zeros and poles of a function, and calculate orders for them too

script/research/ec/ordp.sage

@@ -63,7 +63,7 @@ def ordp(P, original_f, debug=True):
 
     return k
 
-if __name__ == "__main__":
+def _ordp_test():
     K.<x, y> = GF(11)[]
     EC_A = 4
     EC_B = 0

script/research/ec/zeros_poles.sage

@@ -0,0 +1,23 @@
+K.<x, y> = GF(11)[]
+EC_A, EC_B = 4, 0
+C = y^2 - x^3 - EC_A*x - EC_B
+S = K.quotient(C).fraction_field()
+X, Y = S(x), S(y)
+
+foo = (X^2 - Y) / (X - 2)
+f, g = foo.numerator().lift(), foo.denominator().lift()
+
+I = ideal(C, f)
+J = ideal(C, g)
+
+load("ordp.sage")
+
+for info in I.variety():
+    Px, Py = P = info[x], info[y]
+    k = ordp(P, f, debug=False)
+    print(f"ordp(({Px}, {Py}), {f}) = {k}")
+for info in J.variety():
+    Px, Py = P = info[x], info[y]
+    k = ordp(P, g, debug=False)
+    print(f"ordp(({Px}, {Py}), {g}) = {k}")
+