Recent content by rukawakaede

Thanks willem. I just realized that I made some mistake in my code and horner's method is less accurate that (x-1)^4. Thank you very much.

epsi00, thanks. I think I understand now. I nearly forgot catastrophic cancellation.

Alright. I agree that needs some time. Thanks. This is what I am looking for. Could you please explain a little bit more on how numerical errors accumulate for (x-1)^4 when is x is about 1? I am still not fully understand.

Well, it is just the binomial expansion of (x-1)^4. I don't understand why we should not evaluate the f(x) directly using (x-1)^4 in terms of computational efficiency. I believe this is something trivial, but I can't see it myself. Hope someone could give some idea. I wrote some codes and...

Firstly, I am not sure if I am in the right section. Pardon me. I was reading something related to computational efficiency when evaluating polynomials. Suppose we want to evaluate f(x)=1-4 x+6 x^2-4 x^3+x^4 it would take n=4 additions and (n^2+n)/2 =10 multiplications to evaluate this f(x) on...

No worries.

Yes, there are two solutions if c > 1. Thanks, I will look at the product log function stuff.

Hi, Could anyone give me some ideas on how to solve the following question: log (x) - x + 2 = 0 or generally log (x) -x + c = 0 where c is a constant. I know how to approximate this by graphing but is there any general method(s) to obtain an exact solution for equations of this...

I am pretty sure it is Z[x]/(1-x)(x^{p-1}+...+x+1) = Z/pZ it would be good that you write out why you think it is not the case.

Thanks HallsofIvy for your reply. I was trying to work out why \int_a^{a+h} f(x)dx= f(a)h when h infinitely small. Could you tell me more about why this is true? or could you explain the differential form? I am still not fully understand yet.

here dt is an infinitely small number. and i don't think the RHS is an integral. maybe you can refer to http://en.wikipedia.org/wiki/Probability_density_function#Further_details the last line of the Further details

Hi Could anyone show to me that: If dt is an infinitely small number, the probability that X is included within the interval (t, t + dt) is equal to f(t) dt ,i.e. Pr(t<X<t+dt) = f(t)dt where f is the probability density function. this sentence is from wikipedia but I could not prove this to...

Hi, could anyone solve my confusion? Let p be a prime and let x=\zeta_p to be a primitive pth root of unity. How could we conclude \frac{\mathbf{Z}[x]/(1-x)}{(x^{p-1}+\cdots+x+1)}=\mathbf{Z}/p\mathbf{Z}=\mathbb{F}_p ? This should be obvious but it seems that I missed something. Could anyone...

Could you make it in an elegant single formula? and explain or prove how it works?

A counterexample to the formula gcd(a/b,c/d)=\frac{gcd(a,c)}{lcm(b,d)} is: a=2, b=4, c=4, d=8 gcd(a,c)=2 lcm(b,d)=8 gcd(a,c)/lcm(b,d)=1/4 but gcd(a/b,c/d)=gcd(1/2,1/2)=1/2 Moreover, you can see the error if you investigate the formula further...