magma_utils

class_grp_arith.cc

@@ -47,7 +47,7 @@ int main() {
   cin >> D2;
 
   // The following assertion should be true for a nodal curve
-  assert(g == C.degree() - E.degree());
+  assert(g == ((C.degree()-1)*(C.degree()-2))/2 - E.degree());
 
   EffectiveDivisor R = AddReduced(g, O, E, D1, D2);
   

example_rrspace_input

 1009
 [ 5 [863 161 817 949 344 184] [132 747 1002 226 891] [768 119 991 128] [645 84 865] [351 37] [1] ]
+< [1] [] >
 { < [503 216 395 835 891 697 316 553 1] [773 952 513 814 518 605 87 42] > < [510 1] [928] > }

magma_utils/magma_utils.mgm

+// In this file, we provide some magma functions to test that the output of rrspace is correct.
+
+RRSPACE_PATH="/users/pspaenle/repos/rrspace"
+
+// Given a function f and a finite set B of functions on a curve, check if the k-vector space generated by B
+// contains f
+// The base curve should be defined over a finite field.
+// This is a probabilistic algorithm.
+function CheckBelongsSpan(f, B)
+    assert (Parent(f) eq Universe(B));
+    FF := Universe(B);
+    assert Type(FF) eq FldFunFracSch;
+    K := BaseRing(BaseRing(FF));
+    assert Type(K) eq FldFin;
+    C := Curve(FF);
+    nbtests := 2*#B + 2;
+    lM := [];
+    lv := [];
+    for i in [1..nbtests] do
+	repeat
+	    P := Random(C);
+	until P ne Infinity() and
+	      &and[Evaluate(g, P) ne Infinity() : g in B] and
+	      Evaluate(f, P) ne Infinity();
+	lM cat:= [Evaluate(g, P) : g in B];
+	lv cat:= [Evaluate(f, P)];
+    end for;
+    M := Matrix(K, nbtests, #B, lM);
+    return IsConsistent(Transpose(M), Matrix(K, 1, nbtests, lv));
+end function;
+	
+// Given two finite sets of functions on a curve, check if they span the same k-vector space in k(C)
+function CheckEqualSpan(B1, B2)
+    return &and[CheckBelongsSpan(g, B2) : g in B1] and
+	   &and[CheckBelongsSpan(g, B1) : g in B2];
+end function;
+
+// Set variable order y > x > z
+function Check_rrspace(C, D)
+    // first compute the input representation for rrspace
+    K := BaseRing(C);
+    assert Type(K) eq FldFin;
+    assert AmbientSpace(C) eq ProjectiveSpace(K, 2);
+    Dp, Dm := SignDecomposition(D);
+    Ip := Ideal(Dp);
+    Im := Ideal(Dm);
+    R := Universe(Generators(Ip));
+    Gp := GroebnerBasis(ChangeOrder(Ip+Ideal(R.3-1), "lex"));
+    Gm := GroebnerBasis(ChangeOrder(Im+Ideal(R.3-1), "lex"));
+    assert(Degree(Gp[2]) eq Degree(Ip));
+    assert(Degree(Gm[2]) eq Degree(Im));
+    Runiv := PolynomialRing(K);
+    fp := Evaluate( Gp[2], [0, Runiv.1, 0]);
+    gp := Evaluate(-Gp[1], [0, Runiv.1, 0]);
+    fm := Evaluate( Gm[2], [0, Runiv.1, 0]);
+    gm := Evaluate(-Gm[1], [0, Runiv.1, 0]);
+