Substitutions for GenericSeries and MathematicalExpression

[vhirtham]

I do not want to include this into the first version of the GenericSeries since it is already enough work, but I think we should definitely consider it in the future:

Sometimes there are expressions that have repetitive terms. For example, consider the following I used in the GenericSeries tutorial:

expr = "tanh((x-t)/5) - tanh(x-t-10)"

Here the term x-t is used twice. Not so bad you might think and it isn't as long as you do not start using units. Here x is a spatial dimension with a length unit and t is time. Also, consider that tanh requires an angular unit or no unit at all and suddenly you get a total mess. To get everything sorted out, you need to bloat this subterm to a * x + b * t where a and b are parameters that are just there to clear the units. And no, clearing the units from the variables in advance (before we evaluate) is also no option because x and t might appear in other terms where the unit does not need to be cleared. The simple solution would be to have a substitution like this:

expr = "tanh(s/5) - tanh(s-10)"
subs = {"s": "a * x + b * t"}

Apart from some minor difficulties, this shouldn't be a big issue since it can be a simple text replacement in the beginning and get some more depth later (strings are not the only method to define a math expression or think of chained substitutions). This should probably be implemented as a feature of the MathematicalExpression

[CagtayFabry]

I think a string replacement before evaluation is a good (and simple) solution, everything else might be a bit overkill for the scope of weldx for now

PS: just seeing tanh(x-t-10) makes my skin crawl when thinking about the units (and we should avoid automatically ' just clearing' units because this would defeat the whole purpose in the first place. There is no such thing as 'clearing units', there is only conversion 📜

[vhirtham]

PS: just seeing tanh(x-t-10) makes my skin crawl when thinking about the units

It's not that bad. Not much worse as when describing a sine weaving motion, just with an extra (incompatible) dimension.
The equation is just a modified version of a traveling wave 😉

(and we should avoid automatically ' just clearing' units because this would defeat the whole purpose in the first place.

exactly

There is no such thing as 'clearing units', there is only conversion 📜

have a word with my 🧽

[CagtayFabry]

PS: just seeing tanh(x-t-10) makes my skin crawl when thinking about the units

It's not that bad. Not much worse as when describing a sine weaving motion, just with an extra (incompatible) dimension. The equation is just a modified version of a traveling wave 😉

I meant concerning that it should always be in the form of tanh(a*x+b*t-10) (which looks pretty ⭐ )

[vhirtham]

PS: just seeing tanh(x-t-10) makes my skin crawl when thinking about the units

It's not that bad. Not much worse as when describing a sine weaving motion, just with an extra (incompatible) dimension. The equation is just a modified version of a traveling wave 😉

I meant concerning that it should always be in the form of tanh(a*x+b*t-10) (which looks pretty ⭐ )

True, but that's the target equation. In the tutorial, we start simple (no parameters, no units) and get there step by step 😉