' - - File: Identities1.txt  in Appendix file \ ValidityTest
'    File to test operations by using identities. See Walk Thru for comments.

a = 12.3E-2                                        ' Any constant; + numbers if Sqrt[ or logs are used.

G{t} = (t - a^.5)^2 + Log[t + a^3]                ' Any function
F{t}  = G{t + 2} + Log[Abs[t+1.4E1]]         ' Any function that references another function.

A<t> = <t, t^3, Sqrt[t] >                              ' Any vector
B<t> = <G, Sinh[t^2], F >                          ' Any vector that references functions.


' - - - - - - - - - - -  Check math using Trig ID: Sin[....]^2 + Cos[....]^2 = 1 - - - - - - - - - - - - - - - -
Tr{t} = Sin[F{t}]^2 + Cos[F{t}]^2	               ' --> should be one. 
Dr{t} = Diff[Tr,t]                                                             ' --> should be zero.

' The parsing program knows nothing about the trig identity. The diff operator cranks out
'      derivative of Tr{t} with no prior knowledge of the unique identity.l

' - - - - - - - - - - - - Check Identities for the Dot product & Cross product - - - - - - - - - - - - - -
Au<t> = vUnit[A]                                         ' Au / |Au|
Do{t} = sDot[Au,Au]                                   ' Should be one.

Cr<t> = vCross[A,A]                                   ' A x A --> should be <0, 0, 0>

<t = 12.43E-1>


