adds some documentation for data types

Author: ederc

docs/make.jl

@@ -4,6 +4,8 @@ using LinearAlgebra
 using AlgebraicSolving
 using Documenter
 
+push!(LOAD_PATH, "../src")
+
 include("../src/imports.jl")
 include("../src/exports.jl")
 
@@ -22,6 +24,7 @@ makedocs(
     pages = Any[
         "Introduction" => "index.md",
         "User Guide" => Any[
+            "Data Types" => "types.md",
             "Algorithms" => ["algorithms/groebner-bases.md",
                     "algorithms/solvers.md"],
             "Examples" => "examples/katsura.md"

docs/mkdocs.yml

@@ -33,15 +33,15 @@ reverse lexicographical order. One can either directly add the number of
 variables of the first block via the `eliminate` parameter in the
 `groebner_basis` call. We have also implemented an alias for this call:
 
-```@docs
-function eliminate(
-        I::Ideal{T} where T <: MPolyElem,
-        eliminate::Int,
-        initial_hts::Int=17,
-        nr_thrds::Int=1,
-        max_nr_pairs::Int=0,
-        la_option::Int=2,
-        complete_reduction::Bool=true,
-        info_level::Int=0
-        )
-```
+%% ```@docs
+%% function eliminate(
+%%         I::Ideal{T} where T <: MPolyElem,
+%%         eliminate::Int,
+%%         initial_hts::Int=17,
+%%         nr_thrds::Int=1,
+%%         max_nr_pairs::Int=0,
+%%         la_option::Int=2,
+%%         complete_reduction::Bool=true,
+%%         info_level::Int=0
+%%         )
+%% ```

docs/src/algorithms/groebner-bases.md

@@ -0,0 +1,42 @@
+```@meta
+CurrentModule = AlgebraicSolving
+```
+
+# Data Types
+
+## Introduction
+
+AlgebraicSolving handles ideals in multivariate polynomial rings over a prime 
+field of characteristic $0$ or $p$ where $p$ is a prime number $<2^{31}$.
+
+## Polynomial Rings
+
+We use [Nemo](https://www.nemocas.org/index.html)'s multivariate polynomial 
+ring structures:
+
+```@repl
+using AlgebraicSolving
+R, (x,y,z) = PolynomialRing(QQ, ["x", "y", "z"], ordering=:degrevlex)
+```
+The above example defines a multivariate polynomial ring in three variables `x`, 
+`y`, and `z` over the rationals using the dgree reverse lexicographical ordering 
+for printing polynomials in the following. One can also define polynomial rings 
+over finite fields:
+
+```@repl
+using AlgebraicSolving
+R, (x,y,z) = PolynomialRing(GF(101), ["x", "y", "z"], ordering=:degrevlex)
+```
+
+## Ideals
+
+Ideals can be constructed by giving an array of generators. Ideals cache varies 
+data structures connected to ideals in order to make computational algebra more 
+effective:
+
+```@repl
+using AlgebraicSolving
+R, (x,y,z) = PolynomialRing(QQ, ["x", "y", "z"], ordering=:degrevlex)
+I = Ideal([x+y+1, y*z^2-13*y^2])
+```
+