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Old 2021-08-02, 04:12   #27

5·7·79 Posts

Originally Posted by Nick View Post
For anyone looking for a fun bit of summer reading..
Hi Nick,
I haven't been doing any math for the last several months with the exception of occasional sporadic jottings of approaches to solving a multivariate equation of degree 4. ie X^4*(a*b*c*d*e+...)+X^3*(b^2*d*e...)+..+X^0*(c*d..). The variables (there are up to five with their associated combinations) within the brackets where each variable does not exceed degree 2 but they may all be of degree 2.

Do you know of any math books, notes or approaches that apply to solving such expressions? I have a few that apply but I'm wondering about some other clever ideas that may exist. I've considered operational calculus, umbral calculus, trig. substitutions, iterative programming... Since this is a fourth degree form, I was also considering moments of inertia, chemical equations.. any thoughts you may have would be appreciated.

Just to provide some context, all of the variables exist as part of a Cartesian coordinate frame (with a slight modification). The expression exists under a radical so it represents solution(s) which may be +ve/-ve or complex...algebraic in any case. The variables composing the expression were combined from several merged general equations. There are some interesting facets regarding the interpretation of this degree four equation and I would like to obtain as broad a perspective as possible by encapsulating it via mathematical theory and utility. The coordinate frame mentioned previously represents the scaffolding for actual measurable figures. Further, that coordinate frame exists in conjunction with another required coordinate frame which has its own special features, some of which extend directly into lattice theory. Perhaps this context helps or perhaps not but at the very least I hope it provides you with an idea that a solid theoretical foundation exists within some elementary mathematics. Without being disingenuous, I'd like the final construct to display some ingenuity when the crank is turned and meaningful numbers are either turned out in one direction or meaningful concepts are turned out in the reverse direction...yes, there is also some thermodynamic reasoning involved with a 50/50 probability of some quantum logic involved as well.

Last fiddled with by jwaltos on 2021-08-02 at 05:09
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