From 4b41360359121ac906bc41292b4aefa1219ac6b3 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Fri, 8 Mar 2024 00:26:31 +0100
Subject: Create directory for examples

---
 examples/readme.py | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 examples/readme.py

diff --git a/examples/readme.py b/examples/readme.py
new file mode 100644
index 0000000..82a27d8
--- /dev/null
+++ b/examples/readme.py
@@ -0,0 +1,43 @@
+try:
+    import mdpoly
+except ModuleNotFoundError:
+    import sys
+    import pathlib
+    parent = pathlib.Path(__file__).resolve().parent.parent
+    sys.path.append(str(parent))
+
+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)
+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)
+            monomial_str += f"{var}^{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)
-- 
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