# Questions tagged [computer-algebra]

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### Floating point binary number to a 7 segment decimal display

I have covered floating point (32 bit) conversion from float to decimal and decimal to float. I am happy with the theory and I have created a conversion tool in Excel VBA which works just fine ...
14 views

### Designing a turing machine based on a starting and ending point [closed]

Hello i am a self taught software developer i am trying to learn turing machine in depth , i came to a problem which i can not solve , can you please help me with the design of the turing machine, ...
39 views

### What is the time complexity of the following triple nested loop? Kindly solve in term of n

I want to ask that what is the time complexity of this function (triple nested loop) .Kindly analysis completely so that I can understand. ...
130 views

### Do we need to check for mantissa overflow in floating point multiplication?

We do check for the mantisas overflow in floating point addition e.g. If we are adding $8.02 \times 10^3 + 9.01 \times 10^3 =17.03 \times 10^3$ i.e we get an overflow, so we shift the number right ...
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### Is the constant pi (not Raspberry) ever used in general computer science?

Is the constant pi (not Raspberry) ever used in general computer science? If so, how so or when is it applicable?
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### Is it standard for VMs to run *= computationallyHeavyFunction() if the left hand side is 0?

What is the standard way for VMs to deal with 0 *= computationallyHeavyFunction()? Given that once the VM sees that left hand factor is 0, it would know that the result of ...
63 views

### Basic Set Theory problem

So i'm relatively new to computer science and have been learning set theory and am stumped on a question in it. The question specifies that we're only looking at subsets of universe U = {0,...,n-1}. ...
26 views

### When an algorithm says Summation this, and Integral that, what does it mean in coding terms?

I'm a student at a college with only two units of mathematics and I don't know if I'm asking in the right place so please bear with me. I'm currently reading GPU Gems by nvidia and I have a question....
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180 views

### Simplifying SOP: implementing OR with NAND

I am learning how to implement basic logic gates using NAND. I have learnt that you can use De Morgan's theorem as such: $a+b = \bar{\bar a} + \bar{\bar b} = \overline{(\bar a *\bar b)}$ In other ...
38 views

### What is the computational cost of automatic differentiation compared to symbolic and numerical differentiation?

Automatic differentiation is a set of techniques to numerically evaluate the derivative of a function. Quoting from Wikipedia (emphasis mine): These classical methods run into problems: symbolic ...
Let $c_1,...,c_n,c':\mathbb{Z^d}\rightarrow \{0,1\}$ all have finite support. Let $C$ be the linear, shift-invariant code generated by $c_1,..,c_n$. It is possible to calculate the nearest codeword $... 1answer 68 views ### How to compute quotient subgroup efficiently? Let$G$be a finite group given by the table representation and a normal subgroup$H$of$G$is given. I want to compute$G/H$that is quotient group. Model of computation is RAM For all pair of$a$... 0answers 52 views ### Provably correct algorithm/CAS for checking term equalities Within my research of term rewriting systems (TRS) I stumbled upon a paper (Siekmann, J., and P. Szabó. “The Undecidability of the DA-Unification Problem.” The Journal of Symbolic Logic, vol. 54, no. ... 1answer 2k views ### cannot construct the infinite type [closed] I am trying to learn haskell and could not configure it out, why following code snippet can not get compiled: ... 0answers 18 views ### Is there evidence to suggest Macsyma was directed at the Diophantine equations in the Entscheidungsproblem? I'm reading the book The Annotated Turing by Charles Petzold. In it he mentions the Diophantine equations - which was a joy to read. This then lead to Hilbert's 10th problem - finding an algorithm ... 2answers 368 views ### Using Brzozowski's derivatives method to construct a minimal DFA so I am currently learning about dfa and nfa and i came across the following question which requires me to use Brzozowski's derivatives method to construct a minimal DFA recognizing the language ... 1answer 583 views ### How to calculate sum of binomial coefficients efficiently? I want to compute the sum $$\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\binom{n}{6}+\dots+\binom{n}{k} \bmod 10^9+7$$ where$n$and$k$can be up to$10^{14}$and$k\le n$. I found several links on ... 2answers 299 views ### Constant problem for discrete functions Is there an algorithm to decide whether a closed-form expression over integer variables using, say,$\{+,-,\times,\div,\text{^},\lfloor\text{lg}\rfloor,!,()\}$, or some other useful set of operators, ... 1answer 53 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 ... 2answers 164 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, ... 1answer 752 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 ... 0answers 26 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). ... 1answer 211 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 ... 1answer 326 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, ... 1answer 122 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 ... 1answer 69 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 ... 4answers 4k 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? ... 1answer 49 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? 1answer 54 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? 1answer 74 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 ... 1answer 602 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$df/dxof f? ... 0answers 829 views ### Does Automatic Differentiation handle conditional branches, if yes how? I'm trying to understand how Automatic Differentiation (AD) works. For simple algebraic operation, I get the chain rule thing. But, when the code contains conditional statement like ... 2answers 94 views ### Solve modulus with constraints for multiple equations I'm trying write a program to solve equations from the following form: \begin{align} a \bmod x &= t_1 \\ b \bmod x &= t_2 \\ \end{align} wherea$,$b$,$t_1$and$t_2$are known ... 4answers 611 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, ... 2answers 258 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 ... 2answers 276 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 ... 3answers 1k 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 ... 0answers 228 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\\ \...
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 ...