doc for hilbert functions

Author: rprebet

docs/src/hilbert.md

@@ -0,0 +1,40 @@
+```@meta
+CurrentModule = AlgebraicSolving
+DocTestSetup = quote
+  using AlgebraicSolving
+end
+```
+
+```@setup algebraicsolving
+using AlgebraicSolving
+```
+
+```@contents
+Pages = ["hilbert.md"]
+```
+
+# Hilbert series of an ideal
+
+## Introduction
+
+AlgebraicSolving allows to compute the Hilbert series for the ideal spanned
+by given input generators over finite fields of characteristic smaller
+$2^{31}$ and over the rationals.
+
+The underlying engine is provided by msolve.
+
+## Functionality
+
+```@docs
+    hilbert_series(I::Ideal{T}) where T <: MPolyRingElem
+```
+
+In addition, from the same input, AlgebraicSolving can also compute the dimension and degree of the ideal, as well as the Hilbert polynomial and index of regularity.
+
+```@docs
+    hilbert_dimension(I::Ideal{T}) where T <: MPolyRingElem
+
+    hilbert_degree(I::Ideal{T}) where T <: MPolyRingElem
+
+    hilbert_polynomial(I::Ideal{T}) where T <: MPolyRingElem
+```