2c/texmf.cnf? That is, according to the comments at the top of the former file, customisations should not me made in the latter but only the former. – cfr Apr 19 at 21:04
@cfr yes but you need to look in the system one to see the current settings. In general better to then put the new values in a local cfg so not overwritten by updates, although tl2014 isn't likely to be updated now anyway. – David Carlisle Apr 20 at 8:05
@DavidCarlisle Yes, of course. But your answer here is being taken as a template for making changes for later editions of TeX Live and interpreted as telling people to make the changes in the system file. Since this is not good practice, it would be better, in my opinion, not to encourage it. That is, you may know not to make the changes in the system file for TL 2015 or 2016 or whatever, but your answer suggests it is fine to do that. I know it doesn't say that. But that's the way it is being interpreted, which is the only reason I commented. (& if David says it is OK, it must be, right?) – cfr Apr 20 at 17:20


text:
### Author Topic: Will the laplacian in other coordinates be given on the term test?  (Read 1003 times)

#### George Lu

• Jr. Member
• Posts: 8
• Karma: 5
##### Will the laplacian in other coordinates be given on the term test?
« on: March 21, 2018, 04:57:51 PM »
Similarly, how familiar should we be with Euler equations?


text:
# [Tugindia] Fancyhdr

Dhiraj Khanna dhirajkhanna at gmail.com
Mon Mar 27 18:04:37 CEST 2006

Hello All,
I am using the fancyhdr package to change the page numbering of my report so
that it appears at the bottom right hand cornor using the following code:
\tableofcontents
\clearpage
\pagestyle{fancy}
\fancyfoot{}
\pagenumbering{arabic}
\rfoot{\thepage}
\input{Intro}
For the first page of each chapter I inserted the following code to ensure
that the first page of each chapter is also bottom right justified:
\chapter{Introduction}
\thispagestyle{fancy}
(Pg 92 of the LaTeX Companion)
However, the same doesn't seem to be working for my bibliography. I tried
inserting the same command in my .bbl file
\begin{thebibliography}{10}
\thispagestyle{fancy}
In spite of this, the page number on the first page of Bibliography appears
in the bottom center, leaving me quite perplexed.
Can someone come up with a fancy solution to this rather unfancy fancyhdr
problem?????

Thanks,
Dhiraj


text:
## Motivation.

The quaternion form of Maxwell’s equations as stated in [2] is nearly indecipherable. The modern quaternionic form of these equations can be found in [1]. Looking for this representation was driven by the question of whether or not the compact geometric algebra representations of Maxwell’s equations $$\grad F = J$$, was possible using a quaternion representation of the fields.

As quaternions may be viewed as the even subalgebra of GA(3,0), it is possible to the quaternion representation of Maxwell’s equations using only geometric algebra, including source terms and independent of the heat considerations discussed in [1]. Such a derivation will be performed here. Examination of the results appears to answer the question about the compact representation in the negative.

## Quaternions as multivectors.

Quaternions are vector plus scalar sums, where the vector basis $$\setlr{ \Bi, \Bj, \Bk }$$ are subject to the complex like multiplication rules
\label{eqn:complex:240}
\begin{aligned}
\Bi^2 &= \Bj^2 = \Bk^2 = -1 \\
\Bi \Bj &= \Bk = -\Bj \Bi \\
\Bj \Bk &= \Bi = -\Bk \Bj \\
\Bk \Bi &= \Bj = -\Bi \Bk.
\end{aligned}

We can represent these basis vectors in terms of the \R{3} unit bivectors
\label{eqn:quaternion2maxwellWithGA:260}
\begin{aligned}
\Bi &= \Be_{3} \Be_{2} = -I \Be_1 \\
\Bj &= \Be_{1} \Be_{3} = -I \Be_2 \\
\Bk &= \Be_{2} \Be_{1} = -I \Be_3,
\end{aligned}

where $$I = \Be_1 \Be_2 \Be_3$$ is the ordered product of the \R{3} basis elements. Within geometric algebra, the quaternion basis “vectors” are more properly viewed as a bivector space basis that happens to have dimension three.

Following [1], we may introduce a quaternionic spacetime gradient, and express that in terms of geometric algebra
\label{eqn:quaternion2maxwellWithGA:280}
\frac{d}{dr} = \inv{c} \PD{t}{}
+ \Bi \PD{x}{}
+ \Bj \PD{y}{}
+ \Bk \PD{z}{}
=

Of particular interest is how do we write the curl, divergence and time partials in terms of the quaternionic spacetime gradient or its components. Like [1], we will use modern commutator notation for an antisymmetric difference of products
\label{eqn:quaternion2maxwellWithGA:600}
\antisymmetric{a}{b} = a b – b a,

and anticommutator notation for a symmetric difference of products
\label{eqn:quaternion2maxwellWithGA:620}
\symmetric{a}{b} = a b + b a.

The curl of a vector $$\Bf$$ in terms of vector products with the gradient is
\label{eqn:quaternion2maxwellWithGA:300}
\begin{aligned}
&= \inv{2} \antisymmetric{ -I \spacegrad }{ \Bf } \\
&= \inv{2} \antisymmetric{ \frac{d}{dr} }{ \Bf },
\end{aligned}

where the last step takes advantage of the fact that the timelike contribution of the spacetime gradient commutes with any vector $$\Bf$$ due to its scalar nature, so cancels out of the commutator. In a similar fashion, the dot product may be written as an anticommutator
\label{eqn:quaternion2maxwellWithGA:480}
=
=

as can the scalar time derivative
\label{eqn:quaternion2maxwellWithGA:500}
\PD{t}{\Bf}
= \inv{2} \symmetric{ \inv{c} \PD{t}{} } { c \Bf }.

