Kernel: SageMath 9.4
Hello Sage 9.4
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'SageMath version 9.4, Release Date: 2021-08-22'
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{ (x, y) ∈ Vector space of dimension 2 over Rational Field : x^2 + 3*y^2 <= 42 }
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{ (x, y) ∈ Ambient free module of rank 2 over the principal ideal domain Integer Ring : abs(sin(1/2*pi*x + 1/2*pi*y)) < (1/1000) }
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{ (x, y) ∈ Free module of degree 2 and rank 2 over Integer Ring
Echelon basis matrix:
[1 0]
[0 1] : x^2 + 3*y^2 <= 42, abs(sin(1/2*pi*x + 1/2*pi*y)) < (1/1000) }
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(x, y) |--> x^2 + y^2 == x^2 + y^2
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{ (x, y, z) ∈ Ambient free module of rank 3 over the principal ideal domain Integer Ring : sqrt(x^2 + y^2 + z^2) < 12 }
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Id_M: M → M
(x, y) ↦ (x, y)
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v = -y ∂/∂x + x ∂/∂y
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v⊗df = -2*x*y ∂/∂x⊗dx - 2*y^2 ∂/∂x⊗dy + 2*x^2 ∂/∂y⊗dx + 2*x*y ∂/∂y⊗dy
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True
FlatVeeringTriangulation(Triangulation("(0,1,2)(~2,~0,~1)"), [(1, 2), (-2, -1), (1, -1), (-1, 1), (2, 1), (-1, -2)])
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TranslationSurface built from 1 polygon
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H_2(2)
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'0.4.1'
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(1,2)(3)
(1,3)(2)
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[0.333283800731917]
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H_5(2^4)
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Bär–Faddeev–LeVerrier algorithm for the Pfaffian of skew-symmetric matrices
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CPU times: user 853 µs, sys: 0 ns, total: 853 µs
Wall time: 8.53 ms
Polyhedral geometry
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*-insertion algorithm from https://arxiv.org/abs/1911.08732:
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Spheres added to the manifold catalog
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3d plots
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