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[Merged by Bors] - feat(algebra/module/zlattice): prove some results about Z-lattices #18266

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@xroblot xroblot commented Jan 23, 2023

For a ℤ-lattice L given by L := submodule.span ℤ (set.range b) where b is a basis of finite dimensional real vector space E, this PR defines the fundamental domain of L and proves that it is a fundamental domain in the sense of measure_theory.group.fundamental_domain.

It also introduces most of the tools that will be needed to prove that a discrete subgroup of E that spans E over is a
ℤ-lattice, see #18477


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@xroblot xroblot added WIP Work in progress t-number-theory Number theory (also use t-algebra or t-analysis to specialize) labels Jan 23, 2023
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@xroblot xroblot marked this pull request as ready for review February 23, 2023 21:23
@xroblot xroblot added awaiting-review The author would like community review of the PR and removed WIP Work in progress labels Feb 23, 2023
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I wonder how general we should make this file, clearly some of the bits at the end are quite specific to Z inside R, but results like zspan.mem_span_iff seem useful more generally for quite arbitrary spans of subrings?

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@mathlib-dependent-issues-bot mathlib-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Mar 6, 2023
@xroblot xroblot requested review from a team as code owners March 6, 2023 10:22
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Thanks!

bors d+

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bors bot commented Jun 9, 2023

✌️ xroblot can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@leanprover-community-bot-assistant leanprover-community-bot-assistant added delegated The PR author may merge after reviewing final suggestions. and removed awaiting-review The author would like community review of the PR labels Jun 9, 2023
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@eric-wieser eric-wieser changed the title feat(zlattice): prove some results about Z-lattices feat(algebra/module/zlattice): prove some results about Z-lattices Jun 9, 2023
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xroblot commented Jun 9, 2023

bors r+

bors bot pushed a commit that referenced this pull request Jun 9, 2023
…18266)

For a ℤ-lattice `L` given by `L := submodule.span ℤ (set.range b)` where `b` is a basis of finite dimensional real vector space `E`, this PR defines the fundamental domain of `L` and proves that it is a fundamental domain in the sense of `measure_theory.group.fundamental_domain`. 

It also introduces most of the tools that will be needed to prove that a discrete subgroup of `E` that spans `E` over  `ℝ` is a 
ℤ-lattice, see #18477
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@bors bors bot changed the title feat(algebra/module/zlattice): prove some results about Z-lattices [Merged by Bors] - feat(algebra/module/zlattice): prove some results about Z-lattices Jun 9, 2023
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@bors bors bot deleted the xfr-zlattices branch June 9, 2023 21:07
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