Polynomial solver

Problem Statement

You are required to design a system to represent and manipulate polynomials.
Assume that you have 3 available polynomial variables: A, B and C, that can be set by the user and one variable R that acts as an accumulator for the results of operations on other polynomials.
You should order the polynomial terms in descending order by the exponent.
Create a user-friendly, menu-driven system that performs the following operations:

• Read in a polynomial and store it in variable A, B, or C.
• Output a polynomial using a form that clearly displays it.
• Add two polynomials and store the result in R.
• Subtract two polynomials and store the result in R.
• Multiply two polynomials and store the result in R.
• Evaluate a polynomial at some point, 'a', where 'a' is a constant. In other words, substitute by the given value in your polynomial.
• Clear a polynomial.

Note that: a polynomial whose value is cleared or initially unset cannot be involved in an operation.
The core of the application should throw a runtime exception when it encounters any invalid input or operation. You should print "Error" in case you catch any exceptions.

Input Format

set: set the values of coeffecients for a polynomial (exponents should be in desending order) given the name of polynomial (A,B,C).
print: prints a polynomial in a readble format given its name.
add: adds two polynomials given their names.
sub: subtracts the first polynomial from he second given their names.
mult: multiplies two polynomials given their names.
clear: clears a polynomial given its name.
eval: evaluates a polynomial given its name.

Sample Input 1

set
A
[1,-3,2]
print
A
set
B
[1,-5,6]
print
B
set
C
[1,-9,26,-24]
print
C

Sample Output 1

x^2-3x+2
x^2-5x+6
x^3-9x^2+26x-24

Sample Input 2

set
A
[1,-9,26,-24]
set
B
[5,10,4,30]
add
A
B

Sample Output 2

6x^3+x^2+30x+6

Sample Input 3

set
A
[1,-13,50,-56]
eval
A
5

Sample Output 3

-6

Sample Input 4

set
A
[20,46,-30,-78]
set
B
[5,41,-50,0]
sub
A
B

Sample Output 4

15x^3+5x^2+20x-78

Sample Input 5

set
A
[32,41,67]
set
B
[2,3,1]
mult
A
B

Sample Output 5

64x^4+178x^3+289x^2+242x+67