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standardSols -- find the "standard solutions" for the oscillator system associated to a graph

Description

The oscillator ideal associated to a graph constructed by oscQuadrics always contains the "standard solutions" as a minimal prime. These standard solutions are the Segre variety $\mathbb{P}^1\times \mathbb{P}^{n-1}$, where $n$ is the number of vertices of the graph. These are the solutions where all the angles are the same.

i1 : G = graph({0,1,2,3}, {{0,1},{1,2},{2,3},{0,3}});
i2 : R = oscRing(G);
i3 : I = oscQuadrics(G, R);

o3 : Ideal of R
i4 : any(decompose I, P -> P == standardSols(G, R))

o4 = true

See also

Ways to use standardSols:

  • standardSols(Graph)
  • standardSols(Graph,Ring)

For the programmer

The object standardSols is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/Oscillators/Documentation.m2:444:0.