# Questions tagged [math]

Programming questions that are significantly affected or best defined by the underlying mathematics of the problem.

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### Prerequisite math skill for Introduction to Algorithms (CLRS) book [closed]

I already have knowledge about basic algorithms. Now I plan to study more advance algorithms and I decide to go with Introduction to Algorithms. I'm not sure, do I need to refresh my math's skill ...
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### Should absolute value functions be overloaded to give the norm of vector-like data structures?

The absolute value function is an instance of the norm function in one dimension. I've seen instances of libraries where the absolute value function is overloaded to also take the norm of higher ...
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### What is the difference between BigInt and “Computer Algebra System” integers?

Obviously I imagine a CAS does more than BigInt does. But I'm wondering if there is a difference in implementation between BigInt integers and CAS integers (whatever they may be, symbols?). Wondering ...
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### How to minimize size of data given the need for a null pointer?

So I don't know how to formulate this clearly, as it's quite confusing. Hence the reason for asking this question, to overcome the confusion. I will do my best to make it clear, but part of the ...
51 views

### Suitable way to round results returned by any function of a class

Assume there is a class Shape. The class has two functions area() and perimeter(). Let's say Circle and Square inherit from Shape and override these methods. Obviously the results are going to be ...
676 views

### Algorithm for windowed online covariance

I'm trying to adapt an algorithm to calculate covariance to work over a rolling window on the data. Wikipedia has an algorithm for online covariance: def online_covariance(data1, data2): mean1 = ...
643 views

### What rationale is used when programming language designers decide what sign the result of modulo operation takes?

Going through Modulo operation (the avenue I entered while exploring the difference between rem and mod) I came across: In mathematics the result of the modulo operation is the remainder of the ...
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### Resolving Dependencies and Incompatibilities Deterministically

Problem Description I'm working in Python and I've been having a problem designing something to handle the following (abstracted) system: I have some objects (lets call them Nodes) that can be in ...
119 views

### Is there a way to specify a two-way relationship between variables?

Let's say we have two variables, eta and phi related by eta = cos(phi). Is there a way to link these variables in any programming language such that there's no need for two different functions, ...
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### Given a number which is power of 2, check if it is even power or odd power

I am given a number n , which is always a power of 2. I want to check whether n is odd power of 2 or even power of 2. For example: n=4 , ans= even n=8, ans=odd (because 8 is 2^3) n=1024 , ans=even. ...
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### How is fundamental mathematics efficiently evaluated by programming languages?

As I get more and more involved with the theory behind programming, I find myself fascinated and dumbfounded by seemingly simple things.. I realize that my understanding of the majority of fundamental ...
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### Treating a 1D data structure as 2D grid

I am working with a native class that represents a 2D image as a 1D array. If you want to change one pixel, for example, you need to now how to derive the index from the x,y coordinates. So, let's ...
179 views

### What effects does memory space have on bitwise shifts?

It is true that the bitwise left shift operation (shl) doubles the value of the integer being shifted. However, when constrained to a finite space, such as 8 bits for example, left shift will begin to ...
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### Why is the norm of a complex number in the C++ complex library actually the square of the norm?

In the C++ complex library, the method norm() of a complex number actually returns the square of what I have learned is usually called the "Norm". Reference: std::norm For example, std::norm() of (3,...
162 views

### Loan Amortization Schedule - Precision and rounding

I have been playing around making amortization schedules in PHP. My php.ini currently has the precision set to 14. I understand going into this that there will be rounding errors however I am hoping ...
320 views

### Smallest Rubik's cube state representation

I'm trying to determine what is the fewest number of bits I need to represent the state of a Rubik's cube. (EDIT: I am assuming the cube is a valid Rubik's cube that has not been altered and only ...
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### How to do grid systems with floats given precision causes problems

I've been trying to create a grid system that can use any grid size and start at any given anchor point rather than always at 0,0. The problem however is imprecision makes it impossible, even the ...
47k views

### How to check if 4 points form a square?

Assume I have 4 points (they are 2-dimension), which are different from each other, and I want to know whether they form a square. How to do it? (let the process be as simple as possible.)
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### Why does division and multiplication by 2 use the shift operator rather than division operator?

While looking at the code in C for division/multiplication by 2, it is found that shift operator is used rather than division operator. What is the advantage of using shift over division operator?
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### How can I calculate the radius of an arc given by a series of points

Given a series of points, I need to assert that the plotted points form an arc (with a certain level of confidence), and I need to approximate the radius of the arc. For example, the following points ...
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### Randomly Generate Points in a Spiral Motion using Javascript

So I have a javascript program that currently gets random points, it generates a random x,y,z value around the center point, within the radius r var maxArms = 3; var i = 0; var color = []; ...
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### Seeking appropriate design pattern(s) to describe most function-based mathematical problems

I have been looking for a good, general design pattern to implement simple mathematical structures where functions have the following properties: know which parameters they contain, parameters are "...
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### Big-O Notation and Calculus [closed]

I was wondering if there are any calculus relationships implicit in Big-O notation. For example, an algorithm linear according to Big-O notation reduces the size of the problem by a constant amount ...
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### Is it good practice to replace division with multiplication when possible?

