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Calculators may associate exponents to the left or to the right. For example, the expression a ^ b ^ c is interpreted as a ( b c ) on the TI-92 and the TI-30XS MultiView in "Mathprint mode", whereas it is interpreted as ( a b ) c on the TI-30XII and the TI-30XS MultiView in "Classic mode".
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.
Lexicographic order (lex) first compares exponents of x 1 in the monomials, and in case of equality compares exponents of x 2, and so forth. The name is derived from the similarity with the usual alphabetical order used in lexicography for dictionaries, if monomials are represented by the sequence of the exponents of the indeterminates.
In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
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]
Once a monomial ordering is fixed, the terms of a polynomial (product of a monomial with its nonzero coefficient) are naturally ordered by decreasing monomials (for this order). This makes the representation of a polynomial as a sorted list of pairs coefficient–exponent vector a canonical representation of the polynomials (that is, two ...
This pen-and-paper method uses the same algorithm as polynomial long division, but mental calculation is used to determine remainders. This requires less writing, and can therefore be a faster method once mastered. The division is at first written in a similar way as long multiplication with the dividend at the top, and the divisor below it.