In Java create a program that will manage polynomials in three variables (x, y, and z) with non-zero integer coeficients, and non-negative integer exponents. Three variable polynomials are of the following form:

p(x,y,z) = c₁x^A₁y^B₁z^C₁ + ··· + c_nx^A_ny^B_nz^C_n

where c_i is coeficient, and A_i, B_i and C_i represent the exponents of variables.

To simplify the project, we only deal with polynomials in the above form, under the following assumptions.

1. We assume that every term in a polynomial follows xyz sequence. We only deal with a term like 5x⁶y³z², and we won’t deal with a term like 5y³x⁶z².

2. We assume that a coeficient can only occur at the beginning of a term. We only deal with a term like 6x⁸y⁴z⁵. We won’t deal with a term like 3x⁸ · 2y⁴z⁵.

3. We assume that no term in a polynomial contains division operator. We won’t deal with a term like 4x³/(y⁷z⁵).

2 Requirements

2.1 Input Representation of Polynomials

The purpose of your program is to interact with users by inserting, deleting, updating, and searching named polynomials. By following the assumptions defined in Section 1, we can simplify how a polynomial can be input into the program. In a polynomial, each term is represented by 4 integers separated by commas:

• coeficient

• exponent for variable x • exponent for variable y • exponent for variable z

and multiple terms are separated by space characters. For example, if the polynomial is

A = 6x⁹y⁶z³ + 5x⁴z⁵ − 3

its input should be

A 6,9,6,3 5,4,0,5 -3,0,0,0

Your program must be able to handle/parse the input correctly.

2.2 Output Representation of Polynomials

The program output of polynomials is similar to standard mathematical form with simplifications. For example, if the polynomial is

B = −2x³y⁷z² + x4z⁵ − 8y³z + 9

its output should be

B = - 2(x^3)(y^7)(z^2) + (x^4)(z^5) - 8(y^3)(z) + 9

To ensure correct output formats, please attend to the following items.

1. Pay attention to the usage of parentheses in the above example.

2. Pay attention to the spaces around operators in the above example.

3. If the coeficient of the first term is positive, do not display the plus sign for the first term. For example, B = 2(x^3)(y^7)(z^2) + (x^4)(z^5) - 8(y^3)(z) + 9

4. If the coeficient of a term is 0, do not display this term. An exception is that if the polynomial contains no terms at all, display 0.

5. If the coeficient of a term is 1, do not display the coeficient. The exception is that if the exponents of x, y and z are all 0, and the coeficient is 1, 1 must be displayed for this term. For example, B = - 2(x^3)(y^7)(z^2) + (x^4)(z^5) - 8(y^3)(z) + 1

6. If the exponent of a variable is 0, do not display this variable.

7. If the exponent of a variable is 1, just display the variable itself, and keep the parentheses.

2.3 Polynomial Management Operations

Your program must maintain a list of named polynomials. The management operations are as follows.

INSERT Insert a new polynomial into the list. If the insert operation is successful, output the polynomial. The insert operation can fail if there is already a polynomial in the list with the same name. In the case of an insertion failure, display the message POLYNOMIAL ALREADY INSERTED.

DELETE Delete an existing named polynomial from the list. If the delete operation is successful, display the message POLYNOMIAL SUCCESSFULLY DELETED. If the named polynomial does not exist, display the message POLYNOMIAL DOES NOT EXIST.

UPDATE Update an existing polynomial in the list. If it is found in the list, the existing poly-nomial is replaced by the newly entered one, and output the updated polynomial. If the polynomial does not exist, display the message POLYNOMIAL DOES NOT EXIST.

SEARCH Search for a named polynomial in the list. If it is found in the list, output the polyno-mial. If the polynomial does not exist, display the message POLYNOMIAL DOES NOT EXIST.

QUIT This command makes the program properly exit. The QUIT command should remove all the polynomials from the list, and then exit the program.

To review, the following examples are provided.

INSERT A 3,2,0,0 5,1,1,0 -8,0,2,0 4,1,0,0 -3,0,1,0 12,0,0,0

A = 3(x^2) + 5(x)(y) - 8(y^2) + 4(x) - 3(y) + 12

INSERT B 1,3,0,0 6,0,2,0 -15,1,0,0 11,0,0,0

B = (x^3) + 6(y^2) - 15(x) + 11

INSERT A 2,1,0,0 3,0,1,0 -5,0,0,0

POLYNOMIAL A ALREADY INSERTED

DELETE B

POLYNOMIAL B SUCCESSFULLY DELETED

DELETE C

POLYNOMIAL C DOES NOT EXIST

UPDATE A 1,1,0,0 -4,0,1,0 1,0,0,0

A = (x) - 4(y) + 1

UPDATE B 4,2,2,2 8,1,1,1 16,0,0,0

POLYNOMIAL B DOES NOT EXIST

SEARCH A

A = (x) - 4(y) + 1

SEARCH B

POLYNOMIAL B DOES NOT EXIST

3 Data Structures and Design

3.1 Term Class

Each polynomial is composed of many polynomial terms. You are to create a Term class that only holds the information for a polynomial term. This class should have necessary private fields for a polynomial term (1 coeficient and 3 exponents), proper constructors, getters, and setters. In addition, the class should also override the method toString(). It returns a String, which shows a polynomial term in proper format.

3.2 DLList Class

Use the implemented DLList class.

3.3 Polynomial Class

Building up from the Term class and DLList class, Polynomial is composed of two private fields:

1. The name of the polynomial

3

2. A doubly linked list of Terms.

Polynomial class should have proper constructors, getters, setters, and other useful methods if needed.

3.4 PolyList Class

Building up from the Polynomial class and DLList class, PolyList is a doubly linked list of Polynomials. This class should implement all the polynomial management operations.

3.5 Project3 Class

In this project, Project3 class should handle all the input from users. This class is also the entrance of the program.