CoCalc provides the best real-time collaborative environment for Jupyter Notebooks, LaTeX documents, and SageMath, scalable from individual users to large groups and classes!
CoCalc provides the best real-time collaborative environment for Jupyter Notebooks, LaTeX documents, and SageMath, scalable from individual users to large groups and classes!
| Download
Project: Testing 18.04
Path: sage-9.1.ipynb
Views: 799Kernel: SageMath 9.1
Sage 9.1 on CoCalc
In [1]:
'SageMath version 9.1, Release Date: 2020-05-20'
In [2]:
[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]
In [3]:
In [0]:
In [12]:
Polyhedral geometry
There is now a catalog for common polyhedral cones, e.g.
In [13]:
5-d cone in 5-d lattice N
New features for polyhedra:
In [8]:
A 3-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 8 vertices
In [0]:
In [0]:
In [0]:
In [7]:
64
In [8]:
Integral curves over finite fields
In [9]:
Affine Plane Curve over Finite Field in z4 of size 2^4 defined by x^3*y + y^3 + x
In [10]:
Function field in y defined by y^3 + x^3*y + x
In [11]:
3
In [12]:
[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))]
In [13]:
[(x + z4)/x, 1/x^2*y + (z4^2 + z4)/x]
In [14]:
[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
In [15]:
Manifolds
More functionalities in index notation for tensors
In [16]:
True
In [17]:
Vector field on the Euclidean plane E^2
In [18]:
Tensor field of type (0,2) on the Euclidean plane E^2
In [19]:
(X^j, X_ij, X_ji)
In [20]:
Field of symmetric bilinear forms on the Euclidean plane E^2
In [0]:
In [0]:
In [0]:
In [0]:
In [0]:
In [21]:
In [0]:
In [22]:
In [0]:
In [0]:
In [23]:
Graftal Lace Cellular Automata with rule 20336027
In [24]:
In [0]:
In [25]:
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]
In [26]:
In [0]:
In [0]: