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 Factor

factor a polynomial
 Syntax
 ``` Factor(F:POLY):LIST ```

 Description
This function factors a polynomial in its ring of definition. Multivariate factorization is not yet supported over finite fields. (For information about the algorithm, consult Pointers to the Literature.)

The function returns a list of the form [[F_1, N_1],...,[F_r, N_r]] where F_1^N_1 ... F_r^N_r = F and the F_i are irreducible in the polynomial ring of F.

 Example
 ``` Use R ::= QQ[x,y]; F := x^12 - 37x^11 + 608x^10 - 5852x^9 + 36642x^8 - 156786x^7 + 468752x^6 - 984128x^5 + 1437157x^4 - 1422337x^3 + 905880x^2 - 333900x + 54000; Factor(F); [[x - 2, 1], [x - 4, 1], [x - 6, 1], [x - 3, 2], [x - 5, 3], [x - 1, 4]] --------------------------------- G := Product([W[1]^W[2] | W In It]); -- check solution F = G; TRUE --------------------------------- Factor((8x^2+16x+8)/27); -- the "content" appears as a factor of degree 0; -- it is not factorized into prime factors. [[x + 1, 2], [8/27, 1]] --------------------------------- F := (x+y)^2*(x^2y+y^2x+3); F; x^4y + 3x^3y^2 + 3x^2y^3 + xy^4 + 3x^2 + 6xy + 3y^2 ------------------------------- Factor(F); -- multivariate factorization [[x^2y + xy^2 + 3, 1], [x + y, 2]] ------------------------------- Use ZZ/(37)[x]; Factor(x^6-1); [[x - 1, 1], [x + 1, 1], [x + 10, 1], [x + 11, 1], [x - 11, 1], [x - 10, 1]] --------------------------------- Factor(2x^2-4); -- over a finite field the factors are made monic; -- leading coeff appears as "content" if it is not 1. [[x^2 - 2, 1], [2, 1]] --------------------------------- ```