discriminant_form: Remove redundant computations.

* src/discriminant_form.cpp (internal::babai_near_vector): Take inverse
of `trans' as parameter.
(DiscriminantForm::theta_series_direct): Compute `trans_inv' here and
pass it as argument, calculate `::get_gram_wrt_smith_basis' only once.

src/discriminant_form.cpp

@@ -92,9 +92,9 @@ namespace weil
 		}
 
 		mpq_vector
-		babai_near_vector(const mpq_matrix& trans, const mpq_vector& v)
+		babai_near_vector(const mpq_matrix& trans, const mpq_matrix& trans_inv, const mpq_vector& v)
 		{
-			mpq_vector mapped{ trans.inverse() * v };
+			mpq_vector mapped{ trans_inv * v };
 			mpq_vector rounded{ v.rows() };
 			// round to nearest integer
 			for (int64_t i = 0; i < v.rows(); i++) {
@@ -405,13 +405,14 @@ start_printing:
 		const mpq_matrix D_inv{ D.inverse() };
 		const mpz_matrix g{ this->get_gram_wrt_smith_basis() };
 		const mpq_matrix trans{ lll_gram(g).cast<mpq_class>()};
+		const mpq_matrix trans_inv{ trans.inverse() };
 
 		std::vector<mpq_vector> representatives;
 		// find representatives of the shifted lattices with small norms
 		for (const auto& o : orbits) {
 			const mpq_matrix lifted_repr{ o.representative.cast<mpq_class>() };
 			mpq_vector v{ -(D_inv * lifted_repr) };
-			representatives.push_back(lifted_repr + D * internal::babai_near_vector(trans, v));
+			representatives.push_back(lifted_repr + D * internal::babai_near_vector(trans, trans_inv, v));
 		}
 
 		mpq_class max_offset_norm;
@@ -422,7 +423,7 @@ start_printing:
 			}
 		}
 
-		const mpq_matrix S{ this->get_gram_wrt_smith_basis().cast<mpq_class>() };
+		const mpq_matrix S{ g.cast<mpq_class>() };
 
 		for (uint64_t i = 0; i < representatives.size(); i++) {
 			out[orbits[i].representative].offset = this->q(orbits[i].representative);