HOMEWORK 2: DUE: March 22, 2000 (Q1) Please download the CORE library from http://cs.nyu.edu/exact/core/, and install it in your working directory. Now modify your program from hw1 to include the CORE library. This may be as simple as just inserting the following line of code #include "core.h" at the beginning of your original program. Normally, this include statement should follow all your other standard inclusions, such as #include#include The reason is this: we actually change the definition of types "double" and "long", but we do not want this change to modify the standard libraries. Now compile and run your program on the same data as in hw1. Report your results. Also, please report any additional changes to your original program needed to make your program with the CORE library, and how you fixed it. (Q2) Implement Sturm's algorithm for determining the number of roots of a polynomial within any given interval. We want you to use the Big Number packages in the CORE library for this exercise. Do this as simply as possible, not worrying about efficiency. To do this, you need to first implement a simple polynomial package in which coefficients are arbitrary BigIntegers. Then you need to implement Euclid's algorithm for computing the GCD of two polynomials. Please talk to me if you need help with this algorithm. (Q3) Isolate all the real roots of the following polynomials using your algorithm in (Q2): A(X) = X^4 + 14 X^2 - 8X + 49 B(X) = X^16 - 8 X^14 + 8X^12 + 64 X^10 - 98 X^8 -184 X^6 +200 X^4 + 224 X^2 - 113.