Whenever I need division, for example, condition checking, I would like to refactor the expression of division into multiplication, for example: Original version: if(newValue / oldValue >= ...
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### Generic way to describe data synchronization between systems?

Is there a generic way (useful formalisms) to think about data synchronization between two systems, especially in the case of slightly asymmetric roles (eg, one system contain master data, another one ...
231 views

### Gerstner Wave equation from tessendorf paper, mesh penetrates itself

I have been learning to create water waves in a mesh from a paper commonly known as the Tessendorf paper. Which is quite well known. But those who don't know this is the equations it mentions in the ...
63 views

### Best way to encode a queryable number to another unique queryable number? (database outsourcing)

So lets say you want to outsource your database to a third party and be able to query on it on their server but you want to "encode" the salary column of the users on their server, aka hide the real ...
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### Find two horizontal lines to minimize distance to scattered points

I am having trouble with a coding question that I found practicing for a interview: A scatter graph of points on a page, draw two horizontal lines (these lines are parallel) across the page such that ...
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### How do deal with angle wraparounds when comparing them?

Angle A is a degree angle that keeps increasing by increments and Angle B is the stopping point of Angle A (think 'Spin-the-bottle' where Angle A is the current angle of the bottle Angle B is the ...
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### get weighted random item

I have, for example, this table +-----------------+ | fruit | weight | +-----------------+ | apple | 4 | | orange | 2 | | lemon | 1 | +-----------------+ I need to return a random ...
861 views

### Division by zero Java [closed]

The behavior of Java is explained in this topic. But, is Infinity useful for something? Float: public class DivisionByZeroFloat{ public static void main(String[] args) { System.out....
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### How to properly decide what is the appropriate rounding off error for a mathematical function?

In the space of 3D geometry, I need to compute the magnitude of the cross product of two Line3D because I want to check whether these two Lines are "parallel" to each other. Line3D is consisted of 4 ...
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### Will a computer attempt to divide by zero?

We all know 0/0 is Undefined and returns an error if I were to put it into a calculator, and if I were to create a program (in C at least) the OS would terminate it when I try to divide by zero. But ...
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### Simplistic non-secure example of public key encryption

I'm giving a lecture to novice developers on security and would like to explain ssl and the basics of certificates. For this I would like to convey a vague intuitive understanding of asymmetric key ...
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### Randomized Hash function with no collisions

Related to the question Which hashing algorithm is best for uniqueness and speed? Is there a way to create a hash function, or find one, whose hash length depends completely on the input length, has ...
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### Where are mathematical equations applied in the application stack [closed]

Say I have a program using Java or C, that will interface with a hardware device and either read streaming data or write it to a database before applying a few complex mathematical equations to this ...
316 views

### How do I create a comparable checksum of a number sequence?

Sorry if the title is confusing, but here's an example to illustrate what I'm trying to accomplish. I would like to create a 'checksum' or ID grouping of similar number sequences, so that when you ...
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### Are there any formalized/mathematical theories of software testing?

Googling "software testing theory" only seems to give theories in the soft sense of the word; I have not been able to find anything that would classify as a theory in the mathematical, information ...
318 views

### Interdependent variables

Let's say there are two variables a & b, both a & b would have a value between a predefined range. a = x1 to y1 (range) b = x2 to y2 (range) Variable a & b are interdependent, if the ...
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### How a Proof Assistant Proves ∀ or ∃

Wondering how a proof assistant such as Coq proves forall or exists. For example: Three aspects: If you were to give it a huge set of items like a million, wondering if it would actually iterate ...
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### Which programming languages doesn't use operator precedence besides Lisp like languages? [closed]

And what do you think about operator precedences? Would be harder programming in a language where the operations are executed in sequential order? Ex.: 2 + 3 * 4 == 20 2 + (3 * 4) == 14 Ok, Lisp ...
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### Identify sets differing by one

I have a set of objects with different attributes; e.g. a set of cars with colors, brand etc. I choose subsets by virtue of a specific set of attributes. Now I want to identify pairs of such subsets ...
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### Algorithm: Identify same Outlets / Supermarkets

We have a database with stores Outlets / Supermarkets (mainly in germany but other countries are also possible). We store some informations of this outlets / supermarkets like name, street, ...
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### Does any programming language use variables as they're in maths?

In maths, a variable means you can put any number there, and an equation will still be true: root(square(x)) = abs(x) In programming languages, this is not so: a var can change. In Python: y = (x**...
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### How to use units for a slope calculation?

Simple question: is the result of a slope calculation in Python (say, stats.linregress() function) in units of radians, or unitless (e.g. what's 18 deg or 0.314 rad would be equivalent to 0.2 in the ...
499 views

### How can unums emulate IEEE's negative zero?

I am currently reading "The End of Error - Unum Computing" by John Gustafson (Youtube). What I am still not sure about is how the cases handled in IEEE by negatively signed zero are handled ...
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### Swapping variable values without creating a new one

Recently, I was faced with a question that asked me to swap variable values without creating an extra variable. i.e. A = 10, B = 20. How store 20 to A and 10 to B? The solution is: A = A + B #...