The tag has no wiki summary.

learn more… | top users | synonyms

2
votes
2answers
144 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? ...
0
votes
1answer
28 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?
3
votes
1answer
34 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?
0
votes
1answer
65 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 ...
2
votes
1answer
77 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? ...
2
votes
0answers
80 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 ...
1
vote
2answers
77 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 ...
3
votes
4answers
116 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, ...
3
votes
2answers
147 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 ...
9
votes
2answers
111 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 ...
3
votes
3answers
435 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 ...
7
votes
0answers
174 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\\ ...
11
votes
2answers
1k 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 ...