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Project: Testing 18.04
Path: sage-9.1.ipynb
Views: 809Kernel: SageMath 9.1
Sage 9.1 on CoCalc
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'SageMath version 9.1, Release Date: 2020-05-20'
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[x == (2/3), x == -1, x == (3/2), x == -1/2*I*sqrt(3) - 1/2, x == 1/2*I*sqrt(3) - 1/2, x == 1]
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Polyhedral geometry
There is now a catalog for common polyhedral cones, e.g.
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5-d cone in 5-d lattice N
New features for polyhedra:
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A 3-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 8 vertices
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64
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Integral curves over finite fields
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Affine Plane Curve over Finite Field in z4 of size 2^4 defined by x^3*y + y^3 + x
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Function field in y defined by y^3 + x^3*y + x
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3
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[Point (x, y),
Point (x + (z4), y + (z4^3 + z4^2)),
Point (x + (z4^2), y + (z4^3 + z4^2 + z4 + 1)),
Point (x + (z4^3), y + (z4^2 + z4)),
Point (x + (z4 + 1), y + (z4^3 + z4)),
Point (x + (z4^2 + z4), y + (z4^2 + z4 + 1)),
Point (x + (z4^2 + z4), y + (z4^3 + 1)),
Point (x + (z4^2 + z4), y + (z4^3 + z4^2 + z4)),
Point (x + (z4^3 + z4^2), y + (z4^2 + z4 + 1)),
Point (x + (z4^2 + 1), y + (z4^3)),
Point (x + (z4^3 + z4), y + (z4^2 + z4 + 1)),
Point (x + (z4^2 + z4 + 1), y + (z4^2 + z4)),
Point (x + (z4^2 + z4 + 1), y + (z4^3 + z4 + 1)),
Point (x + (z4^2 + z4 + 1), y + (z4^3 + z4^2 + 1)),
Point (x + (z4^3 + z4^2 + z4 + 1), y + (z4^2 + z4))]
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[(x + z4)/x, 1/x^2*y + (z4^2 + z4)/x]
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[Place (x + z4, y^2 + (z4^3 + z4^2)*y + z4^2 + z4 + 1),
Place (x + z4, y + z4^3 + z4^2)]
Generator for cube-connected cycles
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Manifolds
More functionalities in index notation for tensors
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True
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Vector field on the Euclidean plane E^2
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Tensor field of type (0,2) on the Euclidean plane E^2
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(X^j, X_ij, X_ji)
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Field of symmetric bilinear forms on the Euclidean plane E^2
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Graftal Lace Cellular Automata with rule 20336027
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Elementary cellular automata with rule 151 and initial state [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
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