## Quaternionic form of Maxwell’s equations.

Using geometric algebra as an intermediate transformation, let’s see directly how to express Maxwell’s equations in terms of this quaternionic operator. Our starting point is Maxwell’s equations in their standard macroscopic form

\label{eqn:ece2500report:20}
\spacegrad \cross \BH = \BJ + \PD{t}{\BD}

\label{eqn:quaternion2maxwellWithGA:340}

\label{eqn:quaternion2maxwellWithGA:360}
\spacegrad \cross \BE = – \PD{t}{\BB}

\label{eqn:quaternion2maxwellWithGA:380}

Inserting these into Maxwell-Faraday and into Gauss’s law for magnetism we have
\label{eqn:quaternion2maxwellWithGA:400}
\begin{aligned}
\inv{2} \antisymmetric{ \frac{d}{dr} }{ \BE } &= – \symmetric{ \inv{c}\PD{t}{} }{ c \BB } \\
\inv{2} \symmetric{ \spacegrad }{ c \BB } &= 0,
\end{aligned}

or
\label{eqn:quaternion2maxwellWithGA:420}
\begin{aligned}
\inv{2} \antisymmetric{ \frac{d}{dr} }{ -I \BE } + \symmetric{ \inv{c}\PD{t}{} }{ -I c \BB } &= 0 \\
\inv{2} \symmetric{ -I \spacegrad }{ -I c \BB } &= 0
\end{aligned}

We can introduce quaternionic electric and magnetic field “vectors” (really bivectors)
\label{eqn:quaternion2maxwellWithGA:440}
\begin{aligned}
\boldsymbol{\mathcal{E}} &= -I \BE = \Bi E_x + \Bj E_y + \Bk E_z \\
\boldsymbol{\mathcal{B}} &= -I \BB = \Bi B_x + \Bj B_y + \Bk B_z,
\end{aligned}

and substitute these and sum to find the quaternionic representation of the two source free Maxwell’s equations
\label{eqn:quaternion2maxwellWithGA:460}
\boxed{
\inv{2} \antisymmetric{ \frac{d}{dr} }{ \boldsymbol{\mathcal{E}} } + \inv{2} \symmetric{ \frac{d}{dr} }{ c \boldsymbol{\mathcal{B}} } = 0.
}

Inserting the quaternion curl, div and time derivative representations into Ampere-Maxwell’s law and Gauss’s law, gives
\label{eqn:quaternion2maxwellWithGA:520}
\begin{aligned}
\inv{2} \antisymmetric{ \frac{d}{dr} }{ \BH } &= \BJ + \inv{2} \symmetric{ \inv{c} \PD{t}{} } { c \BD } \\
\inv{2} \symmetric{ \spacegrad }{ c \BD } &= c \rho,
\end{aligned}

\label{eqn:quaternion2maxwellWithGA:540}
\begin{aligned}
\inv{2} \antisymmetric{ \frac{d}{dr} }{ -I \BH } – \inv{2} \symmetric{ \inv{c} \PD{t}{} } { -I c \BD } &= -I \BJ \\
-\inv{2} \symmetric{ -I \spacegrad }{ -I c \BD } &= c \rho.
\end{aligned}

With quaternionic displacement vector and magnetization, and current densities
\label{eqn:quaternion2maxwellWithGA:580}
\begin{aligned}
\boldsymbol{\mathcal{D}} &= -I \BD = \Bi D_x + \Bj D_y + \Bk D_z \\
\boldsymbol{\mathcal{H}} &= -I \BH = \Bi H_x + \Bj H_y + \Bk H_z \\
\boldsymbol{\mathcal{J}} &= -I \BJ = \Bi J_x + \Bj J_y + \Bk J_z,
\end{aligned}

and summing yields the two remaining two Maxwell equations in their quaternionic form
\label{eqn:quaternion2maxwellWithGA:560}
\boxed{
\inv{2} \antisymmetric{ \frac{d}{dr} }{ \boldsymbol{\mathcal{H}} } – \inv{2} \symmetric{ \frac{d}{dr} } { c \boldsymbol{\mathcal{D}} } = c \rho + \boldsymbol{\mathcal{J}}.
}

## Conclusions.

Maxwell’s equations in the quaternion representation have a structure that is not apparent in the Heaviside-Gibbs notation. There is some elegance to this result, but comes with the cost of having to use commutator and anticommutator operators, which are arguably non-intuitive. The compact geometric algebra representation of Maxwell’s equation does not appear possible with a quaternion representation, as an additional complex degree of freedom would be required (biquaternions?) Such a degree of freedom may also allow a quaternion representation of the (fictitious) magnetic sources that are useful in antenna theory with a quaternion model. Magnetic sources are easily incorporated into the current multivector in geometric algebra, but if done so in the derivation above, yield an odd grade multivector source which has no quaternion representation.

# References

[1] Peter Michael Jack. Physical space as a quaternion structure, i: Maxwell equations. a brief note. arXiv preprint math-ph/0307038, 2003. URL https://arxiv.org/abs/math-ph/0307038.

[2] James Clerk Maxwell. A treatise on electricity and magnetism, volume II. Merchant Books, 1881.