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Is there a way to use SymPy to compute a matrix's characteristic polynomial (`charpoly`) over a finite field (such as GF(2))? If not, can this be added?
The same applies to other matrix operationsβ¦
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Simple test case demonstrating issue:
![master](https://github.com/weymouth/WaterLily.jl/assets/468263/b210b5de-f244-43a4-860d-4ff39a0c0384)
[updated example]
```julia
using WaterLily,StaticArrβ¦
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### What
```[tasklist]
### First steps
- [ ] Extract parts of the iPhone app (https://github.com/openfoodfacts/openfoodfacts-ios)
- [ ] Create a Kotlin package
- [ ] Automate publication
- [ β¦
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There is a problem with the normalization of names of variables which are given automatically for finite fields.
```
sage: K = GF(4)
sage: K._factory_data
(,
(7, 5, 'beta6'),
(4, 'z2', x^2 + x + β¦
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Attempt to compute `discrete_log(M,M)` for a matrix `M` over a finite field results in one of two errors:
> ValueError: No discrete log of ... found to base ...
or
> TypeError: mutable matrices aβ¦
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On my laptop, it takes almost 1 second to create a polynomial of degree 10000 over F_125:
```
sage: k = GF(5^3)
sage: S. = k[]
sage: L = [ k.random_element() for _ in range(10000) ]
β¦
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One would expect the performance of casting the usual way (as in test 1 below) to be at least not much worse than test 2:
```
sage: QQX=QQ['x']
sage: QP=Qp(3,30);
sage: R=QP.residue_field();
sage: β¦
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```
degree(R::GFField)
Return the degree of the given finite field.
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degree(a::FqPolyRepField)
β¦
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The Viff codebase already has a nice python abstraction for finite fields (viff/field.py) and for matrices over finite fields. Polynomials over finite fields are also generally useful. These are alreaβ¦
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### What
- [ ] Implement Search V2 API to the fullest
- [ ] https://wiki.openfoodfacts.org/Open_Food_Facts_Search_API_Version_2
- [ ] https://github.com/openfoodfacts/openfoodfacts-server/blob/mainβ¦