Questions tagged [polish-notation]

For questions on Polish notation. Polish notation, named for the Polish logician Jan Łukasiewicz, is a mathematical notation in which operators precede their operands.

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Given $x\ y\ +\ x\ z\ +\ *\ y\ z\ *\ +$ recover the tree, write it in usual notation and simplify

Given the boolean expression given in reverse Polish notation $$x\ y\ +\ x\ z\ +\ *\ y\ z\ *\ +$$ recover the tree, write it in usual notation and simplify. The usual notation is $$\begin{array}{ll} ...
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1answer
313 views

max in reverse polish notation (RPN) [closed]

I am trying to implement max in my infixToPostfix generator. I did not ask this question on stackoverflow because it is more of a mathematical thing. I hope this is the right place. $(1+2) / max(1,2,...
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2answers
231 views

How to convert summation into reverse polish notation

I'm struggling to find a proper answer to the following question. How to convert a equation (including complex operators like summation) into RPN? Example power series: P(x)=$\sum^\infty_{n=0}a_n(...
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0answers
177 views

Reverse Polish boolean operations with stack size of one.

I'd like to evaluate a boolean expression: $AB + CD + ... + YZ$ But the engine with which I can evaluate expressions operates in reverse polish with a stack size of one. For example, I can evaluate $...
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2answers
1k views

The Polish notation of the expression

The Polish notation of the expression a + b * c + d ( where "+" is left associative): A/ + + a * b c d B/ + a * bc + d C/ + + * a b c d D/ + * bc + ad Can anyone explain why the answer is A ...
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3answers
111 views

Proving the $\lim_\limits{x\to2}\,\, 2x^2-6x+7=3$.

I was just wondering if the following proof makes logical sense and is set out in a manor which is easy to read and understand, to a mathematician. Prove the $\lim_\limits{x\to2}\,\, 2x^2-6x+7=3$. $\...
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1answer
444 views

Calculate a formula in Reverse Polish Notation

I hope I'm writing this post in correct forum. I've got a equation -11*2*(-1)*3 which i transferred into RPN -> ...
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2answers
103 views

Image of a function:

Why is the image of a function written in the following way? $$Im=\{ y \in Y\, | \, y=f(x) \quad 'for\, some' \, \, x \in X\} $$ Why not '$\forall $' ?
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0answers
117 views

Representing operations in reverse Polish notation/postfix that return multiple values

I'm working on a recipe definition language which uses operands ("milk", "eggs"), unary operators ("slice", "chop"), and binary operators ("combine", "fold in"). To avoid ambiguity, I've decided to ...
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1answer
144 views

How Do I Prove the 6 Letter Thesis Cδδ0δp?

There exists a 1951 paper by C. A. Meredith which proves a completeness meta-theorem for the "C, 0, δ, p" system which has as it's sole axiom Cδδ0δp under uniform substitution for propositional ...
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3answers
545 views

Converting from standard to functional, Polish and Reverse Polish notation

I wanted to convert the following expression to Functional, Polish and Reverse Polish notation. $$Y =A + \frac{B+ \dfrac{BA}{B+CA}}{A - \dfrac{BC}{B-C+A}}$$ I know how to do Standard -> Functional ->...
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1answer
2k views

Represent unary and functions in postfix notation

I'm currently working on a math evaluator, which works by converting the infix notation to postfix notation and then evaluating the postfix expression. It was going pretty good, until I ran into the ...
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1answer
1k views

How to transform expressions in polish-notation

Here is an example of a De Morgan transformation of a logic expression: $ \neg ({a} \wedge {b}) $ becomes $ (\neg {a} \vee \neg {b}) $ My intuitive view of this operation is that I'm "moving the ...
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3answers
171 views

Reverse Polish Notation

For example : a + b - c = abc-+ Why is this correct ? xy - z+ = xyz-- as I understand, it has to be : ...
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3answers
501 views

Reverse Polish notation in (abstract) algebra

If I have something like $\phi\circ \psi(x)$ this means first apply $\psi$ and then $\phi$. Going right to left is pretty contrary to my intuition. In computer science some programming languages (and ...
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2answers
765 views

Well Formed Expression (Polish Notation)

In Kunen's book Foundation of Mathematics the definition of a well formed expression (wfe) of a lexicon for Polish notation $\langle W, \alpha \rangle$ ($W$ is a set and $\alpha:W\to\omega$ is a ...
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1answer
142 views

Abstract Algebra Math notation, kernel

So I defined $$\theta:R \rightarrow R\backslash I$$ by $$\theta(x) = [x]_I$$ and $$\phi: R[x]\rightarrow (R\backslash I)[x]$$ by $$\phi(a_nx^n +\dotsb+a_1x+a_0) = \theta(a_n)x^n+\dotsb+\theta(a_1)...
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2answers
526 views

Ambiguity in Reverse Polish notation

Given the infix form: 1 * 2 * 3 What is the Reverse Polish notation? As I see things, two valid answers are: ...
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1answer
2k views

Reverse Polish Notation with power

Perhaps I'm just not understanding RPN correctly, but whenever I translate something like 2^2^3 then I get 22^3^ But if I try ...
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1answer
76 views

Which One of These Logical Theses Does Not Hold for Relevant Logics With a Connective for Conjunction?

I write in Polish notation and have included fully infixed notation here also which indicates parsing order. For every relevant logic simplification fails: Simplifcation: CpCqp or [p$\rightarrow$(...
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2answers
615 views

Reverse Polish Notation and numbers $>9$

Excuse me for the newbish question in advance but how should I make sure I don't make a mistake converting from RPN to infix notation when I don't know if some of the numbers aren't two-digit ones or ...
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3answers
419 views

distributive law in polish notation

On page 18 "Logic as Algebra" Halmos&Givant wrote the distributive law in Polish notation as $$ = \times a + bc + \times ab \times ac $$ I fail to see anything remarkable here, is there a ...
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1answer
167 views

PEDMAS in RPN needed?

In RPN do we still have to take into note the PEDMAS rules? For example these questions: 3 – 4 * 2 3 * 4 – 2 3 * (4 – 2) (3 – 4) * 2 3 – 4 + 2 Answers 342*- 34*...
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2answers
534 views

Calculate an Average in RPN (Reverse Polish Notation)

To calculate an average in reverse polish notation (RPN) is the following correct (assuming a-j are variables representing numbers): ...
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1answer
256 views

Is it possible to omit multiplication operator in polish/prefix notation?

In infix notation, (2/2(3+3)) means (2/(2*(3+3)). The multiplication sign is omitted. In polish/prefix notation, is it possible to omit multiplication sign? For instance, is it acceptable to write ( *...
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3answers
869 views

Practicing Polish/Prefix notation

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