Add polynomial multiplication

main.py

@@ -1,15 +1,59 @@
 import itertools
 
 
+class Poly:
+
+    def __init__(self, elements):
+        self.elements = {}
+
+        i = len(elements) - 1
+        for e in reversed(elements):
+            self.elements[f"x{i}"] = e
+            i -= 1
+
+    def __str__(self):
+        return str(self.elements)
+
+    def __mul__(self, other):
+        elements = {}
+
+        for e in self.elements:
+            for f in other.elements:
+                coefficient = self.elements[e] * other.elements[f]
+                degree = f"x{int(e[1:])+int(f[1:])}"
+
+                if elements.get(f"{degree}") is None:
+                    elements[degree] = coefficient
+                else:
+                    elements[degree] += coefficient
+
+        return Poly(list(reversed(list(elements.values()))))
+
+    def __mod__(self, other):
+        elements = {}
+
 class PolyIntField:
 
     def __init__(self, int_modulo, poly_modulo):
         self.int_modulo = int_modulo
-        self.poly_modulo = poly_modulo
+        self.poly_modulo = Poly(poly_modulo)
         self.elements = list(itertools.product([x for x in range(0, int_modulo)]
                                                , repeat=len(poly_modulo) - 1))
 
+    def get_nilpotents(self):
+        nilpotents = []
+
+        # for element in self.elements:
+
+
+
 if __name__ == "__main__":
-    a = PolyIntField(3, [1, 1, 2, 2])
-    print(a.elements)
-    print(len(a.elements))
+    # a = PolyIntField(3, [1, 1, 2, 2])
+    # print(a.elements)
+    # print(len(a.elements))
+    b = Poly([4, 8, 1, 3])
+    c = Poly([1, 4])
+
+    print(b.elements)
+    print(b * c * c)
+    # c = Poly()