Re: Factor and/or Rules replacements

*To*: mathgroup at smc.vnet.net*Subject*: [mg104493] Re: [mg104443] Factor and/or Rules replacements*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 1 Nov 2009 17:56:14 -0500 (EST)*References*: <200911010856.DAA19674@smc.vnet.net>

On 1 Nov 2009, at 17:56, yves wrote: > Hello everybody, > > Here is the model problem: > I tried to obtain the factorisation of x^2+b x +c and expected to > get something like (x-1/2(-b+Sqrt[b^2-4 c))((x-1/2(-b-Sqrt[b^2-4 c)). > > So I tried > in:Factor[x^2+b x + c] and get > out: c + b x + x^2 > So my first question what should I have done? Nothing. Factor factors only over the field of algebraic numbers, not algebraic functions. > > I tried another way > in:sol=Solve[x^2+b x + c == 0,{x}]; and get the couple of > replacement rules. > Next I defined > in: f=(x-x1)(x-x2) > and finally I replaced x1 and x2 in succession by > in:f /. {(sol[[1]] /. x -> x1), (sol[[2]] /. x -> x2)} > which gave the expected factorisation but enclosed in {}. > My second question is : > Is there a simpler way or more compact to replace x1 and x2? You can do simply: Times @@ (x - (x /. Solve[x^2 + b x + c == 0, x])) (1/2 (b-Sqrt[b^2-4 c])+x) (1/2 (Sqrt[b^2-4 c]+b)+x) Andrzej Kozlowski

**References**:**Factor and/or Rules replacements***From:*yves <yves.dauphin@solvay.com>