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[Merged by Bors] - feat(algebra/module/zlattice): prove some results about Z-lattices - #18266
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[Merged by Bors] - feat(algebra/module/zlattice): prove some results about Z-lattices#18266xroblot wants to merge 90 commits into
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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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…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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For a ℤ-lattice
Lgiven byL := submodule.span ℤ (set.range b)wherebis a basis of finite dimensional real vector spaceE, this PR defines the fundamental domain ofLand proves that it is a fundamental domain in the sense ofmeasure_theory.group.fundamental_domain.It also introduces most of the tools that will be needed to prove that a discrete subgroup of
Ethat spansEoverℝis aℤ-lattice, see #18477