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docs: "Arithmetic" chapter added to absolute quantities post

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Mateusz Pusz
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docs/blog/posts/introducing-absolute-quantities.md
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@ -159,6 +159,44 @@ std::cout << "Kinetic energy: " << E_k.in<double>(J) << "\n";
```
## Arithmetic
Affine space arithmetic is well-defined. However, we are adding a new type to the library
that lands between points and deltas. This is why we must agree on the arithmetic for all
possible combinations.
Let's try to define them here, assuming that points and absolute values share
a common origin.
!!! note
If points and absolute values do not share a common absolute point origin
the operation should fail to compile.
### Addition
In case of addition, a more constrained type is preserved (except for adding two points,
which is undefined):
| Lhs \ Rhs | Point | Absolute | Delta |
|--------------|:----------------------:|:--------:|:--------:|
| **Point** | :material-close-thick: | Point | Point |
| **Absolute** | Point | Absolute | Absolute |
| **Delta** | Point | Absolute | Delta |
### Subtraction
Subtraction is more tricky. To verify the logic below, it might be helpful to ask whether
a result may be negative when two arguments are non-negative. If the answer is true,
the result should be a delta quantity.
| Lhs \ Rhs | Point | Absolute | Delta |
|--------------|:----------------------:|:--------:|:--------:|
| **Point** | Delta | Point | Point |
| **Absolute** | Delta | Delta | Absolute |
| **Delta** | :material-close-thick: | Delta | Delta |
## New opportunities
The new syntax simplifies API as one `quantity` class template will now serve all quantity