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Topic: Polish notation

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	PlanetMath: Polish notation
		Whereas operators are traditionally placed between operands, with parentheses used to override operator precedence, it is possible to place each operator to the left of its operands, thus eliminating ambiguity and the need for parentheses, and even the need for rules of operator precedence.
		Polish notation is a system of notating mathematical operations (whether arithmetic, logical, etc.) where the operators precede their operands and the ambiguities of operator precedence and the need for parentheses are altogether eliminated.
		This is version 16 of Polish notation, born on 2006-08-11, modified 2006-10-23.
	planetmath.org /encyclopedia/PolishNotation.html (506 words)

	Polish notation - Wikipedia, the free encyclopedia
		Polish notation, also known as prefix notation, is a method of mathematical expression.
		While the examples above use parentheses, one of the benefits of Polish notation is that, assuming the arity of each operator is known, parentheses are unnecessary: the order of operations is unique and easy to determine, provided that the expression is well-formed.
		Polish notation has not seen wide application, but a variant called reverse Polish notation, or postfix notation, is used in many stack-based programming languages, and is the operating principle of certain calculators, notably from Hewlett-Packard.
	en.wikipedia.org /wiki/Polish_notation (161 words)

	Reverse Polish notation - Wikipedia, the free encyclopedia
		Reverse Polish notation (RPN), also known as postfix notation, was invented by Australian philosopher and computer scientist Charles Hamblin in the mid-1950s, to enable zero-address memory stores.
		It is derived from the Polish notation, which was introduced in 1920 by the Polish mathematician Jan Łukasiewicz.
		As a user interface for calculation the notation was first used in Hewlett-Packard's desktop calculators from the late 1960s and then in the HP-35 handheld scientific calculator launched in 1972.
	en.wikipedia.org /wiki/Reverse_Polish_Notation (1283 words)

	PlanetMath: reverse Polish notation
		Whereas operators are traditionally placed between operands, with parentheses used to override operator precedence, it is possible to place operators to the right of operands, thus eliminating ambiguity and the need for parentheses, and even the need for rules of operator precedence.
		Invented by Australian philosopher Charles Hamblin, reverse Polish notation requires that the number of operands of a given operator be defined in advance.
		This is version 3 of reverse Polish notation, born on 2006-08-14, modified 2006-11-10.
	planetmath.org /encyclopedia/ReversePolishNotation.html (327 words)

	Reverse Polish Notation \| World of Computer Science
		The Polish notation, named after its creator Polish mathematician Jan Lukasiewicz (1878-1956), was created in the 1920s for use in evaluating expressions in symbolic logic.
		Reverse Polish Notation is a way of expressing arithmetic expressions fully and unambiguously while avoiding the use of brackets to define operator precedence.
		In the Reverse Polish Notation, numbers and operators are listed one after the other, and an operator always acts on the closest numbers on the list.
	www.bookrags.com /research/reverse-polish-notation-wcs (808 words)

	[No title]
		In Reverse Polish Notation, or RPN, there is no concept of precedence, nor is there any requirement for parentheses or an equals key.
		RPN, or reverse polish notation requires that the user enter the problem to be calculated in a fashion completely different than what most people are accustomed to.
		The parsing algorithm for terms is actually applicable to Polish notation in general, and shows that Polish notation is unambiguous.
	www.lycos.com /info/reverse-polish-notation.html (391 words)

	Siris: Polish Notation (Site not responding. Last check: 2007-10-21)
		Polish notation is a prefix notation for invented by the great Łukasiewicz in order to simplify propositional logic (it was expanded from there and later standardized).
		In Polish notation, of course, they are all letters of the alphabet, so you have to get used to how they work, and that takes more doing than in Peano-Russell.
		That's why people trained in Peano-Russell have difficulty reading Polish notation, despite the fact that the two are merely different notations portraying exactly the same logical operations: they aren't seeing the logical operations at all.
	branemrys.blogspot.com /2006/07/polish-notation.html (1327 words)

	Reverse Polish Notation (Site not responding. Last check: 2007-10-21)
		Polish notation was described in the 1920s by Polish mathematician Jan Lukasiewicz as a logical system for the specification of mathematical equations without parentheses.
		Equation with parenthesis (1 + 2) * 3 Prefix notation * 3 + 1 2 or * + 1 2 3 Postfix notation 1 2 + 3 * or 3 1 2 + *
		The basic reverse Polish calculator algorithm is to key in a number.
	users.ece.gatech.edu /~mleach/revpol (1173 words)

