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  2. Z3 Theorem Prover - Wikipedia

    en.wikipedia.org/wiki/Z3_Theorem_Prover

    [6] [7] In 2018, Z3 received the Test of Time Award from the European Joint Conferences on Theory and Practice of Software (ETAPS). [8] Microsoft researchers Nikolaj Bjørner and Leonardo de Moura received the 2019 Herbrand Award for Distinguished Contributions to Automated Reasoning in recognition of their work in advancing theorem proving ...

  3. Linear congruential generator - Wikipedia

    en.wikipedia.org/wiki/Linear_congruential_generator

    Two modulo-9 LCGs show how different parameters lead to different cycle lengths. Each row shows the state evolving until it repeats. The top row shows a generator with m = 9, a = 2, c = 0, and a seed of 1, which produces a cycle of length 6. The second row is the same generator with a seed of 3, which produces a cycle of length 2.

  4. Primitive root modulo n - Wikipedia

    en.wikipedia.org/wiki/Primitive_root_modulo_n

    The remainders in the period, which are 3, 2, 6, 4, 5, 1, form a rearrangement of all nonzero remainders modulo 7, implying that 3 is indeed a primitive root modulo 7. This derives from the fact that a sequence ( g k modulo n ) always repeats after some value of k , since modulo n produces a finite number of values.

  5. Microsoft Math Solver - Wikipedia

    en.wikipedia.org/wiki/Microsoft_Math_Solver

    Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.

  6. Multiplicative order - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_order

    The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or ...

  7. Satisfiability modulo theories - Wikipedia

    en.wikipedia.org/wiki/Satisfiability_modulo_theories

    In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.

  8. Matrix congruence - Wikipedia

    en.wikipedia.org/wiki/Matrix_congruence

    Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space: two matrices are congruent if and only if they represent the same bilinear form with respect to different bases.

  9. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.