An experiment to see if Swift can help with writing physics lab reports. Still at a conceptual level.

Managing complicated calculations in Python as well as updating the results in your paper can be very challanging.

• Create expressions using operator overloads in a type safe way

• Deriving expressions using common derivation rules
• Solve simple equations
• Render expressions as LaTeX

As seen in Experiment.playground you could do this:

let f = sin(x.self) // type is Function<x>
f[0] // 0
f´ // Function<x> = cos(x)

The requirement to call .self to reference the type will perhaps go away in future Swift versions, so this is perhaps not as crazy as it initially seems.

How this scales to multi-variable expressions and equation systems I don't know.

• Plot equations automatically in an appropriate interval if derivatives can be found.
• Better LaTeX support
• Linear Regressions etc.
• Measurements with uncertainties (preferably inferred based on significant digits)
• Better Unit system
• Leverage type system if possible
• More algebraeic functionality
• MathJax?