From 3d9396e5d166349eb052966ec623b86e2e82ac60 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Sun, 3 Mar 2024 18:33:39 +0100
Subject: Update README, switch to reStructuredText

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 README.rst | 64 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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 create mode 100644 README.rst

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+``mdpoly`` or Multidimensional Polynomials
+==========================================
+
+*Work in progress!*
+
+Quick Start
+-----------
+
+There is still a big part of the API missing but the snipped below works enough
+to give an overview.
+
+.. code:: py
+
+        from mdpoly import State, Variable, Parameter
+        from mdpoly.representations import SparseRepr
+
+        # Construct an expression
+        x, y = Variable.from_names("x, y") # or just Variable("x")
+        k = Parameter("k")
+
+        p = (x + 2 * y) ** 3 + y ** 2 + k
+        print(f"{p = }")
+
+        # Expressions can be easily reparametrized
+        w = Parameter("w")
+        q = p.replace(y, w).replace(k, k ** 2) # createas a copy
+        print(f"{q = }")
+
+        # Make a concrete representation
+        state = State(parameters={k: 3.14}) # try to replace with empty dict
+        sparse, state = p.to_repr(SparseRepr, state)
+
+        # Look inside the representation
+        for entry in sparse.entries():
+            print(f"at (row, col) = {entry.row, entry.col} there is a polynomial:")
+            for term in sparse.terms(entry):
+                monomial_str = ""
+                for idx in term:
+                    var = state.from_index(idx.var_idx)
+                    monomial_str += f"{var.name}^{idx.power} "
+
+                # Get the coefficient
+                coeff = sparse.at(entry, term)
+                print(" - the monomial", monomial_str, "has coefficient", coeff)
+
+        # You can also simply iterate over it
+        for entry, term, coeff in sparse:
+            print(entry, term, coeff)
+
+There is some advanced stuff that is still broken but the idea is that it will
+work soon-ish.
+
+.. code:: py
+
+        from mdpoly import Variable, MatrixVariable
+        from mdpoly.types import Shape
+
+        x = Variable("x")
+        V = MatrixVariable("V", Shape.column(3))
+
+        print(x.shape, V.shape)
+
+        z = x + V # error
+        scalar = V.T @ V # no error (TODO)
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