Polynomial Identities

Math 242 practice problems

Name: _________________

Learning Goals: Develop and implement an algorithm to solve a mathematical problem, and interpret your results. Formulate precise mathematical conjectures supported by computational evidence. Explore generalizations of known mathematical ideas.

Your task: Complete Exercises 2.35 and 2.36 from our Computational Mathematics text. These exercises are reprinted below.

Due: Friday, March 1, at 5:00pm. Upload your solution as a Mathematica notebook to the Polynomial Identities assignment (Moodle link).

Grading: If you implement the requested functions and use them to compute the requested quantities, you will earn a Satisfactory grade.

Need help? Review the notes from class (which are posed on the course web site), talk with your classmates, email Prof. Wright, or visit the help session.

Problem 1: Exercise 2.35

Write a function findFibCoeffs that implements Algorithm 2.17 from page 76 in the text. Verify that it works properly for the 3n and 5n cases. Specifically, confirm that:

findFibCoeffs(3) returns {5,0,3}

findFibCoeffs(5) returns {25,0,25, 0, 5}

Then find coefficients for the Fibonacci Q n identities for Q=7,9,11,...,25. Report on any patterns that you observe.

Problem 2: Exercise 2.36

Write a function verifyFibIdentity that implements Algorithm 2.18 from page 77 in the text. Check whether your coefficients from the previous exercise produce identities that hold for even integers n up to 100 or more.