The tag has no usage guidance.

learn more… | top users | synonyms

0
votes
1answer
21 views

The symbolic differentiation of univariate expressions

I was reading "Doug McIlroy: McCarthy Presents Lisp" and the phrase "symbolic differentiation of univariate expressions" triggered a faint memory of a demonstration of differentiation done in haskell ...
8
votes
2answers
81 views

Decidability of checking an antiderivative?

Let's suppose I have two functions $F$ and $G$ and I'm interested in determining whether $$F(x) = \int G(x)dx.$$ Let's suppose that my functions are composed of elementary functions (polynomials, ...
1
vote
1answer
246 views

Difficult Question to Understand (Computer Artitechture) [closed]

You are designing an elevator controller for a building with 25 floors. The controller has two inputs: UP and DOWN. It produces an output indicating the floor that the elevator is on. There is no ...
1
vote
0answers
13 views

How to simplify a rational function with floating point real coefficients (GCF)

How does one compute the simplified form of a rational function where the coefficients of the polynomial are floating point numbers (real, though I expect using complex numbers would be the same). ...
2
votes
0answers
18 views

Properties of Reverse Polish Notation expressions that are algebraically invariant

The RPN expressions a b + c * and f d e + * are algebraically equivalent, though the names of the variables are different ...
4
votes
1answer
117 views

Abstract algebra and programming languages

Quite often, I stumble upon abstract algebra concepts like initial algebra, free algebra, and similar while reading papers on programming languages. For instance, in papers on algebraic data types, ...
1
vote
1answer
57 views

Introduction to number theory [closed]

What is the best book for a beginner in Introduction to number theory? I am new to this field and getting deeper into cryptography, so I think reading some intro books about number theory can be of ...
2
votes
1answer
53 views

Multiplication of two or more algebraic quantities [closed]

Recently, I was facing the problem how to multiply to two or more algebraic quantities in c++. For example, if the two algebraic quantities are $$x^2-2x+3, \text{and } x-5$$ then the result of ...
3
votes
3answers
906 views

Why do Computers use Hex Number System at assembly language?

Why do computer use Hex Number System at assembly language? Why don't they use any other number system like binary, octal, decimal? What thing forced computer designer to use hex system at assembly? ...
1
vote
1answer
32 views

Is everything in CS either a numeric method or a symbolic method?

Or maybe also a combination of the two, but not something else, whether numeric, nor symbolic. Do they cover the whole field?
4
votes
1answer
43 views

How does mathematical software evaluate symbolic sums?

Wolfram alpha is able to compute this sum: $$ \sum_{j=1}^n \binom{j}{2} = \frac{1}{6}(n-1)n(n+1). $$ How can Wolfram alpha do it? What kind of algorithm does it use?
1
vote
1answer
68 views

An algorithm for making 2 carts meet [closed]

Say I have 2 carts on an infinite railroad, each cart is initially under a lamp. There are only 2 lamps, and they are at a fixed location, hence they don't change their location. The distance between ...
3
votes
1answer
130 views

How does automatic differentiation work?

What is the intuitive idea behind automatic differentiation? If I have a program which computes $f(x, y)=x^2+yx$, which steps lead to the program which computes the derivative $df/dx$ of f? ...
3
votes
0answers
135 views

Does Automatic Differentiation handle conditional branches, if yes how?

I'm trying to understand how Automatic Differentiation (AD) works. For simple algebraic operation, I get the chain rule thing. But, when the code contains conditional statement like ...
2
votes
2answers
83 views

Solve modulus with constraints for multiple equations

I'm trying write a program to solve equations from the following form: $$ \begin{align} a \bmod x &= t_1 \\ b \bmod x &= t_2 \\ \end{align} $$ where $a$, $b$, $t_1$ and $t_2$ are known ...
4
votes
4answers
237 views

Using a computer algebra system to optimize mathematical expressions

This is something I've been wondering for years. Software like Mathematica is great at manipulating expressions into simplified, factorized, and other forms. I'm wondering if there's a way, ...
4
votes
2answers
192 views

Computer Algebra: Algorithms for solving equations symbolically

As a hobby, I have written a basic computer algebra system. My CAS handles expressions as trees. I have advanced it to the point where it can simplify expressions symbolically (i.e., sin(pi/2) returns ...
10
votes
2answers
133 views

Decidability of a problem concerning polynomials

I have come across the following interesting problem: let $p,q$ be polynomials over the field of real numbers, and let us suppose that their coefficients are all integer (that is, there is a finite ...
4
votes
3answers
736 views

Constructing a data structure for a computer algebra system

In thinking about how to approach this problem I think several things will be required, some tivial: An expression tree where non-leaf node is an operation (not sure if that part is redundant), but ...
8
votes
0answers
198 views

Complexity of computer algebra for systems of trigonometric equations

As discussed in this question, I drafted a spec algorithm that hinges on finding a specific root of a system of trigonometric equations satisfying the following recurrence: $\qquad f_{p_0} = 0\\ ...
12
votes
2answers
2k views

Complexity of computing matrix powers

I am interested in calculating the $n$'th power of a $n\times n$ matrix $A$. Suppose we have an algorithm for matrix multiplication which runs in $\mathcal{O}(M(n))$ time. Then, one can easily ...