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New wrapper for Singular triangular decompositions #4765

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Merged
merged 12 commits into from
Apr 2, 2025
33 changes: 33 additions & 0 deletions docs/oscar_references.bib
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Expand Up @@ -1573,6 +1573,15 @@ @Article{Haz12
doi = {10.3390/axioms1020149}
}

@MastersThesis{Hil99,
author = {Hillebrand, D.},
title = {Triangulierung nulldimensionaler Ideale - Implementierung und Vergleich zweier Algorithmen},
note = {Refereed by Prof. Dr. H.M. Moeller},
address = {Fachbereich Mathematik},
year = {1999},
school = {Universitaet Dortmund}
}

@Article{Hul22,
author = {Hulpke, Alexander},
title = {The perfect groups of order up to two million},
Expand Down Expand Up @@ -2053,6 +2062,18 @@ @Book{Lan71
doi = {10.1007/978-1-4757-1949-9}
}

@Article{Laz92,
author = {Lazard, D.},
title = {Solving Zero-Dimensional Algebraic Systems},
journal = {Journal of Symbolic Computation},
volume = {13},
number = {2},
pages = {117--131},
year = {1992},
month = feb,
doi = {10.1016/S0747-7171(08)80086-7}
}

@PhDThesis{Lev05,
author = {Viktor Levandovskyy},
title = {Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and
Expand Down Expand Up @@ -2170,6 +2191,18 @@ @Book{Mar18
doi = {10.1007/978-3-319-90233-3}
}

@Article{Moe93,
author = {Moeller, H. Michael},
title = {On Decomposing Systems of Polynomial Equations with Finitely Many Solutions},
journal = {Applicable Algebra in Engineering, Communication and Computing},
volume = {4},
number = {4},
pages = {217--230},
year = {1993},
month = dec,
doi = {10.1007/BF01200146}
}

@Article{Nik79,
author = {Nikulin, V. V.},
title = {Integer symmetric bilinear forms and some of their geometric applications},
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9 changes: 8 additions & 1 deletion docs/src/CommutativeAlgebra/ideals.md
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Expand Up @@ -256,9 +256,16 @@ equidimensional_hull(I::MPolyIdeal)
equidimensional_hull_radical(I::MPolyIdeal)
```

### Triangular Decomposition

```@docs
triangular_decomposition(::MPolyIdeal)
```


## Homogenization and Dehomogenization

Referring to [KR05](@cite) for definitions and technical details, we discuss homogenization and dehomogenization in the context of $\mathbb Z^m$-gradings.
Referring to [KR05](@cite) for definitions and technical details, we discuss homogenization and dehomogenization in the context of $\mathbb Z^m$-gradings.

```@docs
homogenizer(P::MPolyRing{T}, h::VarName; pos::Int=1+ngens(P)) where T
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