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April 29th, 2014, 09:36 PM   #1
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Question 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^(r−1)−1, check that multiplying f(x) and g(x) by the Karatsuba method requires 3^(r−1) multiplications in the field F.

If you need a reference, textbook can be found at:
http://igortitara.files.wordpress.co...r-algebra1.pdf
Problems are on page 382 #s 6 and 10.
Thanks from agentredlum

Last edited by jmomo; April 29th, 2014 at 09:39 PM.
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April 30th, 2014, 08:12 AM   #2
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I was able to figure out part a and only need help on part b please!
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algebra, applied algebra, fields, karatsuba, karatsuba method, method, primitive, primitive root of unity, root, unity



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