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Besides respecting multiplication, monomial orders are often required to be well-orders, since this ensures the multivariate division procedure will terminate.There are however practical applications also for multiplication-respecting order relations on the set of monomials that are not well-orders.
In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First ("first" terms of each binomial are multiplied together)
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.Two definitions of a monomial may be encountered: A monomial, also called a power product or primitive monomial, [1] is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. [2]
On currently available processors, a bit-wise shift instruction is usually (but not always) faster than a multiply instruction and can be used to multiply (shift left) and divide (shift right) by powers of two. Multiplication by a constant and division by a constant can be implemented using a sequence of shifts and adds or subtracts. For ...
In mathematics, in the area of algebra studying the character theory of finite groups, an M-group or monomial group is a finite group whose complex irreducible characters are all monomial, that is, induced from characters of degree 1.
The monomials in are those monomials such that there exists such and . [2] If a monomial is represented by the point (,) in the plane, the figure formed by the monomials in is often called the staircase of , because of its shape. In this figure, the minimal generators form the inner corners of a Young diagram.