Solving Multiplication Tables in Z2[X]/(x^3+x^2+x+1): Steps and Examples

  • Thread starter Thread starter mikki
  • Start date Start date
  • Tags Tags
    Multiplication
mikki
Messages
7
Reaction score
0
have a question about finding the multiplication table of say
Z2[X]/(x^3+x^2+x+1). What are the steps in solving problems like this? Because I keep doing different problems and I end up making a mistake. All I need is an example or an explanantion. Any help is greatly appreciated
 
Physics news on Phys.org
mikki said:
have a question about finding the multiplication table of say
Z2[X]/(x^3+x^2+x+1).

Can you explain the notation? It's not familiar to me
 
the polynomial ring over the integers mod 2: Z2[x]
 
Last edited:
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top