id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
30714,Tensor Arithmetics on Minimal Amount of Domains,Michael Jung,,"If I get the code correctly, operations between two tensor fields on non-parallelizable manifolds are performed as follows:
1. get common domains from the `_restrictions` dictionary,
2. perform the corresponding operation on each of those domains.
However, in most cases not all domains are necessary to fully determine the result. It is enough to find a minimal set of common domains which cover the manifold and perform the computation on those. The wanted restrictions of the result can then be computed on demand.
Allow me an example:
{{{
sage: M = Manifold(2, 'S^2') # the 2-dimensional sphere S^2
sage: U = M.open_subset('U') # complement of the North pole
sage: c_xy. = U.chart() # stereographic coordinates from the North pole
sage: V = M.open_subset('V') # complement of the South pole
sage: c_uv.__ = V.chart() # stereographic coordinates from the South pole
sage: M.declare_union(U,V) # S^2 is the union of U and V
sage: xy_to_uv = c_xy.transition_map(c_uv, (x/(x^2+y^2), y/(x^2+y^2)),
....: intersection_name='W',
....: restrictions1=x^2+y^2!=0,
....: restrictions2=u^2+v^2!=0)
sage: uv_to_xy = xy_to_uv.inverse()
sage: W = U.intersection(V)
sage: eU = c_xy.frame()
sage: eV = c_uv.frame()
sage: v = M.vector_field(name='v')
sage: v[eU,:] = [1, -2]
sage: v.add_comp_by_continuation(eV, W, chart=c_uv)
sage: v._restrictions
{Open subset U of the 2-dimensional differentiable manifold S^2: Vector field v on the Open subset U of the 2-dimensional differentiable manifold S^2,
Open subset W of the 2-dimensional differentiable manifold S^2: Vector field v on the Open subset W of the 2-dimensional differentiable manifold S^2,
Open subset V of the 2-dimensional differentiable manifold S^2: Vector field v on the Open subset V of the 2-dimensional differentiable manifold S^2}
}}}
Now, if you add `v` and another vector field defined similarly, the addition would be performed on `U`, `V` and `W`. Even though the computation on `W` is not necessary.",enhancement,new,major,sage-9.8,manifolds,,,Eric Gourgoulhon Travis Scrimshaw Matthias Köppe,,,,N/A,,,,,
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