	Reverse Polish notation - Uncyclopedia, the content-free encyclopedia
		Reverse Polish notation is a variant of the Russian reversal techniques invented by the Warsaw Pact during the Cold War.
		Reverse Polish notation was used in the manufacture of poor-quality calculators by oppressive Soviet-controlled Warsaw Pact régimes.
		The Warsaw Pact forces were ultimately defeated by the US-backed armies of Texas Instruments, ending the menace of reverse Polish notation once and for all.
	uncyclopedia.org /wiki/Reverse_polish_notation (269 words)

	GameDev.net - Understanding Reverse Polish Notation
		The conventional mathematical notation we learned in high school is known as "Algebraic Notation." In this notation, the operators are placed either between or in front of the arguments.
		This method is known as Reverse Polish Notation, or RPN, in honor of the original method.
		RPN, like Polish Notation, is unambiguous: the order and only the order of arguments and operators will determine the result.
	www.gamedev.net /reference/articles/article430.asp (1179 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-21)
		The original(prefix) Polish Notation for this is -+ABC and it is AB+C- in (postfix) Reverse Polish Notation.
		He invented (Forward) Polish Notation, where the operator (+, *, etc) is placed to the left of the operands.
		The inventor of Reverse Polish Notation was the Australian philosopher, Charles Hamblin (1922-1985), who implemented it in the computer language GEORGE in 1957.
	mathforum.org /library/drmath/view/60850.html (515 words)

	Reverse Polish Notation
		In the 1920's, Jan Lukasiewicz developed a formal logic system which allowed mathematical expressions to be specified without parentheses by placing the operators before (prefix notation) or after (postfix notation) the operands.
		Prefix notation is known as Polish Notation after the nationality of Lukasiewicz.
		Similarly, postfix notation is known as Reverse Polish Notation (RPN).
	home.att.net /~srschmitt/reversepolish.html (491 words)

	RPN - Reverse Polish Notation
		Most complex expressions could not be expressed in conventional arithmetic notation without brackets, and they are often used in computer programming even when they are not strictly required, simply to eliminate confusion.
		Polish Notation was invented in the 1920's by Polish mathematician Jan Lukasiewicz, who showed that by writing operators in front of their operands, instead of between them, brackets were made unnecessary.
		Although Polish Notation was developed for use in the fairly esoteric field of symbolic logic, Lukasiewicz noted that it could also be applied to arithmetic.
	www.calculator.org /rpn.html (830 words)

	Liturgica.com \| Liturgics \| Eastern Orthodox Liturgics \| Chant Development \| Lesser Known Varieties Of Russian Chant
		Whereas the Kondakarian notation is an independent system of neumes, the Put’ notation is derived in part from the established Stolp notation or “kriuki” used for Znammeny Chant.
		Later it was transcribed into both stolp neumation and “Kievan” staff notation, the former for the use of Old Ritualists and the latter for use in the state Church.
		The demise of the kondakarian notation, as we have seen, accompanied a great liturgical transition originating in Byzantium and spreading to Rus’: the demise of the old rite of the Great Church, and the transition from the Studite to the Sabbaite Typikon, which became the norm for both monastic and ‘secular’ churches.
	www.liturgica.com /html/litEOLitMusDev6.jsp?hostname=liturgica (2086 words)

	Polish Notation (Site not responding. Last check: 2007-10-21)
		Polish Notation is a way of expressing arithmetic expressions that avoids the use of brackets to define priorities for evaluation of operators.
		The 'reversed' form, Reverse Polish Notation (RPN), has however been found more convenient from a computational point of view.
		In Polish Notation, one has to parse the expression recursively to obtain the operands for each operator.
	c2.com /cgi/wiki?PolishNotation (440 words)

	Reverse Polish Notation (Site not responding. Last check: 2007-10-21)
		The principle of precendence of operators can be used to determine the structure of expressions and transform them into an equivalent, parenthesis free, notation called 'post-fix' or Reverse Polish notation.
		The method requires the use of a stack for holding the operators, and each operator to have a priority value assigned to it, as in the operator precedence method.
		In this notation no parentheses are necessary to regulate the order of evaluation.
	www.cs.um.edu.mt /~hzarb/CSM201/notes/lecture6/node8.html (218 words)

	RPN
		Prefix notation also came to be known as Polish Notation in honor of Lukasiewicz.
		HP adjusted the postfix notation for a calculator keyboard, added a stack to hold the operands and functions to reorder the stack.
		By contrast, expressions with parentheses and precedence (infix notation) require that operators be delayed until some later point.
	www.hpmuseum.org /rpn.htm (1759 words)

	HP calculators / RPN, An Introduction to Reverse Polish Notation
		Reverse Polish Notation was developed in 1920 by Jan Lukasiewicz as a way to write a mathematical expression without using parentheses and brackets.
		Hewlett-Packard Co., realizing that Lukasiewicz's method was superior to standard algebraic(1) expressions when using calculators and computers, adapted RPN for its first hand-held scientific calculator, the HP35, in 1972.
		Algebraic mode: This is the name of the mathematic notation used on all non-RPN calculators where you enter a mathematic equation like this: 1+3*(3+(2-5)/3).
	www.hp.com /calculators/news/rpn.html (719 words)

