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Exponentiating Algebraic Polynomials

IP.com Disclosure Number: IPCOM000078966D
Original Publication Date: 1973-Apr-01
Included in the Prior Art Database: 2005-Feb-26
Document File: 3 page(s) / 228K

Publishing Venue

IBM

Related People

Rehwald, W: AUTHOR

Abstract

Terms or members of algebraic polynomials may take the form of -6ac/2/de/3/, for example. If the polynomial merely consists of members including variables, parameters and functions symbolized by the letters a, b, c, d, and e, then -6ac/2/de/3/ can also be written as -6 10213, provided the one-digit exponents of the variables a, b, c, d, and e are combined in alphabetical order to an even number. In this example, the six is not represented, a 0 rather appearing in its corresponding order position. Written in this form, polynomials can be exponentiated by program. In this case, the coefficients -6 and the exponents 10213 are processed in different ways. The coefficients are to be multiplied, whereas the exponents are to be added.

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Exponentiating Algebraic Polynomials

Terms or members of algebraic polynomials may take the form of - 6ac/2/de/3/, for example. If the polynomial merely consists of members including variables, parameters and functions symbolized by the letters a, b, c, d, and e, then -6ac/2/de/3/ can also be written as -6 10213, provided the one-digit exponents of the variables a, b, c, d, and e are combined in alphabetical order to an even number. In this example, the six is not represented, a 0 rather appearing in its corresponding order position. Written in this form, polynomials can be exponentiated by program. In this case, the coefficients -6 and the exponents 10213 are processed in different ways. The coefficients are to be multiplied, whereas the exponents are to be added. From the mixed members, only that is computed in which the combined terms occur in the given order.

The flow chart of Fig. 1 shows an example of a program for a z-member polynomial, which is to be raised to the power of five. For calling the stored coefficients and exponents of the z members, the five address parameters 1 to z are varied. Equality or inequality of the successive address parameters determines whether a member is generated by combining only one or several terms, and simultaneously serves to establish the polynomial coefficient which is subject to the following defining equation: p = n!/II nu(i)!.

Thus, the highest possible polynomial coefficient for n = 5 is 120. In addition, there are t...