### MA 362 - Elementary Modern Algebra II Assignment

Added on - 28 May 2020

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Assignment Ma3626A) We may assume that t is of the order 27^m-1 since it is a 27 letter alphabet. So log t ~ m-1.Putting these values to calculate the number of operations for simple division and multiplication weget

And f being a continuous function attains every value in [0, infinity) at least once for some z in [0,infinity) by intermediate value theorem.This guarantees a solution. Now we can use the bisection method by choosing z1 and z2 such thatand f(z2) is greater than or equal to c and then then if f(z1) = c or f(z2)=c we are done.Else if f((z1+z2)/2)= c, we are doneElse if f((z1+z2)/2) > c : z2= (z1+z2)/2Else if f((z1+z2)/2) < c : z1= (z1+z2)/2This algorithim iterated upon itself will solve for z,

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