	Parsing Polish notation (Site not responding. Last check: 2007-10-21)
		Polish notation as introduced by Jan Lukasiewicz, where operators (capital letters) precede their operands, is extremely compact, free of parentheses and yet unambiguous, and can easily be entered on a keyboard, but are hard to read, e.g.
		Conventional notation is more intuitive and closer to algebraic formulas, but uses special characters that you need a good Unicode font for.
		Polish notation is best parsed from right to left (that's why Reverse Polish Notation is more popular - see RPN in Tcl), so first I reverse the order of the PN symbols.
	wiki.tcl.tk /2456 (229 words)

	Reverse Polish notation Summary
		Reverse Polish notation (RPN), also known as postfix notation, was invented by Australian philosopher and computer scientist Charles Hamblin in the mid-1950s, to enable zero-address memory stores.
		It is derived from the Polish notation, which was introduced in 1920 by the Polish mathematician Jan Łukasiewicz.
		For a computer, it is easier and faster to evaluate mathematical expressions written in RPN than mathematical expressions written in infix notation.
	www.bookrags.com /Reverse_Polish_notation (2199 words)

	Polish notation definition - Dictionary - MSN Encarta
		Polish notation definition - Dictionary - MSN Encarta
		Search for "Polish notation" in all of MSN Encarta
		type of notation for symbolic logic: a notation for symbolic logic where the logical operators are placed as prefixes in front of formulas instead of between them, allowing parentheses to be dispensed with.
	encarta.msn.com /encnet/features/dictionary/DictionaryResults.aspx?refid=1861738207 (110 words)

	reverse polish notation
		Reverse Polish Notation is a way of expressing arithmetic expressions that avoids the use of brackets to define priorities for evaluation of operators.
		Polish Notation was devised by the Polish philosopher and mathematician Jan Lucasiewicz (1878-1956) for use in symbolic logic.
		In his notation, the operators preceded their arguments, so that the expression above would be written as
	www.ch.cam.ac.uk /cil/SGTL/rpn.html (307 words)

	postfix notation from FOLDOC (Site not responding. Last check: 2007-10-21)
		(Or "Reverse Polish Notation", RPN) One of the possible orderings of functions and operands: in postfix notation the functions are preceded by all their operands.
		Postfix notation is well suited for stack based architectures but modern compilers reduced this advantage considerably.
		The best-known language that with strictly postfix syntax is FORTH.
	lgxserver.uniba.it /lei/foldop/foldoc.cgi?Reverse+Polish+Notation (87 words)

	What is Polish notation? - a definition from Whatis.com - see also: Polish logic, prefix notation, postfix notation
		- Polish notation, also known as prefix notation, is a symbolic logic invented by Polish mathematician Jan Lukasiewicz in the 1920's.
		In Polish notation, the order (and only the order) of operations and operands determines the result, making parentheses unnecessary.
		Reverse Polish notation provided a straightforward solution for calculator or computer software mathematics because it treats the instructions (operators) and the data (operands) as "objects" and processes them in a last-in, first-out (LIFO) basis.
	searchcio.techtarget.com /sDefinition/0,,sid19_gci824619,00.html (522 words)

	Linguistic Annotation
		The added notations may include transcriptions of all sorts (from phonetic features to discourse structures), part-of-speech and sense tagging, syntactic analysis, "named entity" identification, co-reference annotation, and so on.
		HIAT is a transcription system based on a score notation, developed in the 1970's by Ehlich and Rehbein, and widely used in Europe.
		The project grows out of the experience with CHILDES and LDC corpora, and aims to support the methodologies and notations of a broad range of disciplines including: classroom discourse, conversation analysis, discourse, language acquisition, gesture, signed languages, ethology, anthropology, field linguistics, speech analysis.
	www.ldc.upenn.edu /annotation (3735 words)

	[No title]
		PLN stands for Postfix Literal Notation (sometimes referred to as “reverse Polish notation” with reference to the Polish logician Jan Lukasiewicz, who substituted the letters of Polish words for the operators used by Russell and Whitehead).
		Its particular advantage is its adaptability to the computer, both in making use of an ordinary keyboard and in the relative ease of programming when it is the final letter of a string that expresses the operation in that string.
		RPN is simply a way to express mathematical expressions with operators placed after the operands instead of the familiar "infix notation" where operators are placed between operands.
	www.lycos.com /info/reverse-polish-notation--keys.html (378 words)

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