Factors
inert factors function
Calling Sequence
Parameters
Description
Examples
Factors(a, K)
a
-
multivariate polynomial
K
optional specification for an algebraic extension
The Factors function is a placeholder for representing the factorization of the multivariate polynomial a over U, a unique factorization domain. The construct Factors(a) produces a data structure of the form u,f1,e1,...,fn,en such that a=u⁢f1e1⁢⋯⁢fnen, where each f[i] is a primitive irreducible polynomial.
The difference between the Factors function and the Factor function is only the form of the result. The Factor function, if defined, returns a Maple sum of products more suitable for interactive display and manipulation.
The call Factors(a) mod p computes the factorization of a over the integers modulo p, a prime integer. The polynomial a must have rational coefficients or coefficients over a finite field specified by RootOfs.
The call Factors(a, K) mod p computes the factorization over the finite field defined by K, an algebraic extension of the integers mod p where K is a RootOf.
The call modp1(Factors(a),p) computes the factorization of the polynomial a in the modp1 representation modulo p a prime integer.
The call evala(Factors(a, K)) computes the factorization of the polynomial a over an algebraic number (or function) field defined by the extension K, which is specified as a RootOf or a set of RootOfs. The polynomial a must have algebraic number (or function) coefficients. The factors are monic for the ordering of the variables chosen by Maple.
Factors(2*x^2+6*x+6) mod 7;
2,x+6,1,x+4,1
Factors(x^5+1) mod 2;
1,x+1,1,x4+x3+x2+x+1,1
alias(alpha=RootOf(x^2+x+1));
α
Factors(x^5+1,alpha) mod 2;
1,α⁢x+x2+1,1,x+1,1,α⁢x+x2+x+1,1
alias(sqrt2=RootOf(x^2-2)):
evala(Factors(2*x^2-1,sqrt2));
2,x+sqrt22,1,x−sqrt22,1
alias(sqrtx=RootOf(y^2-x,y)):
evala(Factors(x*y^2-1,sqrtx));
x,y−sqrtxx,1,y+sqrtxx,1
expand((x^3+y^5+2)*(x*y^2+3)) mod 7;
x⁢y7+x4⁢y2+3⁢y5+3⁢x3+2⁢x⁢y2+6
Factors((7)) mod 7;
1,y5+x3+2,1,x⁢y2+3,1
Factors(x^2+2*x*y+y^2+1+x+y,alpha) mod 5;
1,y+x+4⁢α,1,y+x+α+1,1
Factors(x^2*y+x*y^2+2*alpha*x*y+alpha*x^2+4*alpha*x+y+alpha) mod 5;
1,α⁢x+x⁢y+1,1,y+x+α,1
See Also
AFactor
AFactors
Expand
Factor
factors
ifactors
Irreduc
mod
modp1
Sqrfree
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