Add in an extensible formula library of successful plots

[marcnoon]

When graphing a formula I want to keep a history of formulas and their graphs. So the graph can be generated again when selected. y = sinx, a = -complex.sqrt(sin(x)), b = complex.sqrt(cos(x)) etc.. Most of the test cases will be in 1d, 2,d graphs but eventually move to 3d graphs and higher as get better at graphing the simpler equations. But the goal is to start with an alpha prototype for saving each graph into a a file or json file of some sort that can be reloaded... injected into a func or function... and then iterated over and plotted in the x,y,z etc... Thinking that this will be easy to create an alpha prototype for specific functions... but will become very hard to generalize creating a func for any formula or equation that is plottable. Also think about creating an IPlottable interface... what makes it be able to be plotable and what if missing will make it fail.

Also have history of the offset, the zoom, whether the an axis like x or y or z axis is visible, radian axis is available, polar axis etc..

1. Have a formula library that keeps track of named formulas and un-named formulas.. that can be added by anyone.
2. Keep track locally of history of any formulas ran and their specific setting like any offsets, translations, scaling, combining with other equations or formulas... runs, like multiple runs at the same time, or immediately after the first graph runs with its settings like scale, zoom, offset, etc...
3. Each equation can also have image or notes attached to it to describe the run and can be shared to a larger community within the app - like via a equation ran feed.
4. Attempt to make equations and formulas added be in text form, or some general form that an interpretter can generate a plot or graph from.
5. Have the equations be written in a function or func ... that is downloadable and shareable... and the return value is anything that can be plotted. <--- this is the optimum solution... if something can generate a func that can then be ran ... that would be amazing.

Describe the solution you'd like
Be able to write a text solution that generates a saved func or funcs that an then be ran for each iteration and ran in a run. A run is a plot of a function which generates a graphic that can be viewed in this program. Also have plots or runs that can change the shape of the line, the color, the thickness, the direction or vector, and any other attribute.

Describe alternatives you've considered
This library of equations should be equations that can be graphed, or have graphable properties that are able to be exploited into a graph of some sort. So solving equations could also be an option, but perhaps using ML to solve and predict the graph of a given equation and have the ML generate equations based on requested results.

Additional context
Runs...
So a run might show y=x ... and plot that. Then plot y = sinx and plot that. Then plot the sombination of y = xsinx and plot that and show how the combine. So if you run each one independently and then run them together should be able to combine equations in run on different threads easy with this solution.

[marcnoon]

Added a Formula class which is indexed. Need to test it and see if it works for the currently hard coded graph plot/s.