-
Notifications
You must be signed in to change notification settings - Fork 260
Add principal ideal construction #2857
New issue
Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.
By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.
Already on GitHub? Sign in to your account
base: quotient-rings
Are you sure you want to change the base?
Conversation
|
As with the (admittedly fiddly) factorisation of the Binomial Theorem in #1928 , consider refactoring this so that:
UPDATED: might usefully need to define the |
To help justify this to future me who may have forgotten this, the scalar multiples of the identity matrix commute with all square matrices (over a commutative ring) |
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
I know it's still draft, I'm still approving!
| ; _+ᴹ_ = _+_ | ||
| ; _*ₗ_ = _*_ | ||
| ; _*ᵣ_ = _*_ | ||
| ; 0ᴹ = 0# | ||
| ; -ᴹ_ = -_ |
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
Can these be recreated by record { RawBimodule rawBimodule hiding (_≈ᴹ_); _≈ᴹ_ = _≈_ on a *_ }, with rawBimodule brought into scope by the opening of subbimodule in Ideal?
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
Can we even lift out the definition ι = a *_ in a where clause, so that this could 'just' be _≈ᴹ_ = _≈_ on ι ?
| ; 0ᴹ = 0# | ||
| ; -ᴹ_ = -_ | ||
| } | ||
| ; ι = a *_ |
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
... and here?
| ; ⁻¹-homo = λ x → sym (-‿distribʳ-* a x) | ||
| } | ||
| ; *ₗ-homo = x∙yz≈y∙xz a | ||
| ; *ᵣ-homo = λ r x → sym (*-assoc a x r) |
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
Is there nothing under Algebra.Properties.(Commutative)Semigroup that could be deployed here, as on the previous line, mentioning only a?
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
I don't think so, and certainly not with this argument order
On top of #2855, taken from #2729