Scheme Functions 4.0

##### Part I, Polynomials A data abstraction for polynomials was discussed in class. Create the file *[login to view URL]* and implement the following: 1. Constant **zp**. The zero polynomial. 2. Procedure **degree**. (degree p) ; returns the degree of polynomial *p* 3. Procedure **lc**. (lc p) ; returns the leading coefficient for polynomial *p* 4. Procedure **prest**. (reset p) ; returns the rest of polynomial *p* except leading term. 5. Constructor **pcons**. (pcons n a p) ; returns polynomial created from *a*xn and polynomial *p* Note! The underlying implementation must use a list of 2-element vectors to represent the polynomial. Zero terms should not be included. 6. Procedure **mt**. (mt d c) ; returns term created as *c*xd 7. Procedure **lt**. (lt p) ; returns the leading term from polynomial *p*. 8. Procedure **p+**. (p+ p1 p2) ; returns the sum of polynomials *p1* and *p2*. 9. Procedure **p***. (p* p1 p2) ; returns the product of polynomials *p1* and *p2*. 10. Procedure **np**. (np p) ; returns the negation for polynomial *p*. 11. Procedure **p-**. (p- p1 p2) ; returns the difference of polynomials *p1* and *p2*. 12. Procedure **v**. (v p n) ; returns the value of polynomial *p* when *x* is equal to *n*. ## Deliverables Part II, Binary Numbers. Implement the binary number functions discussed in class. Create the file *[login to view URL]* for the following: 1. Procedure **d->p** Parameter: list of binary digits Return: polynomial of degree 1 less than number of digits with digits as coefficients 2. Procedure **binary->decimal** Parameter: list of digits representing a binary number Return: decimal value 3. Procedure **p->d** Parameter: decimal number Return: list of digits in binary representation 4. Procedure **decimal->binary** Parameter: decimal value Return: list of digits representing the binary equivalent Part III, Number Conversion Implement the number conversion functions listed below. Create the file *[login to view URL]* for the following: Look over the programs for **b->d** and **d->b** and determine what changes have to be made to get definitions for the four procedurs: octal->decimal hexadecimal->decimal decimal->octal decimal->hexadecimal Since we are representing our hexadecimal numbers as lists of digits, we can use the number 10 for *A*, 11 for *B*, and so on, so that (12 5 10) is the list representation of the hexadecimal number *C5A*. Define one pair of conversion procedures **base->decimal** and **decimal->base** that takes two arguments, the number to be converted and the base, where the base can be any positive integer Then define a procedure **change-base** that changes a number *num* from base *b1* to base *b2*, where *num* is a list of digits. Thus *(change-base num b1 b2)* is a list of digits that gives the base *b2* representation of *num*. The following are some examples: (change-base '(5 11) 16 8) => (1 3 3) (change-base '(6 6 2) 8 2) => (1 1 0 1 1 0 0 1 0) (change-base '(1 0 1 1 1 1 1 0 1) 2 16) => (1 7 13) ## Platform Write Scheme source code for the above functions. The requried interpreter is SISC Version 1.8.7 which can be downloaded free from [login to view URL] Below are a few restrictions that have to be kept in mind when writing code. 1) Each of the functions must be specified using the full *lambda expression* to emphasize that they are first class entities in the language. 2)If you decide to use *define* anywhere in your code it is to be used for values bound at the top-level only. Local functions should be declared using *let* or one of its variants. The attached zip file has the specifications and requirements for the project in case anything is hard to read. **THE DUE DATE FOR THIS IS MONDAY MAY 3RD 04**. **_HE DUE DATE FOR THIS IS MONDAY MAY 3RD 04_**.