Re: Factor and/or Rules replacements
- To: mathgroup at smc.vnet.net
- Subject: [mg104502] Re: Factor and/or Rules replacements
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Sun, 1 Nov 2009 17:57:56 -0500 (EST)
- References: <hcjjbj$js5$1@smc.vnet.net>
On 2009.11.01. 10:11, 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
Note that Factor[] works over the integers by default, and also that
there's no way for Mathematica to know that you meant x to be the
variable and {b,c} the coefficients. It assumed that all of them are
variables.
Factoring over the complexes amounts to simply finding all roots.
> So my first question what should I have done?
>
> 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 could do
Solve[x^2 + b x + c == 0, x]
Times @@ (x - (x /. %))
Expand[%]