new function matsmall_complement

algebra/matsmall.c

@@ -175,6 +175,19 @@ matsmall_coker (GEN A, unsigned long p, GEN T) {
     return gerepilecopy(av, shallowtrans(FlxqM_ker(shallowtrans(A), T, p)));
 }
 
+/* Complement of a linear subspace in another subspace.  */
+GEN
+matsmall_complement(GEN V, GEN W, unsigned long p, GEN T) {
+  pari_sp av = avma;
+  long n = lg(V) - 1, d = lg(V) - lg(W), r;
+  GEN Z;
+  do {
+    Z = matsmall_random_subspace(V, d, 0, p, T);
+    r = matsmall_rank(shallowconcat(W, Z), p, T);
+  } while (r < n);
+  return gerepileupto(av, Z);
+}
+
 /*
   Quotient of two linear subspaces  W \subseteq V
   of some ambient vector space.

algebra/matsmall.h

@@ -11,6 +11,7 @@ GEN matsmall_coker (GEN V, unsigned long p, GEN T);
 GEN matsmall_solve (GEN A, GEN B, unsigned long p, GEN T);
 GEN matsmall_solve_left (GEN A, GEN B, unsigned long p, GEN T);
 GEN matsmall_inverse_image (GEN A, GEN V, unsigned long p, GEN T);
+GEN matsmall_complement(GEN V, GEN W, unsigned long p, GEN T);
 GEN matsmall_quotient(GEN V, GEN W, unsigned long p, GEN T);
 GEN matsmall_random (unsigned long rows, unsigned long cols,
 		     unsigned long p, GEN T);