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The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The online vector-matrix-vector problem (OuMv) is a variant of OMv where the algorithm receives, at each round , two Boolean vectors and , and returns the product . This version has the benefit of returning a Boolean value at each round instead of a vector of an n {\displaystyle n} -dimensional Boolean vector.
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
The pictures on the right show how to calculate 345 × 12 using lattice multiplication. As a more complicated example, consider the picture below displaying the computation of 23,958,233 multiplied by 5,830 (multiplier); the result is 139,676,498,390. Notice 23,958,233 is along the top of the lattice and 5,830 is along the right side.
For example, multiplying the lengths (in meters or feet) of the two sides of a rectangle gives its area (in square meters or square feet). Such a product is the subject of dimensional analysis. The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4.
The predecessor of the Magma system was named Cayley (1982–1993), after Arthur Cayley.. Magma was officially released in August 1993 (version 1.0). Version 2.0 of Magma was released in June 1996 and subsequent versions of 2.X have been released approximately once per year.
3. As the n digit multiplication problem grows to ever larger numbers, the number of possible combinations one can use to reach the same answer grows as well; meaning the user can pick and choose the easiest and fastest route to reach the answer to each multiplication problem according to their own specific needs at the time.
Multiplication is a mathematical operation of repeated addition. When two numbers are multiplied, the resulting value is a product. The numbers being multiplied are multiplicands, multipliers, or factors. Multiplication can be expressed as "five times three equals fifteen", "five times three is fifteen" or "fifteen is the product of five and ...