Update README.md

README.md

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-# SymbolicIndexingInterface.jl
+# SymbolicIndexingInterface.jl: Standardized Symbolic Indexing of Julia
+
+SymbolicIndexingInterface.jl is a set of interface functions for handling containers
+of symbolic variables.
+
+## Installation
+
+To install SymbolicIndexingInterface.jl, use the Julia package manager:
+
+```julia
+using Pkg
+Pkg.add("SymbolicIndexingInterface")
+```
+
+## Introduction
+
+The symbolic indexing interface has 2 levels:
+
+1. The user level. At the user level, a modeler or engineer simply uses terms from a
+   domain-specific language (DSL) inside of SciML functionality and will receive the requested
+   values. For example, if a DSL defines a symbol `x`, then `sol[x]` returns the solution
+   value(s) for `x`.
+2. The DSL system structure level. This is the structure which defines the symbolic indexing
+   for a given problem/solution. DSLs can tag a constructed problem/solution with this
+   object in order to endow the SciML tools with the ability to index symbolically according
+   to the definitions the DSL writer wants.
+
+
+## Example
+
+```julia
+using ModelingToolkit, OrdinaryDiffEq, SymbolicIndexingInterface, Plots
+
+@parameters σ ρ β
+@variables t x(t) y(t) z(t) w(t)
+D = Differential(t)
+
+eqs = [D(D(x)) ~ σ * (y - x),
+    D(y) ~ x * (ρ - z) - y,
+    D(z) ~ x * y - β * z,
+    w ~ x + y + z]
+
+@named sys = ODESystem(eqs)
+sys = structural_simplify(sys)
+
+sol[x]
+```