feat(QM): AddZeroClass for UnboundedOperator#999
Open
gloges wants to merge 3 commits intoleanprover-community:masterfrom
Open
feat(QM): AddZeroClass for UnboundedOperator#999gloges wants to merge 3 commits intoleanprover-community:masterfrom
gloges wants to merge 3 commits intoleanprover-community:masterfrom
Conversation
Contributor
Author
|
t-quantum-mechanics |
Contributor
Author
|
RFC |
github-actions
bot
added
t-quantum-mechanics
Member
jstoobysmith
left a comment
jstoobysmith
left a comment
There was a problem hiding this comment.
Looks mainly good to me. Couple of comments
| rw [← add_zero U.toLinearPMap] | ||
| exact add_toLinearPMap_of_dense_closable (by simp [U.dense_domain]) (by simp [U.is_closable]) | ||
|
|
||
| lemma add_assoc {U₁ U₂ U₃ : UnboundedOperator H H'} |
Member
There was a problem hiding this comment.
Could we maybe put some comments on these lemmas. For instance, I think this is the statement that if addition does not give a junk value, then it is associative?
| (hD : Dense (U₁.domain ⊓ U₂.domain ⊓ U₃.domain : Set H)) (hC₁₂ : (U₁.1 + U₂.1).IsClosable) | ||
| (hC₂₃ : (U₂.1 + U₃.1).IsClosable) : U₁ + U₂ + U₃ = U₁ + (U₂ + U₃) := by | ||
| have hD' : Dense (U₁.domain ⊓ (U₂.domain ⊓ U₃.domain) : Set H) := by simp_all [Set.inter_assoc] | ||
| have hD₁₂ : Dense (U₁.domain ⊓ U₂.domain : Set H) := Dense.mono Set.inter_subset_left hD |
Member
There was a problem hiding this comment.
Suggested change
| have hD₁₂ : Dense (U₁.domain ⊓ U₂.domain : Set H) := Dense.mono Set.inter_subset_left hD | |
| have hD₁₂ : Dense (U₁.domain ⊓ U₂.domain : Set H) := hD.mono Set.inter_subset_left |
Member
|
awaiting-author |
github-actions
bot
added
the
awaiting-author
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Defines zero as the zero map with full domain.
Defines addition of unbounded operators, using two junk values:
D(U1) ∩ D(U2)is not dense, use the zero with full domain.D(U1) ∩ D(U2)is dense butU1 + U2is not closable, use the zero map onD(U1) ∩ D(U2).This second junk value will be needed so that smul distributes over addition in all cases. It ensures that
c • (U1 + U2) = c • U1 + c • U2holds for(c : ℂ) = 0whenD(U1) ∩ D(U2)is dense, since the RHS is the zero map onD(U1) ∩ D(U2)regardless of whetherU1 + U2is closable or not.add_assocproves associativity holds when no junk values are encountered(cf. #957, #978)