Determinant and Adjugate Matrix #1165
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This looks like accidentally committed files
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Yes. I have removed it.
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Thanks for opening a PR on this! Determinants would certainly be very useful to have. |
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| {-# OPTIONS --cubical #-} | |||
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| module Minor where | |||
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Module names should always be fully qualified, i.e. Cubical.Algebra.Determinant.Minor in this case.
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Thank you! I have fixed it.
| CommRingR' : CommRingStr (R' .fst) | ||
| CommRingR' = commringstr 0r 1r _+_ _·_ -_ (CommRingStr.isCommRing (snd P')) | ||
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| -- Definition of the minor factor |
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I noticed that there is some redundancy in the Determinat (is that a typo?) .Base file. MF i is just (- 1r) ^ i (_^_ is defined in Cubical.Algebra.CommRing.Properties, and many of the properties of minor factor you prove are already proved there). And +Compat can by proved more simply by cong₂ _+_.
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Thank you! That could very well be the case. There is certainly a lot to improve here. When I wrote that, I had just started with Agda.
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In the four new files, the determinant of a matrix over a commutative ring is introduced through Laplace expansion, and it is proven that the adjugate matrix multiplied by the matrix itself equals the determinant times the identity matrix.
Additionally, it is shown that the determinant is independent of the row or column chosen for expansion, along with a few other minor properties of the determinant.
I am happy to consider any improvements.