From 7435872d4eae7b0e667537b5c917493da60f945f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Mon, 7 Oct 2024 15:55:23 +0200 Subject: [PATCH] Whitespace changes --- .../IntersectionTheory/docs/src/intro.md | 4 ++-- experimental/IntersectionTheory/src/blowup.jl | 24 +++++++++---------- 2 files changed, 14 insertions(+), 14 deletions(-) diff --git a/experimental/IntersectionTheory/docs/src/intro.md b/experimental/IntersectionTheory/docs/src/intro.md index d317d433b711..7b546bf82902 100644 --- a/experimental/IntersectionTheory/docs/src/intro.md +++ b/experimental/IntersectionTheory/docs/src/intro.md @@ -18,14 +18,14 @@ In this chapter, we while Chow is due to Manfred Lehn and Christoph Sorger. Schubert3 as well as the Singular library schubert.lib were written by Dang Tuan Hiep. The basis for all this work, including ours, is the Maple package Schubert written by Sheldon Katz and Stein A. Strømme. - + Throughout the chapter, the varieties we consider are smooth projective varieties over the complex numbers. !!! note The Chow ring of a variety `X` is the group of cycles of `X` modulo an equivalence relation, together with the intersection pairing which defines the multiplication of the ring. Here, in contrast to most textbooks, we consider numerical equivalence classes of cycles rather than - rational equivalence classes. + rational equivalence classes. Our approach is abstract in the sense that we do not work with concrete varieties; that is, our varieties are not given by equations. Instead, we represent a variety by specifying its diff --git a/experimental/IntersectionTheory/src/blowup.jl b/experimental/IntersectionTheory/src/blowup.jl index 1965af4b2690..70f4971dd24a 100644 --- a/experimental/IntersectionTheory/src/blowup.jl +++ b/experimental/IntersectionTheory/src/blowup.jl @@ -195,12 +195,12 @@ function present_finite_extension_ring(F::Oscar.AffAlgHom) V = groebner_basis(J) sect = x -> (y = reduce(BRtoR(x), gens(V)); - ans = elem_type(AR)[]; - for i in 1:g - q = div(y, gs_lift[i]) - push!(ans, RtoAR(q)) - y -= q * gs_lift[i] - end; ans) + ans = elem_type(AR)[]; + for i in 1:g + q = div(y, gs_lift[i]) + push!(ans, RtoAR(q)) + y -= q * gs_lift[i] + end; ans) FM = free_module(R, g) gB = elem_type(FM)[FM(push!([j == i ? R(1) : R() for j in 1:g-1], -gs_lift[i])) for i in 1:g-1] @@ -356,12 +356,12 @@ function blowup(i::AbstractVarietyMap; symbol::String = "e") RX = base_ring(X.ring) RPNtoRX = hom(base_ring(PN.ring), RX, pushfirst!(gens(RX), RX())) jₓ = x -> (xf = simplify(x).f; - RX = base_ring(X.ring); ans = RBl(); - for k in rN-1:-1:0 - q = div(xf, ζ.f^k) - ans += jₓgˣ(X(RPNtoRX(q))) * (-E[end])^k - xf -= q * ζ.f^k - end; Bl(ans)) + RX = base_ring(X.ring); ans = RBl(); + for k in rN-1:-1:0 + q = div(xf, ζ.f^k) + ans += jₓgˣ(X(RPNtoRX(q))) * (-E[end])^k + xf -= q * ζ.f^k + end; Bl(ans)) jₓ = map_from_func(jₓ, PN.ring, Bl.ring) j = AbstractVarietyMap(PN, Bl, jˣ, jₓ)