(Free42, DM42, HP42S): Polynomial Solver

[Namir]

The classical Polynomials have the powers of the terms change by integer values, usually 1, and sometimes 2. Think of this change in power as a tempo. The Shammas Polynomials alter this tempo. If you read my notes on my web sites you will see that I use Shamrmas Polynomials to have a slower tempo—that is increase the powers by non-integer values that are usually less than 1. I use this scheme to perform curve fitting that has the values of the highest terms rise to powers that are less than in classical polynomials with the same number of terms. The advantage here is that rounding errors are reduced.

I used my last name in naming the Shammas Polynomial to avoid using more general names that may, sooner or later, conflict with similar polynomial names proposed by others.

I am a person who thinks outside the box, sometimes as a math heretic. To me that is far more satisfactory that focusing endlessly on topics like calculating pi, logarithm of 2, or calculating trig functions. If mathematicians like Gauss had our powerful computers and software, he would have come up with non-integer polynomials and called them Gauss Polynomials—and the topic would be a classic by now. In fact I have noticed advances on topics like non-integer derivatives and integrals. I am sure these new advances leave some of us scratching their heads!