Eliminating η from η equations

Defining η

Note:  If the i in the equation is not defined, it is assumed to be greater than 2.

c has already been used so cη will be used as the third coefficient. etaValues stores the defination for the η function


etaSubs is a list of transformation rules for η,η',η'' and η'''.This can be extended or shrunk from the segment {j,0,3} The three denotes a table with rules up to the third derivative.


This evaluates etaEqn with etaSubs transformation rules.  NOTE:  This method of evaluating etaSubs requires real numbers for modes.  The subscripts extract the left and right sides of the requations and re-delete higher order terms


etaSubEqn[i_, N_, M_]/;IntegerQ[N] && (N<2 || IntegerQ[M]) := (etaEqn[i, N, M]/.etaSubs)[[1]] + O[α]^2 == (etaEqn[i, N, M]/.etaSubs)[[2]] + O[α]^2

In case a symbolic mode is warrented, the second equation will automatically be used.  This second definition will be slower.


etaSubEqn[i_, N_, M_] := Block[{τ, η, ω}, etaValues ; Block[{τ, η, ω}, etaEqn[i, N, M]]]

Eliminating powers of trig functions

These are the rules we'll be using to simplify etaEqn



etaExpandEqn[i_, N_, M_] := etaExpandEqn[i, N, M] = Collect[ExpandAll[etaSubEqn[i, N, M]]//.TrigRules, α]

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