
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 29th, 2014, 09:36 PM  #1 
Newbie Joined: Apr 2014 From: los angeles Posts: 6 Thanks: 1  Primitive root of unity and Karatsuba method
I am very stuck on these two problems and wanted to see if anyone is able to help me out please? a) In F_17, 2 is a primitive 8th root of unity. Evaluate f(x) = 7x^3+8x^2+3x+5 at the eight powers of 2 in F_17. Verify that the method requires at most 16 multiplications in F_17. b) For polynomials f(x),g(x) of degree d = 2^(râˆ’1)âˆ’1, check that multiplying f(x) and g(x) by the Karatsuba method requires 3^(râˆ’1) multiplications in the field F. If you need a reference, textbook can be found at: http://igortitara.files.wordpress.co...ralgebra1.pdf Problems are on page 382 #s 6 and 10. Last edited by jmomo; April 29th, 2014 at 09:39 PM. 
April 30th, 2014, 08:12 AM  #2 
Newbie Joined: Apr 2014 From: los angeles Posts: 6 Thanks: 1 
I was able to figure out part a and only need help on part b please!


Tags 
algebra, applied algebra, fields, karatsuba, karatsuba method, method, primitive, primitive root of unity, root, unity 
Thread Tools  
Display Modes  
