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Illustrations, and the help page of Factored for details. Printed as (x+1)^2, which is an expression of type "_power". AsĪn example, the result of q:=factor(x^2+2*x+1) is Whenever it is processed further by other MuPAD ® functions.
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Note that the result of factor is printedĪs an expression, and it is implicitly converted into an expression The internal representation of a factored object, i.e., the list [u, List of factors, the call Factored::exponents(g) returns The ordinary index operator, i.e., g = f1^e1, g Integers and u is an arithmetical expression. Of the same type as the input (either polynomials or expressions) e1 through er are It is represented internally by the list [u, Then factor returns a factorization with the single
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To factors of the denominator are negative integers. In this case, the multiplicities e i corresponding Then both the numerator and the denominator are decomposed into a Then it is decomposed into a product of primes, and the result is The auxiliary variables are replaced by the original subexpressions. To factors of the denominator are negative integers see Example 3. The implied coefficient ring, and the multiplicities e i corresponding Of the numerator polynomial and the denominator polynomial. The numerator and theĭenominator are converted into polynomials with coefficient ring Expr via poly, and the impliedĬoefficient ring is the smallest ring containing the coefficients The original and the auxiliary indeterminates. The resulting expression is then written as a quotient of two polynomial expressions in Of the subexpressions, such as the equation cos( x) 2 =Īre not necessarily taken into account. Non-rational subexpressions suchīut not constant algebraic subexpressions such as I and (sqrt(2)+1)^3,Īre replaced by auxiliary variables before factoring. If f is an arithmetical expression but not a number, it isĬonsidered as a rational expression. Performed using numerical calculations and the results will contain = Fis given, then f is factored over the real numbers ℝ or If the second argument F or, alternatively, Domain With the option Adjoin, the elements of adjoin are In particular, the content u isĪn element of the implied coefficient ring. We say that the implied coefficient ring is R.Įlements of the implied coefficient ring are considered to be constantsĪnd are not factored any further. This implied coefficient ring always containsĬoefficient ring R of f is not Expr, then If f is a polynomial with coefficient ring Expr, then f isįactored over the smallest ring containing the coefficients. If f is a polynomial whose coefficient ring is not Expr, then f isįactored over its coefficient ring. Which rewrites its argument as a sum of as many terms as possible. In a certain sense, it is the complementary The distinct primitive irreducible factors of f,įactor rewrites its argument as a product Factor(f) computes a factorization f = u f 1 e 1 … f r e r of