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When a monomial order has been chosen, the leading monomial is the largest u in S, the leading coefficient is the corresponding c u, and the leading term is the corresponding c u u. Head monomial/coefficient/term is sometimes used as a synonym of "leading". Some authors use "monomial" instead of "term" and "power product" instead of "monomial".
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]
The polynomial f is reducible by g if some monomial of f is a multiple lm(g). (So, if f is lead-reducible by g, it is also reducible, but f may be reducible without being lead-reducible.) Suppose that f is reducible by g, and let cm be a term of f such that the monomial m is a multiple of lm(g). A one-step reduction of f by g consists of ...
Let p and q be polynomials with coefficients in an integral domain F, typically a field or the integers. A greatest common divisor of p and q is a polynomial d that divides p and q, and such that every common divisor of p and q also divides d.
In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of all monomials.The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an immediate consequence of the definition of a polynomial).
This expands the product into a sum of monomials of the form for some sequence of coefficients , only finitely many of which can be non-zero. The exponent of the term is n = ∑ i a i {\textstyle n=\sum ia_{i}} , and this sum can be interpreted as a representation of n {\displaystyle n} as a partition into a i {\displaystyle a_{i}} copies of ...
South Korea’s parliament voted to impeach President Yoon Suk Yeol on Saturday in an extraordinary rebuke that came about after his own ruling party turned on him following his refusal to resign ...
Division is also not, in general, associative, meaning that when dividing multiple times, the order of division can change the result. [7] For example, (24 / 6) / 2 = 2, but 24 / (6 / 2) = 8 (where the use of parentheses indicates that the operations inside parentheses are performed before the operations outside parentheses).
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