The expression and summation of the unary polynomial

Symbolic polynomial operation, has become a typical use case for table processing, mathematically, a unary polynomial pn (x) can be written according to ascending:

Pn (x) =p0+p1x1+p2x2+p3x3+...+pnxn

It is determined only by the n+1 coefficients alone. Therefore, in a computer, it can be represented by a linear table P:

p= (p0,p1,p2,p3,..., PN)

The exponent I of each item is implied in the ordinal of its coefficient pi.

This section will focus on how to use the basic operation of a linear list to implement the operation of a unary polynomial.

Using the basic operation of linear list to realize the operation of one-element sparse polynomial, the abstract data type polynomial is realized.

ADT polynomial{
Data objects: d={ai | ai∈termset, i=1,2,..., m, m≥0
Each element in the Termset contains a real number representing the coefficients and an integer representing the exponent}
Data relations: r1={<ai-1, Ai>|ai-1, ai∈d, and exponential value ai-1 in <ai, i=2,......,n}
Basic operation:
Creatpolyn (&P,M)
Operation Result: Enter the coefficients and exponent of M term, establish the unary polynomial p.
Destroypolyn (&P)
Initial conditions: A unary polynomial p already exists.
Operation Result: Destroy the unary polynomial p.
Printpolyn (P)
Initial conditions: A unary polynomial p already exists.
Operation Result: Print out the unary polynomial p.
Polynlength (P)
Initial conditions: A unary polynomial p already exists.
Operation Result: Returns the number of items in a unary polynomial p.
Addpolyn (&PA,&PB)
Initial conditions: A unary polynomial pa and PB already exist.
Operation Result: completes the polynomial summation operation, namely: PA=PA+PB, and destroys one meta-polynomial Pb.
Subtractpolyn (&PA,&PB)
Initial conditions: A unary polynomial pa and PB already exist.
Operation Result: Complete the polynomial subtraction operation, namely: PA=PA-PB, and destroy the unary polynomial Pb.
Multiplypolyn (&PA,&PB)
Initial conditions: A unary polynomial pa and PB already exist.
Operation Result: complete polynomial multiplication operation, namely: PA=PAXPB, and destroy one meta-polynomial Pb.
}adt polynomial

To achieve the above definition of the unary polynomial, it is obvious that the chain storage structure should be adopted. How to implement the multi-phase addition operation represented by this linear table.

Arithmetic rules based on the addition of a unary polynomial: for the two unary polynomial all exponents of the same term, the corresponding coefficients are added, if they are not zero, it constitutes one of the "and polynomial", and for the two unary polynomial in all the index is different, then copied to the "and polynomial".

The expression and summation of the unary polynomial