Search results
2 dni temu · The Chinese remainder theorem is a theorem which gives a unique solution to simultaneous linear congruences with coprime moduli. In its basic form, the Chinese remainder theorem will determine a number p p that, when divided by some given divisors, leaves given remainders.
6 dni temu · Given a prime $p$ and integers $a_1, \ldots, a_n, a_{n+1}>0$, I have to compute and store all the solutions in $\mathbb{Z}/p\mathbb{Z}$ of the following equation: $$ a_1x_1 + \dots + a_nx_n = a_...
21 cze 2024 · A modular system \pmod{n} allows only a fixed set of remainder values, \(0,1,2,\ldots,n-1\). One practical approach to solving modular equations, at least when n is reasonably small, is to simply try all these integers.
15 cze 2024 · The program can find solutions to simultaneous linear congruences in integer theory. The program calculates the minimum positive value and the general solution of the solution.
15 cze 2024 · Simultaneous congruence formula (I) The program can find solutions to simultaneous linear congruences in integer theory. The program will calculate the smallest positive solution and the general solution.
3 dni temu · To solve higher degree equations, we can use substitution to convert the given equation into a quadratic equation, then solve the quadratic equation to determine the solutions to the original equation. For example, suppose we have the equation: \(ax^4+bx^2+c=0\)
20 cze 2024 · Steps for Cholesky Decomposition. To decompose or factorize any Hermitian symmetric matrix, we can use the following steps: Step 1: First write the given matrix in the decomposed form. Let A be the positive definite symmetric matrix which can be decomposed as A = LL*. Step 2: Now, we have to evaluate matrix L where L is defined as:
