675 s6 = s8 + y[4] * y[0] * x[4] * z[3] - 2.0 * y[4] * z[0] * x[4] * y[7] +
676 2.0 * y[4] * x[0] * y[7] * z[4] - y[4] * z[0] * x[4] * y[3] -
677 y[4] * x[0] * y[7] * z[3] + y[4] * z[0] * x[3] * y[7] -
678 y[4] * y[0] * x[3] * z[4] + y[0] * x[4] * y[3] * z[7] -
679 y[0] * x[7] * y[3] * z[4] - y[0] * x[3] * y[4] * z[7] +
680 y[0] * x[7] * y[4] * z[3] + x[2] * y[7] * y[7] * z[3] -
681 z[2] * x[3] * y[7] * y[7] - 2.0 * z[2] * x[0] * y[3] * y[3] +
682 2.0 * y[0] * z[1] * x[0] * y[4] + s7;
683 s8 = -2.0 * y[0] * y[1] * x[0] * z[4] - y[0] * y[1] * x[0] * z[5] -
684 y[0] * y[0] * x[3] * z[7] - z[1] * x[0] * y[3] * y[3] -
685 y[0] * x[1] * y[5] * z[0] - 2.0 * z[0] * x[7] * y[3] * y[3] +
686 x[0] * y[3] * y[3] * z[4] + 2.0 * x[0] * y[3] * y[3] * z[7] -
687 z[0] * x[4] * y[3] * y[3] + 2.0 * x[2] * y[3] * y[3] * z[0] +
688 x[1] * y[3] * y[3] * z[0] + 2.0 * y[7] * z[6] * x[7] * y[3] +
689 2.0 * y[7] * y[6] * x[3] * z[7] - 2.0 * y[7] * y[6] * x[7] * z[3] -
690 2.0 * y[7] * x[6] * y[3] * z[7];
691 s7 = s8 + y[4] * x[4] * y[3] * z[7] - y[4] * x[4] * y[7] * z[3] +
692 y[4] * x[3] * y[7] * z[4] - y[4] * x[7] * y[3] * z[4] +
693 2.0 * y[4] * y[0] * x[4] * z[7] - 2.0 * y[4] * y[0] * x[7] * z[4] +
694 2.0 * x[6] * y[7] * y[7] * z[3] + y[4] * x[0] * y[3] * z[4] +
695 y[0] * y[1] * x[5] * z[0] + y[0] * z[1] * x[0] * y[5] -
696 x[2] * y[0] * y[0] * z[3] + x[4] * y[3] * y[3] * z[7] -
697 x[7] * y[3] * y[3] * z[4] - x[5] * y[4] * y[4] * z[1] +
698 y[3] * z[0] * x[3] * y[4];
699 s8 = y[3] * y[0] * x[4] * z[3] + 2.0 * y[3] * y[0] * x[7] * z[3] +
700 2.0 * y[3] * y[2] * x[0] * z[3] - 2.0 * y[3] * y[2] * x[3] * z[0] +
701 2.0 * y[3] * z[2] * x[3] * y[0] + y[3] * z[1] * x[3] * y[0] -
702 2.0 * y[3] * x[2] * y[0] * z[3] - y[3] * x[1] * y[0] * z[3] -
703 y[3] * y[1] * x[3] * z[0] - 2.0 * y[3] * x[0] * y[7] * z[3] -
704 y[3] * x[0] * y[4] * z[3] - 2.0 * y[3] * y[0] * x[3] * z[7] -
705 y[3] * y[0] * x[3] * z[4] + 2.0 * y[3] * z[0] * x[3] * y[7] +
706 y[3] * y[1] * x[0] * z[3] + z[5] * x[1] * y[4] * y[4];
707 s5 = s8 - 2.0 * y[0] * y[0] * x[3] * z[4] -
708 2.0 * y[0] * x[1] * y[4] * z[0] + y[3] * x[7] * y[4] * z[3] -
709 y[3] * x[4] * y[7] * z[3] + y[3] * x[3] * y[7] * z[4] -
710 y[3] * x[3] * y[4] * z[7] + y[3] * x[0] * y[7] * z[4] -
711 y[3] * z[0] * x[4] * y[7] - 2.0 * y[4] * y[5] * x[0] * z[4] + s6 +
712 y[7] * x[0] * y[3] * z[7] - y[7] * z[0] * x[7] * y[3] +
713 y[7] * y[0] * x[7] * z[3] - y[7] * y[0] * x[3] * z[7] +
714 2.0 * y[0] * y[1] * x[4] * z[0] + s7;
715 s8 = -2.0 * y[7] * x[7] * y[3] * z[4] -
716 2.0 * y[7] * x[3] * y[4] * z[7] + 2.0 * y[7] * x[4] * y[3] * z[7] +
717 y[7] * y[0] * x[4] * z[7] - y[7] * y[0] * x[7] * z[4] +
718 2.0 * y[7] * x[7] * y[4] * z[3] - y[7] * x[0] * y[4] * z[7] +
719 y[7] * z[0] * x[7] * y[4] + z[5] * x[4] * y[7] * y[7] +
720 2.0 * z[6] * x[4] * y[7] * y[7] - x[5] * y[7] * y[7] * z[4] -
721 2.0 * x[6] * y[7] * y[7] * z[4] + 2.0 * y[7] * x[6] * y[4] * z[7] -
722 2.0 * y[7] * z[6] * x[7] * y[4] + 2.0 * y[7] * y[6] * x[7] * z[4];
723 s7 = s8 - 2.0 * y[7] * y[6] * x[4] * z[7] - y[7] * z[5] * x[7] * y[4] -
724 y[7] * y[5] * x[4] * z[7] - x[0] * y[7] * y[7] * z[3] +
725 z[0] * x[3] * y[7] * y[7] + y[7] * x[5] * y[4] * z[7] +
726 y[7] * y[5] * x[7] * z[4] - y[4] * x[1] * y[5] * z[0] -
727 x[1] * y[0] * y[0] * z[2] - y[4] * y[5] * x[1] * z[4] -
728 2.0 * y[4] * z[5] * x[4] * y[0] - y[4] * y[1] * x[0] * z[4] +
729 y[4] * y[5] * x[4] * z[1] + y[0] * z[0] * x[3] * y[7] -
730 y[0] * z[1] * x[0] * y[2];
731 s8 = 2.0 * y[0] * x[1] * y[3] * z[0] + y[4] * y[1] * x[4] * z[0] +
732 2.0 * y[0] * y[1] * x[0] * z[3] + y[4] * x[1] * y[0] * z[5] -
733 y[4] * z[1] * x[5] * y[0] + y[4] * z[1] * x[0] * y[5] -
734 y[4] * z[1] * x[4] * y[0] + y[4] * x[1] * y[0] * z[4] -
735 y[4] * z[5] * x[4] * y[1] + x[5] * y[4] * y[4] * z[6] -
736 z[5] * x[6] * y[4] * y[4] + y[4] * x[5] * y[1] * z[4] -
737 y[0] * z[2] * x[0] * y[3] + y[0] * y[5] * x[4] * z[0] +
738 y[0] * x[1] * y[2] * z[0];
739 s6 = s8 - 2.0 * y[0] * z[0] * x[4] * y[3] -
740 2.0 * y[0] * x[0] * y[4] * z[3] - 2.0 * y[0] * z[1] * x[0] * y[3] -
741 y[0] * x[0] * y[7] * z[3] - 2.0 * y[0] * y[1] * x[3] * z[0] +
742 y[0] * x[2] * y[3] * z[0] - y[0] * y[1] * x[2] * z[0] +
743 y[0] * y[1] * x[0] * z[2] - y[0] * x[2] * y[1] * z[3] +
744 y[0] * x[0] * y[3] * z[7] + y[0] * x[2] * y[3] * z[1] -
745 y[0] * y[2] * x[3] * z[0] + y[0] * y[2] * x[0] * z[3] -
746 y[0] * y[5] * x[0] * z[4] - y[4] * y[5] * x[4] * z[6] + s7;
747 s8 = s6 + y[4] * z[6] * x[5] * y[7] - y[4] * x[6] * y[7] * z[5] +
748 y[4] * x[6] * y[5] * z[7] - y[4] * z[6] * x[7] * y[5] -
749 y[4] * x[5] * y[6] * z[4] + y[4] * z[5] * x[4] * y[6] +
750 y[4] * y[5] * x[6] * z[4] - 2.0 * y[1] * y[1] * x[0] * z[5] +
751 2.0 * y[1] * y[1] * x[5] * z[0] - 2.0 * y[2] * y[2] * x[6] * z[3] +
752 x[5] * y[1] * y[1] * z[4] - z[5] * x[4] * y[1] * y[1] -
753 x[6] * y[2] * y[2] * z[7] + z[6] * x[7] * y[2] * y[2];
754 s7 = s8 - x[1] * y[5] * y[5] * z[0] + z[1] * x[0] * y[5] * y[5] +
755 y[1] * y[5] * x[4] * z[1] - y[1] * y[5] * x[1] * z[4] -
756 2.0 * y[2] * z[2] * x[3] * y[6] + 2.0 * y[1] * z[1] * x[0] * y[5] -
757 2.0 * y[1] * z[1] * x[5] * y[0] + 2.0 * y[1] * x[1] * y[0] * z[5] -
758 y[2] * x[2] * y[3] * z[7] - y[2] * z[2] * x[3] * y[7] +
759 y[2] * x[2] * y[7] * z[3] + y[2] * z[2] * x[7] * y[3] -
760 2.0 * y[2] * x[2] * y[3] * z[6] + 2.0 * y[2] * x[2] * y[6] * z[3] +
761 2.0 * y[2] * z[2] * x[6] * y[3] - y[3] * y[2] * x[6] * z[3];
762 s8 = y[3] * y[2] * x[3] * z[6] + y[3] * x[2] * y[6] * z[3] -
763 y[3] * z[2] * x[3] * y[6] - y[2] * y[2] * x[7] * z[3] +
764 2.0 * y[2] * y[2] * x[3] * z[6] + y[2] * y[2] * x[3] * z[7] -
765 2.0 * y[1] * x[1] * y[5] * z[0] - x[2] * y[3] * y[3] * z[6] +
766 z[2] * x[6] * y[3] * y[3] + 2.0 * y[6] * x[2] * y[5] * z[6] +
767 2.0 * y[6] * x[6] * y[2] * z[5] - 2.0 * y[6] * x[5] * y[2] * z[6] +
768 2.0 * y[3] * x[2] * y[7] * z[3] - 2.0 * y[3] * z[2] * x[3] * y[7] -
769 y[0] * z[0] * x[7] * y[3] - y[0] * z[2] * x[1] * y[3];
770 s4 = s8 - y[2] * y[6] * x[7] * z[2] + y[0] * z[2] * x[3] * y[1] +
771 y[1] * z[5] * x[1] * y[4] - y[1] * x[5] * y[4] * z[1] +
772 2.0 * y[0] * z[0] * x[3] * y[4] + 2.0 * y[0] * x[0] * y[3] * z[4] +
773 2.0 * z[2] * x[7] * y[3] * y[3] - 2.0 * z[5] * x[7] * y[4] * y[4] +
774 x[6] * y[4] * y[4] * z[7] - z[6] * x[7] * y[4] * y[4] +
775 y[1] * y[1] * x[0] * z[3] + y[3] * x[6] * y[7] * z[2] -
776 y[3] * z[6] * x[2] * y[7] + 2.0 * y[3] * y[2] * x[3] * z[7] + s5 +
778 s8 = s4 + y[2] * x[6] * y[7] * z[2] - y[2] * y[6] * x[7] * z[3] +
779 y[2] * y[6] * x[2] * z[7] - y[2] * z[6] * x[2] * y[7] -
780 y[2] * x[6] * y[3] * z[7] + y[2] * y[6] * x[3] * z[7] +
781 y[2] * z[6] * x[7] * y[3] - 2.0 * y[3] * y[2] * x[7] * z[3] -
782 x[6] * y[3] * y[3] * z[7] + y[1] * y[1] * x[4] * z[0] -
783 y[1] * y[1] * x[3] * z[0] + x[2] * y[6] * y[6] * z[3] -
784 z[2] * x[3] * y[6] * y[6] - y[1] * y[1] * x[0] * z[4];
785 s7 = s8 + y[5] * x[1] * y[0] * z[5] + y[6] * x[2] * y[7] * z[3] -
786 y[6] * y[2] * x[6] * z[3] + y[6] * y[2] * x[3] * z[6] -
787 y[6] * x[2] * y[3] * z[6] + y[6] * z[2] * x[6] * y[3] -
788 y[5] * y[1] * x[0] * z[5] - y[5] * z[1] * x[5] * y[0] +
789 y[5] * y[1] * x[5] * z[0] - y[6] * z[2] * x[3] * y[7] -
790 y[7] * y[6] * x[7] * z[2] + 2.0 * y[6] * y[6] * x[2] * z[7] +
791 y[6] * y[6] * x[3] * z[7] + x[6] * y[7] * y[7] * z[2] -
792 z[6] * x[2] * y[7] * y[7];
793 s8 = -x[2] * y[1] * y[1] * z[3] + 2.0 * y[1] * y[1] * x[0] * z[2] -
794 2.0 * y[1] * y[1] * x[2] * z[0] + z[2] * x[3] * y[1] * y[1] -
795 z[1] * x[0] * y[2] * y[2] + x[1] * y[2] * y[2] * z[0] +
796 y[2] * y[2] * x[0] * z[3] - y[2] * y[2] * x[3] * z[0] -
797 2.0 * y[2] * y[2] * x[3] * z[1] + y[1] * x[1] * y[3] * z[0] -
798 2.0 * y[6] * y[6] * x[7] * z[2] + 2.0 * y[5] * y[5] * x[4] * z[1] -
799 2.0 * y[5] * y[5] * x[1] * z[4] - y[6] * y[6] * x[7] * z[3] -
800 2.0 * y[1] * x[1] * y[0] * z[2];
801 s6 = s8 + 2.0 * y[1] * z[1] * x[2] * y[0] -
802 2.0 * y[1] * z[1] * x[0] * y[2] + 2.0 * y[1] * x[1] * y[2] * z[0] +
803 y[1] * x[2] * y[3] * z[1] - y[1] * y[2] * x[3] * z[1] -
804 y[1] * z[2] * x[1] * y[3] + y[1] * y[2] * x[1] * z[3] -
805 y[2] * x[1] * y[0] * z[2] + y[2] * z[1] * x[2] * y[0] +
806 y[2] * x[2] * y[3] * z[0] - y[7] * x[6] * y[2] * z[7] +
807 y[7] * z[6] * x[7] * y[2] + y[7] * y[6] * x[2] * z[7] -
808 y[6] * x[6] * y[3] * z[7] + y[6] * x[6] * y[7] * z[3] + s7;
809 s8 = s6 - y[6] * z[6] * x[3] * y[7] + y[6] * z[6] * x[7] * y[3] +
810 2.0 * y[2] * y[2] * x[1] * z[3] + x[2] * y[3] * y[3] * z[1] -
811 z[2] * x[1] * y[3] * y[3] + y[1] * x[1] * y[0] * z[4] +
812 y[1] * z[1] * x[3] * y[0] - y[1] * x[1] * y[0] * z[3] +
813 2.0 * y[5] * x[5] * y[1] * z[4] - 2.0 * y[5] * x[5] * y[4] * z[1] +
814 2.0 * y[5] * z[5] * x[1] * y[4] - 2.0 * y[5] * z[5] * x[4] * y[1] -
815 2.0 * y[6] * x[6] * y[2] * z[7] + 2.0 * y[6] * x[6] * y[7] * z[2];
816 s7 = s8 + 2.0 * y[6] * z[6] * x[7] * y[2] -
817 2.0 * y[6] * z[6] * x[2] * y[7] - y[1] * z[1] * x[4] * y[0] +
818 y[1] * z[1] * x[0] * y[4] - y[1] * z[1] * x[0] * y[3] +
819 2.0 * y[6] * y[6] * x[7] * z[5] + 2.0 * y[5] * y[5] * x[6] * z[4] -
820 2.0 * y[5] * y[5] * x[4] * z[6] + x[6] * y[5] * y[5] * z[7] -
821 y[3] * x[2] * y[1] * z[3] - y[3] * y[2] * x[3] * z[1] +
822 y[3] * z[2] * x[3] * y[1] + y[3] * y[2] * x[1] * z[3] -
823 y[2] * x[2] * y[0] * z[3] + y[2] * z[2] * x[3] * y[0];
824 s8 = s7 + 2.0 * y[2] * x[2] * y[3] * z[1] -
825 2.0 * y[2] * x[2] * y[1] * z[3] + y[2] * y[1] * x[0] * z[2] -
826 y[2] * y[1] * x[2] * z[0] + 2.0 * y[2] * z[2] * x[3] * y[1] -
827 2.0 * y[2] * z[2] * x[1] * y[3] - y[2] * z[2] * x[0] * y[3] +
828 y[5] * z[6] * x[5] * y[7] - y[5] * x[6] * y[7] * z[5] -
829 y[5] * y[6] * x[4] * z[7] - y[5] * y[6] * x[5] * z[7] -
830 2.0 * y[5] * x[5] * y[6] * z[4] + 2.0 * y[5] * x[5] * y[4] * z[6] -
831 2.0 * y[5] * z[5] * x[6] * y[4] + 2.0 * y[5] * z[5] * x[4] * y[6];
832 s5 = s8 - y[1] * y[5] * x[0] * z[4] - z[6] * x[7] * y[5] * y[5] +
833 y[6] * y[6] * x[7] * z[4] - y[6] * y[6] * x[4] * z[7] -
834 2.0 * y[6] * y[6] * x[5] * z[7] - x[5] * y[6] * y[6] * z[4] +
835 z[5] * x[4] * y[6] * y[6] + z[6] * x[5] * y[7] * y[7] -
836 x[6] * y[7] * y[7] * z[5] + y[1] * y[5] * x[4] * z[0] +
837 y[7] * y[6] * x[7] * z[5] + y[6] * y[5] * x[7] * z[4] +
838 y[5] * y[6] * x[7] * z[5] + y[6] * y[5] * x[6] * z[4] -
839 y[6] * y[5] * x[4] * z[6] + 2.0 * y[6] * z[6] * x[5] * y[7];
840 s8 = s5 - 2.0 * y[6] * x[6] * y[7] * z[5] +
841 2.0 * y[6] * x[6] * y[5] * z[7] - 2.0 * y[6] * z[6] * x[7] * y[5] -
842 y[6] * x[5] * y[7] * z[4] - y[6] * x[6] * y[7] * z[4] +
843 y[6] * x[6] * y[4] * z[7] - y[6] * z[6] * x[7] * y[4] +
844 y[6] * z[5] * x[4] * y[7] + y[6] * z[6] * x[4] * y[7] +
845 y[6] * x[5] * y[4] * z[6] - y[6] * z[5] * x[6] * y[4] +
846 y[7] * x[6] * y[5] * z[7] - y[7] * z[6] * x[7] * y[5] -
847 2.0 * y[6] * x[6] * y[5] * z[2];
848 s7 = s8 - y[7] * y[6] * x[5] * z[7] + 2.0 * y[4] * y[5] * x[4] * z[0] +
849 2.0 * x[3] * y[7] * y[7] * z[4] - 2.0 * x[4] * y[7] * y[7] * z[3] -
850 z[0] * x[4] * y[7] * y[7] + x[0] * y[7] * y[7] * z[4] -
851 y[0] * z[5] * x[4] * y[1] + y[0] * x[5] * y[1] * z[4] -
852 y[0] * x[5] * y[4] * z[0] + y[0] * z[5] * x[0] * y[4] -
853 y[5] * y[5] * x[0] * z[4] + y[5] * y[5] * x[4] * z[0] +
854 2.0 * y[1] * y[1] * x[2] * z[5] - 2.0 * y[1] * y[1] * x[5] * z[2] +
855 z[1] * x[5] * y[2] * y[2];
856 s8 = s7 - x[1] * y[2] * y[2] * z[5] - y[5] * z[5] * x[4] * y[0] +
857 y[5] * z[5] * x[0] * y[4] - y[5] * x[5] * y[4] * z[0] -
858 y[2] * x[1] * y[6] * z[5] - y[2] * y[1] * x[5] * z[6] +
859 y[2] * z[1] * x[5] * y[6] + y[2] * y[1] * x[6] * z[5] -
860 y[1] * z[1] * x[6] * y[5] - y[1] * x[1] * y[6] * z[5] +
861 y[1] * x[1] * y[5] * z[6] + y[1] * z[1] * x[5] * y[6] +
862 y[5] * x[5] * y[0] * z[4] + y[2] * y[1] * x[2] * z[5] -
863 y[2] * z[1] * x[2] * y[5];
864 s6 = s8 + y[2] * x[1] * y[5] * z[2] - y[2] * y[1] * x[5] * z[2] -
865 y[1] * y[1] * x[5] * z[6] + y[1] * y[1] * x[6] * z[5] -
866 z[1] * x[2] * y[5] * y[5] + x[1] * y[5] * y[5] * z[2] +
867 2.0 * y[1] * z[1] * x[5] * y[2] - 2.0 * y[1] * x[1] * y[2] * z[5] -
868 2.0 * y[1] * z[1] * x[2] * y[5] + 2.0 * y[1] * x[1] * y[5] * z[2] -
869 y[1] * y[1] * x[6] * z[2] + y[1] * y[1] * x[2] * z[6] -
870 2.0 * y[5] * x[1] * y[6] * z[5] - 2.0 * y[5] * y[1] * x[5] * z[6] +
871 2.0 * y[5] * z[1] * x[5] * y[6] + 2.0 * y[5] * y[1] * x[6] * z[5];
872 s8 = s6 - y[6] * z[1] * x[6] * y[5] - y[6] * y[1] * x[5] * z[6] +
873 y[6] * x[1] * y[5] * z[6] + y[6] * y[1] * x[6] * z[5] -
874 2.0 * z[1] * x[6] * y[5] * y[5] + 2.0 * x[1] * y[5] * y[5] * z[6] -
875 x[1] * y[6] * y[6] * z[5] + z[1] * x[5] * y[6] * y[6] +
876 y[5] * z[1] * x[5] * y[2] - y[5] * x[1] * y[2] * z[5] +
877 y[5] * y[1] * x[2] * z[5] - y[5] * y[1] * x[5] * z[2] -
878 y[6] * z[1] * x[2] * y[5] + y[6] * x[1] * y[5] * z[2];
879 s7 = s8 - y[1] * z[1] * x[2] * y[6] - y[1] * x[1] * y[2] * z[6] +
880 y[1] * x[1] * y[6] * z[2] + y[1] * z[1] * x[6] * y[2] +
881 y[5] * x[5] * y[6] * z[2] - y[5] * x[2] * y[6] * z[5] +
882 y[5] * x[6] * y[2] * z[5] - y[5] * x[5] * y[2] * z[6] -
883 x[6] * y[5] * y[5] * z[2] + x[2] * y[5] * y[5] * z[6] -
884 y[5] * y[5] * x[4] * z[7] + y[5] * y[5] * x[7] * z[4] -
885 y[1] * x[6] * y[5] * z[2] + y[1] * x[2] * y[5] * z[6] -
886 y[2] * x[6] * y[5] * z[2] - 2.0 * y[2] * y[1] * x[6] * z[2];
887 s8 = s7 - 2.0 * y[2] * z[1] * x[2] * y[6] +
888 2.0 * y[2] * x[1] * y[6] * z[2] + 2.0 * y[2] * y[1] * x[2] * z[6] -
889 2.0 * x[1] * y[2] * y[2] * z[6] + 2.0 * z[1] * x[6] * y[2] * y[2] +
890 x[6] * y[2] * y[2] * z[5] - x[5] * y[2] * y[2] * z[6] +
891 2.0 * x[5] * y[6] * y[6] * z[2] - 2.0 * x[2] * y[6] * y[6] * z[5] -
892 z[1] * x[2] * y[6] * y[6] - y[6] * y[1] * x[6] * z[2] -
893 y[6] * x[1] * y[2] * z[6] + y[6] * z[1] * x[6] * y[2] +
894 y[6] * y[1] * x[2] * z[6] + x[1] * y[6] * y[6] * z[2];
895 s3 = s8 + y[2] * x[5] * y[6] * z[2] + y[2] * x[2] * y[5] * z[6] -
896 y[2] * x[2] * y[6] * z[5] + y[5] * z[5] * x[4] * y[7] +
897 y[5] * x[5] * y[4] * z[7] - y[5] * z[5] * x[7] * y[4] -
898 y[5] * x[5] * y[7] * z[4] + 2.0 * y[4] * x[5] * y[0] * z[4] -
899 y[3] * z[6] * x[3] * y[7] + y[3] * y[6] * x[3] * z[7] +
900 y[3] * x[6] * y[7] * z[3] - y[3] * y[6] * x[7] * z[3] -
901 y[2] * y[1] * x[3] * z[0] - y[2] * z[1] * x[0] * y[3] +
902 y[2] * y[1] * x[0] * z[3] + y[2] * x[1] * y[3] * z[0];
903 s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
904 x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
905 z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
906 y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
907 z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
908 x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
909 s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
910 z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
911 y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
912 z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
913 y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
914 z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
915 s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
916 z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
917 x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
918 y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
919 y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
920 y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
921 s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
922 y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
923 x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
924 y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
925 y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
926 x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
927 s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
928 z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
929 x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
930 y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
931 z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
932 y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
933 s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
934 z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
935 z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
936 y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
937 x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
938 x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
939 s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
940 z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
941 y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
942 x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
943 z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
944 x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
946 s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
947 z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
948 z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
949 x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
950 z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
951 y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
954 const double unknown1 = s1 * s2;
956 s8 = -z[2] * x[1] * y[2] * z[5] + z[2] * y[1] * x[2] * z[5] -
957 z[2] * z[1] * x[2] * y[5] + z[2] * z[1] * x[5] * y[2] +
958 2.0 * y[5] * x[7] * z[4] * z[4] - y[1] * x[2] * z[0] * z[0] +
959 x[0] * y[3] * z[7] * z[7] - 2.0 * z[5] * z[5] * x[4] * y[1] +
960 2.0 * z[5] * z[5] * x[1] * y[4] + z[5] * z[5] * x[0] * y[4] -
961 2.0 * z[2] * z[2] * x[1] * y[3] + 2.0 * z[2] * z[2] * x[3] * y[1] -
962 x[0] * y[4] * z[7] * z[7] - y[0] * x[3] * z[7] * z[7] +
963 x[1] * y[0] * z[5] * z[5];
964 s7 = s8 - y[1] * x[0] * z[5] * z[5] + z[1] * y[1] * x[2] * z[6] +
965 y[1] * x[0] * z[2] * z[2] + z[2] * z[2] * x[3] * y[0] -
966 z[2] * z[2] * x[0] * y[3] - x[1] * y[0] * z[2] * z[2] +
967 2.0 * z[5] * z[5] * x[4] * y[6] - 2.0 * z[5] * z[5] * x[6] * y[4] -
968 z[5] * z[5] * x[7] * y[4] - x[6] * y[7] * z[5] * z[5] +
969 2.0 * z[2] * y[1] * x[2] * z[6] - 2.0 * z[2] * x[1] * y[2] * z[6] +
970 2.0 * z[2] * z[1] * x[6] * y[2] - y[6] * x[5] * z[7] * z[7] +
971 2.0 * x[6] * y[4] * z[7] * z[7];
972 s8 = -2.0 * y[6] * x[4] * z[7] * z[7] + x[6] * y[5] * z[7] * z[7] -
973 2.0 * z[2] * z[1] * x[2] * y[6] + z[4] * y[6] * x[7] * z[5] +
974 x[5] * y[4] * z[6] * z[6] + z[6] * z[6] * x[4] * y[7] -
975 z[6] * z[6] * x[7] * y[4] - 2.0 * z[6] * z[6] * x[7] * y[5] +
976 2.0 * z[6] * z[6] * x[5] * y[7] - y[5] * x[4] * z[6] * z[6] +
977 2.0 * z[0] * z[0] * x[3] * y[4] - x[6] * y[5] * z[2] * z[2] +
978 z[1] * z[1] * x[5] * y[6] - z[1] * z[1] * x[6] * y[5] -
979 z[5] * z[5] * x[4] * y[0];
980 s6 = s8 + 2.0 * x[1] * y[3] * z[0] * z[0] +
981 2.0 * x[1] * y[6] * z[2] * z[2] - 2.0 * y[1] * x[6] * z[2] * z[2] -
982 y[1] * x[5] * z[2] * z[2] - z[1] * z[1] * x[2] * y[6] -
983 2.0 * z[1] * z[1] * x[2] * y[5] + 2.0 * z[1] * z[1] * x[5] * y[2] +
984 z[1] * y[1] * x[6] * z[5] + y[1] * x[2] * z[5] * z[5] +
985 z[2] * z[1] * x[2] * y[0] + z[1] * x[1] * y[5] * z[6] -
986 z[1] * x[1] * y[6] * z[5] - z[1] * y[1] * x[5] * z[6] -
987 z[1] * x[2] * y[6] * z[5] + z[1] * x[6] * y[2] * z[5] + s7;
988 s8 = -x[1] * y[2] * z[5] * z[5] + z[1] * x[5] * y[6] * z[2] -
989 2.0 * z[2] * z[2] * x[3] * y[6] + 2.0 * z[2] * z[2] * x[6] * y[3] +
990 z[2] * z[2] * x[7] * y[3] - z[2] * z[2] * x[3] * y[7] -
991 z[1] * x[6] * y[5] * z[2] + 2.0 * z[1] * x[1] * y[5] * z[2] -
992 2.0 * x[3] * y[4] * z[7] * z[7] + 2.0 * x[4] * y[3] * z[7] * z[7] +
993 x[5] * y[6] * z[2] * z[2] + y[1] * x[2] * z[6] * z[6] +
994 y[0] * x[4] * z[7] * z[7] + z[2] * x[2] * y[3] * z[0] -
995 x[1] * y[2] * z[6] * z[6];
996 s7 = s8 - z[7] * z[2] * x[3] * y[7] + x[2] * y[6] * z[3] * z[3] -
997 y[2] * x[6] * z[3] * z[3] - z[6] * x[2] * y[3] * z[7] -
998 z[2] * z[1] * x[0] * y[2] + z[6] * z[2] * x[6] * y[3] -
999 z[6] * z[2] * x[3] * y[6] + z[6] * x[2] * y[6] * z[3] +
1000 z[2] * x[1] * y[2] * z[0] + z[6] * y[2] * x[3] * z[7] -
1001 z[4] * z[5] * x[6] * y[4] + z[4] * z[5] * x[4] * y[6] -
1002 z[4] * y[6] * x[5] * z[7] + z[4] * z[6] * x[4] * y[7] +
1003 z[4] * x[5] * y[4] * z[6];
1004 s8 = -z[6] * y[2] * x[6] * z[3] - z[4] * y[5] * x[4] * z[6] -
1005 z[2] * y[1] * x[5] * z[6] + z[2] * x[1] * y[5] * z[6] +
1006 z[4] * x[6] * y[4] * z[7] + 2.0 * z[4] * z[5] * x[4] * y[7] -
1007 z[4] * z[6] * x[7] * y[4] + x[6] * y[7] * z[3] * z[3] -
1008 2.0 * z[4] * z[5] * x[7] * y[4] - 2.0 * z[4] * y[5] * x[4] * z[7] -
1009 z[4] * y[6] * x[4] * z[7] + z[4] * x[6] * y[5] * z[7] -
1010 z[4] * x[6] * y[7] * z[5] + 2.0 * z[4] * x[5] * y[4] * z[7] +
1011 z[2] * x[2] * y[5] * z[6] - z[2] * x[2] * y[6] * z[5];
1012 s5 = s8 + z[2] * x[6] * y[2] * z[5] - z[2] * x[5] * y[2] * z[6] -
1013 z[2] * x[2] * y[3] * z[7] - x[2] * y[3] * z[7] * z[7] +
1014 2.0 * z[2] * x[2] * y[3] * z[1] - z[2] * y[2] * x[3] * z[0] +
1015 z[2] * y[2] * x[0] * z[3] - z[2] * x[2] * y[0] * z[3] -
1016 z[7] * y[2] * x[7] * z[3] + z[7] * z[2] * x[7] * y[3] +
1017 z[7] * x[2] * y[7] * z[3] + z[6] * y[1] * x[2] * z[5] -
1018 z[6] * x[1] * y[2] * z[5] + z[5] * x[1] * y[5] * z[2] + s6 + s7;
1019 s8 = z[5] * z[1] * x[5] * y[2] - z[5] * z[1] * x[2] * y[5] -
1020 y[6] * x[7] * z[2] * z[2] + 2.0 * z[2] * x[2] * y[6] * z[3] -
1021 2.0 * z[2] * x[2] * y[3] * z[6] + 2.0 * z[2] * y[2] * x[3] * z[6] +
1022 y[2] * x[3] * z[6] * z[6] + y[6] * x[7] * z[5] * z[5] +
1023 z[2] * y[2] * x[3] * z[7] - z[2] * y[2] * x[7] * z[3] -
1024 2.0 * z[2] * y[2] * x[6] * z[3] + z[2] * x[2] * y[7] * z[3] +
1025 x[6] * y[2] * z[5] * z[5] - 2.0 * z[2] * x[2] * y[1] * z[3] -
1026 x[2] * y[6] * z[5] * z[5];
1027 s7 = s8 - y[1] * x[5] * z[6] * z[6] + z[6] * x[1] * y[6] * z[2] -
1028 z[3] * z[2] * x[3] * y[6] + z[6] * z[1] * x[6] * y[2] -
1029 z[6] * z[1] * x[2] * y[6] - z[6] * y[1] * x[6] * z[2] -
1030 2.0 * x[5] * y[2] * z[6] * z[6] + z[4] * z[1] * x[0] * y[4] -
1031 z[3] * x[2] * y[3] * z[6] - z[5] * y[1] * x[5] * z[2] +
1032 z[3] * y[2] * x[3] * z[6] + 2.0 * x[2] * y[5] * z[6] * z[6] -
1033 z[5] * x[1] * y[5] * z[0] + y[2] * x[3] * z[7] * z[7] -
1034 x[2] * y[3] * z[6] * z[6];
1035 s8 = z[5] * y[5] * x[4] * z[0] + z[3] * z[2] * x[6] * y[3] +
1036 x[1] * y[5] * z[6] * z[6] + z[5] * y[5] * x[7] * z[4] -
1037 z[1] * x[1] * y[2] * z[6] + z[1] * x[1] * y[6] * z[2] +
1038 2.0 * z[6] * y[6] * x[7] * z[5] - z[7] * y[6] * x[7] * z[2] -
1039 z[3] * y[6] * x[7] * z[2] + x[6] * y[7] * z[2] * z[2] -
1040 2.0 * z[6] * y[6] * x[7] * z[2] - 2.0 * x[6] * y[3] * z[7] * z[7] -
1041 x[6] * y[2] * z[7] * z[7] - z[5] * x[6] * y[5] * z[2] +
1042 y[6] * x[2] * z[7] * z[7];
1043 s6 = s8 + 2.0 * y[6] * x[3] * z[7] * z[7] + z[6] * z[6] * x[7] * y[3] -
1044 y[6] * x[7] * z[3] * z[3] + z[5] * x[5] * y[0] * z[4] +
1045 2.0 * z[6] * z[6] * x[7] * y[2] - 2.0 * z[6] * z[6] * x[2] * y[7] -
1046 z[6] * z[6] * x[3] * y[7] + z[7] * y[6] * x[7] * z[5] +
1047 z[7] * y[5] * x[7] * z[4] - 2.0 * z[7] * x[7] * y[3] * z[4] +
1048 2.0 * z[7] * x[3] * y[7] * z[4] - 2.0 * z[7] * x[4] * y[7] * z[3] +
1049 2.0 * z[7] * x[7] * y[4] * z[3] - z[7] * y[0] * x[7] * z[4] -
1050 2.0 * z[7] * z[6] * x[3] * y[7] + s7;
1051 s8 = s6 + 2.0 * z[7] * z[6] * x[7] * y[3] +
1052 2.0 * z[7] * x[6] * y[7] * z[3] + z[7] * x[6] * y[7] * z[2] -
1053 2.0 * z[7] * y[6] * x[7] * z[3] + z[7] * z[6] * x[7] * y[2] -
1054 z[7] * z[6] * x[2] * y[7] + z[5] * y[1] * x[5] * z[0] -
1055 z[5] * z[1] * x[5] * y[0] + 2.0 * y[1] * x[6] * z[5] * z[5] -
1056 2.0 * x[1] * y[6] * z[5] * z[5] + z[5] * z[1] * x[0] * y[5] +
1057 z[6] * y[6] * x[3] * z[7] + 2.0 * z[6] * x[6] * y[7] * z[2] -
1058 z[6] * y[6] * x[7] * z[3];
1059 s7 = s8 + 2.0 * z[6] * y[6] * x[2] * z[7] - z[6] * x[6] * y[3] * z[7] +
1060 z[6] * x[6] * y[7] * z[3] - 2.0 * z[6] * x[6] * y[2] * z[7] -
1061 2.0 * z[1] * y[1] * x[5] * z[2] - z[1] * y[1] * x[6] * z[2] -
1062 z[7] * z[0] * x[7] * y[3] - 2.0 * z[6] * x[6] * y[5] * z[2] -
1063 z[2] * z[6] * x[3] * y[7] + z[2] * x[6] * y[7] * z[3] -
1064 z[2] * z[6] * x[2] * y[7] + y[5] * x[6] * z[4] * z[4] +
1065 z[2] * y[6] * x[2] * z[7] + y[6] * x[7] * z[4] * z[4] +
1066 z[2] * z[6] * x[7] * y[2] - 2.0 * x[5] * y[7] * z[4] * z[4];
1067 s8 = -x[6] * y[7] * z[4] * z[4] - z[5] * y[5] * x[0] * z[4] -
1068 z[2] * x[6] * y[2] * z[7] - x[5] * y[6] * z[4] * z[4] -
1069 2.0 * z[5] * y[1] * x[5] * z[6] + 2.0 * z[5] * z[1] * x[5] * y[6] +
1070 2.0 * z[5] * x[1] * y[5] * z[6] - 2.0 * z[5] * z[1] * x[6] * y[5] -
1071 z[5] * x[5] * y[2] * z[6] + z[5] * x[5] * y[6] * z[2] +
1072 z[5] * x[2] * y[5] * z[6] + z[5] * z[5] * x[4] * y[7] -
1073 y[5] * x[4] * z[7] * z[7] + x[5] * y[4] * z[7] * z[7] +
1074 z[6] * z[1] * x[5] * y[6] + z[6] * y[1] * x[6] * z[5];
1075 s4 = s8 - z[6] * z[1] * x[6] * y[5] - z[6] * x[1] * y[6] * z[5] +
1076 z[2] * z[6] * x[7] * y[3] + 2.0 * z[6] * x[6] * y[2] * z[5] +
1077 2.0 * z[6] * x[5] * y[6] * z[2] - 2.0 * z[6] * x[2] * y[6] * z[5] +
1078 z[7] * z[0] * x[3] * y[7] + z[7] * z[0] * x[7] * y[4] +
1079 z[3] * z[6] * x[7] * y[3] - z[3] * z[6] * x[3] * y[7] -
1080 z[3] * x[6] * y[3] * z[7] + z[3] * y[6] * x[2] * z[7] -
1081 z[3] * x[6] * y[2] * z[7] + z[5] * x[5] * y[4] * z[7] + s5 + s7;
1082 s8 = s4 + z[3] * y[6] * x[3] * z[7] - z[7] * x[0] * y[7] * z[3] +
1083 z[6] * x[5] * y[4] * z[7] + z[7] * y[0] * x[7] * z[3] +
1084 z[5] * z[6] * x[4] * y[7] - 2.0 * z[5] * x[5] * y[6] * z[4] +
1085 2.0 * z[5] * x[5] * y[4] * z[6] - z[5] * x[5] * y[7] * z[4] -
1086 z[5] * y[6] * x[5] * z[7] - z[5] * z[6] * x[7] * y[4] -
1087 z[7] * z[0] * x[4] * y[7] - z[5] * z[6] * x[7] * y[5] -
1088 z[5] * y[5] * x[4] * z[7] + z[7] * x[0] * y[7] * z[4];
1089 s7 = s8 - 2.0 * z[5] * y[5] * x[4] * z[6] + z[5] * z[6] * x[5] * y[7] +
1090 z[5] * x[6] * y[5] * z[7] + 2.0 * z[5] * y[5] * x[6] * z[4] +
1091 z[6] * z[5] * x[4] * y[6] - z[6] * x[5] * y[6] * z[4] -
1092 z[6] * z[5] * x[6] * y[4] - z[6] * x[6] * y[7] * z[4] -
1093 2.0 * z[6] * y[6] * x[5] * z[7] + z[6] * x[6] * y[4] * z[7] -
1094 z[6] * y[5] * x[4] * z[7] - z[6] * y[6] * x[4] * z[7] +
1095 z[6] * y[6] * x[7] * z[4] + z[6] * y[5] * x[6] * z[4] +
1096 2.0 * z[6] * x[6] * y[5] * z[7];
1097 s8 = -2.0 * z[6] * x[6] * y[7] * z[5] - z[2] * y[1] * x[2] * z[0] +
1098 2.0 * z[7] * z[6] * x[4] * y[7] - 2.0 * z[7] * x[6] * y[7] * z[4] -
1099 2.0 * z[7] * z[6] * x[7] * y[4] + z[7] * z[5] * x[4] * y[7] -
1100 z[7] * z[5] * x[7] * y[4] - z[7] * x[5] * y[7] * z[4] +
1101 2.0 * z[7] * y[6] * x[7] * z[4] - z[7] * z[6] * x[7] * y[5] +
1102 z[7] * z[6] * x[5] * y[7] - z[7] * x[6] * y[7] * z[5] +
1103 z[1] * z[1] * x[6] * y[2] + s7 + x[1] * y[5] * z[2] * z[2];
1104 s6 = s8 + 2.0 * z[2] * y[2] * x[1] * z[3] -
1105 2.0 * z[2] * y[2] * x[3] * z[1] - 2.0 * x[1] * y[4] * z[0] * z[0] +
1106 2.0 * y[1] * x[4] * z[0] * z[0] + 2.0 * x[2] * y[7] * z[3] * z[3] -
1107 2.0 * y[2] * x[7] * z[3] * z[3] - x[1] * y[5] * z[0] * z[0] +
1108 z[0] * z[0] * x[7] * y[4] + z[0] * z[0] * x[3] * y[7] +
1109 x[2] * y[3] * z[0] * z[0] - 2.0 * y[1] * x[3] * z[0] * z[0] +
1110 y[5] * x[4] * z[0] * z[0] - 2.0 * z[0] * z[0] * x[4] * y[3] +
1111 x[1] * y[2] * z[0] * z[0] - z[0] * z[0] * x[4] * y[7] +
1112 y[1] * x[5] * z[0] * z[0];
1113 s8 = s6 - y[2] * x[3] * z[0] * z[0] + y[1] * x[0] * z[3] * z[3] -
1114 2.0 * x[0] * y[7] * z[3] * z[3] - x[0] * y[4] * z[3] * z[3] -
1115 2.0 * x[2] * y[0] * z[3] * z[3] - x[1] * y[0] * z[3] * z[3] +
1116 y[0] * x[4] * z[3] * z[3] - 2.0 * z[0] * y[1] * x[0] * z[4] +
1117 2.0 * z[0] * z[1] * x[0] * y[4] + 2.0 * z[0] * x[1] * y[0] * z[4] -
1118 2.0 * z[0] * z[1] * x[4] * y[0] - 2.0 * z[3] * x[2] * y[3] * z[7] -
1119 2.0 * z[3] * z[2] * x[3] * y[7] + 2.0 * z[3] * z[2] * x[7] * y[3];
1120 s7 = s8 + 2.0 * z[3] * y[2] * x[3] * z[7] +
1121 2.0 * z[5] * y[5] * x[4] * z[1] + 2.0 * z[0] * y[1] * x[0] * z[3] -
1122 z[0] * y[0] * x[3] * z[7] - 2.0 * z[0] * y[0] * x[3] * z[4] -
1123 z[0] * x[1] * y[0] * z[2] + z[0] * z[1] * x[2] * y[0] -
1124 z[0] * y[1] * x[0] * z[5] - z[0] * z[1] * x[0] * y[2] -
1125 z[0] * x[0] * y[7] * z[3] - 2.0 * z[0] * z[1] * x[0] * y[3] -
1126 z[5] * x[5] * y[4] * z[0] - 2.0 * z[0] * x[0] * y[4] * z[3] +
1127 z[0] * x[0] * y[7] * z[4] - z[0] * z[2] * x[0] * y[3];
1128 s8 = s7 + z[0] * x[5] * y[0] * z[4] + z[0] * z[1] * x[0] * y[5] -
1129 z[0] * x[2] * y[0] * z[3] - z[0] * z[1] * x[5] * y[0] -
1130 2.0 * z[0] * x[1] * y[0] * z[3] + 2.0 * z[0] * y[0] * x[4] * z[3] -
1131 z[0] * x[0] * y[4] * z[7] + z[0] * x[1] * y[0] * z[5] +
1132 z[0] * y[0] * x[7] * z[3] + z[0] * y[2] * x[0] * z[3] -
1133 z[0] * y[5] * x[0] * z[4] + z[0] * z[2] * x[3] * y[0] +
1134 z[0] * x[2] * y[3] * z[1] + z[0] * x[0] * y[3] * z[7] -
1135 z[0] * x[2] * y[1] * z[3];
1136 s5 = s8 + z[0] * y[1] * x[0] * z[2] + z[3] * x[1] * y[3] * z[0] -
1137 2.0 * z[3] * y[0] * x[3] * z[7] - z[3] * y[0] * x[3] * z[4] -
1138 z[3] * x[1] * y[0] * z[2] + z[3] * z[0] * x[7] * y[4] +
1139 2.0 * z[3] * z[0] * x[3] * y[7] + 2.0 * z[3] * x[2] * y[3] * z[0] -
1140 z[3] * y[1] * x[3] * z[0] - z[3] * z[1] * x[0] * y[3] -
1141 z[3] * z[0] * x[4] * y[3] + z[3] * x[1] * y[2] * z[0] -
1142 z[3] * z[0] * x[4] * y[7] - 2.0 * z[3] * z[2] * x[0] * y[3] -
1143 z[3] * x[0] * y[4] * z[7] - 2.0 * z[3] * y[2] * x[3] * z[0];
1144 s8 = s5 + 2.0 * z[3] * z[2] * x[3] * y[0] + z[3] * x[2] * y[3] * z[1] +
1145 2.0 * z[3] * x[0] * y[3] * z[7] + z[3] * y[1] * x[0] * z[2] -
1146 z[4] * y[0] * x[3] * z[7] - z[4] * x[1] * y[5] * z[0] -
1147 z[4] * y[1] * x[0] * z[5] + 2.0 * z[4] * z[0] * x[7] * y[4] +
1148 z[4] * z[0] * x[3] * y[7] + 2.0 * z[4] * y[5] * x[4] * z[0] +
1149 2.0 * y[0] * x[7] * z[3] * z[3] + 2.0 * y[2] * x[0] * z[3] * z[3] -
1150 x[2] * y[1] * z[3] * z[3] - y[0] * x[3] * z[4] * z[4];
1151 s7 = s8 - y[1] * x[0] * z[4] * z[4] + x[1] * y[0] * z[4] * z[4] +
1152 2.0 * x[0] * y[7] * z[4] * z[4] + 2.0 * x[5] * y[0] * z[4] * z[4] -
1153 2.0 * y[5] * x[0] * z[4] * z[4] + 2.0 * z[1] * z[1] * x[2] * y[0] -
1154 2.0 * z[1] * z[1] * x[0] * y[2] + z[1] * z[1] * x[0] * y[4] -
1155 z[1] * z[1] * x[0] * y[3] - z[1] * z[1] * x[4] * y[0] +
1156 2.0 * z[1] * z[1] * x[0] * y[5] - 2.0 * z[1] * z[1] * x[5] * y[0] +
1157 x[2] * y[3] * z[1] * z[1] - x[5] * y[4] * z[0] * z[0] -
1158 z[0] * z[0] * x[7] * y[3];
1159 s8 = s7 + x[7] * y[4] * z[3] * z[3] - x[4] * y[7] * z[3] * z[3] +
1160 y[2] * x[1] * z[3] * z[3] + x[0] * y[3] * z[4] * z[4] -
1161 2.0 * y[0] * x[7] * z[4] * z[4] + x[3] * y[7] * z[4] * z[4] -
1162 x[7] * y[3] * z[4] * z[4] - y[5] * x[1] * z[4] * z[4] +
1163 x[5] * y[1] * z[4] * z[4] + z[1] * z[1] * x[3] * y[0] +
1164 y[5] * x[4] * z[1] * z[1] - y[2] * x[3] * z[1] * z[1] -
1165 x[5] * y[4] * z[1] * z[1] - z[4] * x[0] * y[4] * z[3] -
1166 z[4] * z[0] * x[4] * y[3];
1167 s6 = s8 - z[4] * z[1] * x[4] * y[0] - 2.0 * z[4] * z[0] * x[4] * y[7] +
1168 z[4] * y[1] * x[5] * z[0] - 2.0 * z[5] * x[5] * y[4] * z[1] -
1169 z[4] * x[1] * y[4] * z[0] + z[4] * y[0] * x[4] * z[3] -
1170 2.0 * z[4] * x[0] * y[4] * z[7] + z[4] * x[1] * y[0] * z[5] -
1171 2.0 * z[1] * x[1] * y[2] * z[5] + z[4] * x[0] * y[3] * z[7] +
1172 2.0 * z[5] * x[5] * y[1] * z[4] + z[4] * y[1] * x[4] * z[0] +
1173 z[1] * y[1] * x[0] * z[3] + z[1] * x[1] * y[3] * z[0] -
1174 2.0 * z[1] * x[1] * y[5] * z[0] - 2.0 * z[1] * x[1] * y[0] * z[2];
1175 s8 = s6 - 2.0 * z[1] * y[1] * x[0] * z[5] - z[1] * y[1] * x[0] * z[4] +
1176 2.0 * z[1] * y[1] * x[2] * z[5] - z[1] * y[1] * x[3] * z[0] -
1177 2.0 * z[5] * y[5] * x[1] * z[4] + z[1] * y[5] * x[4] * z[0] +
1178 z[1] * x[1] * y[0] * z[4] + 2.0 * z[1] * x[1] * y[2] * z[0] -
1179 z[1] * z[2] * x[0] * y[3] + 2.0 * z[1] * y[1] * x[5] * z[0] -
1180 z[1] * x[1] * y[0] * z[3] - z[1] * x[1] * y[4] * z[0] +
1181 2.0 * z[1] * x[1] * y[0] * z[5] - z[1] * y[2] * x[3] * z[0];
1182 s7 = s8 + z[1] * z[2] * x[3] * y[0] - z[1] * x[2] * y[1] * z[3] +
1183 z[1] * y[1] * x[4] * z[0] + 2.0 * z[1] * y[1] * x[0] * z[2] +
1184 2.0 * z[0] * z[1] * x[3] * y[0] + 2.0 * z[0] * x[0] * y[3] * z[4] +
1185 z[0] * z[5] * x[0] * y[4] + z[0] * y[0] * x[4] * z[7] -
1186 z[0] * y[0] * x[7] * z[4] - z[0] * x[7] * y[3] * z[4] -
1187 z[0] * z[5] * x[4] * y[0] - z[0] * x[5] * y[4] * z[1] +
1188 z[3] * z[1] * x[3] * y[0] + z[3] * x[0] * y[3] * z[4] +
1189 z[3] * z[0] * x[3] * y[4] + z[3] * y[0] * x[4] * z[7];
1190 s8 = s7 + z[3] * x[3] * y[7] * z[4] - z[3] * x[7] * y[3] * z[4] -
1191 z[3] * x[3] * y[4] * z[7] + z[3] * x[4] * y[3] * z[7] -
1192 z[3] * y[2] * x[3] * z[1] + z[3] * z[2] * x[3] * y[1] -
1193 z[3] * z[2] * x[1] * y[3] - 2.0 * z[3] * z[0] * x[7] * y[3] +
1194 z[4] * z[0] * x[3] * y[4] + 2.0 * z[4] * z[5] * x[0] * y[4] +
1195 2.0 * z[4] * y[0] * x[4] * z[7] - 2.0 * z[4] * x[5] * y[4] * z[0] +
1196 z[4] * y[5] * x[4] * z[1] + z[4] * x[7] * y[4] * z[3] -
1197 z[4] * x[4] * y[7] * z[3];
1198 s3 = s8 - z[4] * x[3] * y[4] * z[7] + z[4] * x[4] * y[3] * z[7] -
1199 2.0 * z[4] * z[5] * x[4] * y[0] - z[4] * x[5] * y[4] * z[1] +
1200 z[4] * z[5] * x[1] * y[4] - z[4] * z[5] * x[4] * y[1] -
1201 2.0 * z[1] * y[1] * x[2] * z[0] + z[1] * z[5] * x[0] * y[4] -
1202 z[1] * z[5] * x[4] * y[0] - z[1] * y[5] * x[1] * z[4] +
1203 z[1] * x[5] * y[1] * z[4] + z[1] * z[5] * x[1] * y[4] -
1204 z[1] * z[5] * x[4] * y[1] + z[1] * z[2] * x[3] * y[1] -
1205 z[1] * z[2] * x[1] * y[3] + z[1] * y[2] * x[1] * z[3];
1206 s8 = y[1] * x[0] * z[3] + x[1] * y[3] * z[0] - y[0] * x[3] * z[7] -
1207 x[1] * y[5] * z[0] - y[0] * x[3] * z[4] - x[1] * y[0] * z[2] +
1208 z[1] * x[2] * y[0] - y[1] * x[0] * z[5] - z[1] * x[0] * y[2] -
1209 y[1] * x[0] * z[4] + z[1] * x[5] * y[2] + z[0] * x[7] * y[4] +
1210 z[0] * x[3] * y[7] + z[1] * x[0] * y[4] - x[1] * y[2] * z[5] +
1211 x[2] * y[3] * z[0] + y[1] * x[2] * z[5] - x[2] * y[3] * z[7];
1212 s7 = s8 - z[1] * x[2] * y[5] - y[1] * x[3] * z[0] - x[0] * y[7] * z[3] -
1213 z[1] * x[0] * y[3] + y[5] * x[4] * z[0] - x[0] * y[4] * z[3] +
1214 y[5] * x[7] * z[4] - z[0] * x[4] * y[3] + x[1] * y[0] * z[4] -
1215 z[2] * x[3] * y[7] - y[6] * x[7] * z[2] + x[1] * y[5] * z[2] +
1216 y[6] * x[7] * z[5] + x[0] * y[7] * z[4] + x[1] * y[2] * z[0] -
1217 z[1] * x[4] * y[0] - z[0] * x[4] * y[7] - z[2] * x[0] * y[3];
1218 s8 = x[5] * y[0] * z[4] + z[1] * x[0] * y[5] - x[2] * y[0] * z[3] -
1219 z[1] * x[5] * y[0] + y[1] * x[5] * z[0] - x[1] * y[0] * z[3] -
1220 x[1] * y[4] * z[0] - y[1] * x[5] * z[2] + x[2] * y[7] * z[3] +
1221 y[0] * x[4] * z[3] - x[0] * y[4] * z[7] + x[1] * y[0] * z[5] -
1222 y[1] * x[6] * z[2] - y[2] * x[6] * z[3] + y[0] * x[7] * z[3] -
1223 y[2] * x[7] * z[3] + z[2] * x[7] * y[3] + y[2] * x[0] * z[3];
1224 s6 = s8 + y[2] * x[3] * z[7] - y[2] * x[3] * z[0] - x[6] * y[5] * z[2] -
1225 y[5] * x[0] * z[4] + z[2] * x[3] * y[0] + x[2] * y[3] * z[1] +
1226 x[0] * y[3] * z[7] - x[2] * y[1] * z[3] + y[1] * x[4] * z[0] +
1227 y[1] * x[0] * z[2] - z[1] * x[2] * y[6] + y[2] * x[3] * z[6] -
1228 y[1] * x[2] * z[0] + z[1] * x[3] * y[0] - x[1] * y[2] * z[6] -
1229 x[2] * y[3] * z[6] + x[0] * y[3] * z[4] + z[0] * x[3] * y[4] + s7;
1230 s8 = x[5] * y[4] * z[7] + s6 + y[5] * x[6] * z[4] - y[5] * x[4] * z[6] +
1231 z[6] * x[5] * y[7] - x[6] * y[2] * z[7] - x[6] * y[7] * z[5] +
1232 x[5] * y[6] * z[2] + x[6] * y[5] * z[7] + x[6] * y[7] * z[2] +
1233 y[6] * x[7] * z[4] - y[6] * x[4] * z[7] - y[6] * x[7] * z[3] +
1234 z[6] * x[7] * y[2] + x[2] * y[5] * z[6] - x[2] * y[6] * z[5] +
1235 y[6] * x[2] * z[7] + x[6] * y[2] * z[5];
1236 s7 = s8 - x[5] * y[2] * z[6] - z[6] * x[7] * y[5] - z[5] * x[7] * y[4] +
1237 z[5] * x[0] * y[4] - y[5] * x[4] * z[7] + y[0] * x[4] * z[7] -
1238 z[6] * x[2] * y[7] - x[5] * y[4] * z[0] - x[5] * y[7] * z[4] -
1239 y[0] * x[7] * z[4] + y[5] * x[4] * z[1] - x[6] * y[7] * z[4] +
1240 x[7] * y[4] * z[3] - x[4] * y[7] * z[3] + x[3] * y[7] * z[4] -
1241 x[7] * y[3] * z[4] - x[6] * y[3] * z[7] + x[6] * y[4] * z[7];
1242 s8 = -x[3] * y[4] * z[7] + x[4] * y[3] * z[7] - z[6] * x[7] * y[4] -
1243 z[1] * x[6] * y[5] + x[6] * y[7] * z[3] - x[1] * y[6] * z[5] -
1244 y[1] * x[5] * z[6] + z[5] * x[4] * y[7] - z[5] * x[4] * y[0] +
1245 x[1] * y[5] * z[6] - y[6] * x[5] * z[7] - y[2] * x[3] * z[1] +
1246 z[1] * x[5] * y[6] - y[5] * x[1] * z[4] + z[6] * x[4] * y[7] +
1247 x[5] * y[1] * z[4] - x[5] * y[6] * z[4] + y[6] * x[3] * z[7] -
1249 s5 = s8 + x[5] * y[4] * z[6] + z[5] * x[1] * y[4] + y[1] * x[6] * z[5] -
1250 z[6] * x[3] * y[7] + z[6] * x[7] * y[3] - z[5] * x[6] * y[4] -
1251 z[5] * x[4] * y[1] + z[5] * x[4] * y[6] + x[1] * y[6] * z[2] +
1252 x[2] * y[6] * z[3] + z[2] * x[6] * y[3] + z[1] * x[6] * y[2] +
1253 z[2] * x[3] * y[1] - z[2] * x[1] * y[3] - z[2] * x[3] * y[6] +
1254 y[2] * x[1] * z[3] + y[1] * x[2] * z[6] - z[0] * x[7] * y[3] + s7;
1257 const double unknown2 = s1 * s2;
1259 return {unknown0, unknown1, unknown2};
1275 template <
int structdim,
int dim,
int spacedim>
1287 template <
int dim,
int spacedim>
1293 return (accessor.
vertex(1) - accessor.
vertex(0)).norm();
1361 for (
unsigned int d = 0;
d < 3; ++
d)
1363 if (a_max < 1e-14 * accessor.
diameter())
1364 return cross_product_3d(b0, b1).
norm();
1369 constexpr unsigned int n_qp = 4;
1370 const double c1 = 2.0 / 7.0 *
std::sqrt(6.0 / 5.0);
1371 const double w0 = (18.0 -
std::sqrt(30)) / 72.0;
1372 const double w1 = (18.0 +
std::sqrt(30)) / 72.0;
1374 const std::array<double, n_qp> q{{
1380 const std::array<double, n_qp>
w{{w0, w1, w1, w0}};
1383 for (
unsigned int i = 0; i < n_qp; ++i)
1384 for (
unsigned int j = 0; j < n_qp; ++j)
1385 area += cross_product_3d(q[i] * a + b0, q[j] * a + b1).
norm() *
1395 return 0.5 * cross_product_3d(v01, v02).
norm();
1404 template <
int structdim,
int dim,
int spacedim>
1411 return std::numeric_limits<double>::quiet_NaN();
1415 template <
int dim,
int spacedim>
1423 template <
int dim,
int spacedim>
1431 template <
int dim,
int spacedim>
1439 template <
int structdim,
int dim,
int spacedim>
1442 const bool use_interpolation)
1444 if (use_interpolation)
1447 const auto points_and_weights =
1451 points_and_weights.first.end()),
1453 points_and_weights.second.end()));
1457 return get_new_point_on_object(obj);
1467template <
int structdim,
int dim,
int spacedim>
1470template <
int structdim,
int dim,
int spacedim>
1473template <
int structdim,
int dim,
int spacedim>
1481template <
int structdim,
int dim,
int spacedim>
1484 const std::initializer_list<int> &new_indices)
const
1487 this->objects().get_bounding_object_indices(this->present_index);
1492 for (
const auto &new_index : new_indices)
1494 bounding_object_index_ref[i] = new_index;
1501template <
int structdim,
int dim,
int spacedim>
1504 const std::initializer_list<unsigned int> &new_indices)
const
1507 this->objects().get_bounding_object_indices(this->present_index);
1512 for (
const auto &new_index : new_indices)
1514 bounding_object_index_ref[i] = new_index;
1521template <
int structdim,
int dim,
int spacedim>
1527 return ::barycenter(*
this);
1532template <
int structdim,
int dim,
int spacedim>
1538 return ::measure(*
this);
1543template <
int structdim,
int dim,
int spacedim>
1548 std::make_pair(this->vertex(0), this->vertex(0));
1550 const unsigned int n_vertices = this->n_vertices();
1551 for (
unsigned int v = 1; v < n_vertices; ++v)
1554 for (
unsigned int k = 0; k < spacedim; ++k)
1556 boundary_points.first[k] =
std::min(boundary_points.first[k], x[k]);
1557 boundary_points.second[k] =
std::max(boundary_points.second[k], x[k]);
1566template <
int structdim,
int dim,
int spacedim>
1569 const unsigned int )
const
1572 return std::numeric_limits<double>::signaling_NaN();
1583 return this->diameter();
1593 return this->diameter();
1601 const unsigned int lines[2][2] = {
1607 return std::max(this->line(lines[axis][0])->diameter(),
1608 this->line(lines[axis][1])->diameter());
1615 const unsigned int lines[2][2] = {
1621 return std::max(this->line(lines[axis][0])->diameter(),
1622 this->line(lines[axis][1])->diameter());
1630 const unsigned int lines[3][4] = {
1637 double lengths[4] = {this->line(lines[axis][0])->diameter(),
1638 this->line(lines[axis][1])->diameter(),
1639 this->line(lines[axis][2])->diameter(),
1640 this->line(lines[axis][3])->diameter()};
1653 set_manifold_id(manifold_ind);
1655 if (this->has_children())
1656 for (
unsigned int c = 0; c < this->n_children(); ++c)
1657 this->child(c)->set_all_manifold_ids(manifold_ind);
1662 for (
const unsigned int i : this->face_indices())
1663 this->quad(i)->set_manifold_id(manifold_ind);
1664 for (
const unsigned int i : this->line_indices())
1665 this->line(i)->set_manifold_id(manifold_ind);
1669template <
int structdim,
int dim,
int spacedim>
1676 std::array<double, GeometryInfo<structdim>::vertices_per_cell> w;
1680 p[i] = this->vertex(i);
1684 return this->get_manifold().get_new_point(
make_array_view(p.begin(), p.end()),
1691template <
int structdim,
int dim,
int spacedim>
1699 vertices[v] = this->vertex(v);
1702 GridTools::affine_cell_approximation<structdim, spacedim>(
vertices);
1710template <
int structdim,
int dim,
int spacedim>
1713 const bool respect_manifold,
1714 const bool use_interpolation)
const
1716 if (respect_manifold ==
false)
1722 return p / this->n_vertices();
1725 return get_new_point_on_object(*
this, use_interpolation);
1732template <
int spacedim>
1743template <
int spacedim>
1753template <
int spacedim>
1763template <
int spacedim>
1769 if (this->has_children())
1770 for (
unsigned int c = 0; c < this->n_children(); ++c)
1771 this->child(c)->recursively_set_user_flag();
1776template <
int spacedim>
1782 if (this->has_children())
1783 for (
unsigned int c = 0; c < this->n_children(); ++c)
1784 this->child(c)->recursively_clear_user_flag();
1789template <
int spacedim>
1799template <
int spacedim>
1809template <
int spacedim>
1819template <
int spacedim>
1830template <
int spacedim>
1834 set_user_pointer(p);
1836 if (this->has_children())
1837 for (
unsigned int c = 0; c < this->n_children(); ++c)
1838 this->child(c)->recursively_set_user_pointer(p);
1843template <
int spacedim>
1847 clear_user_pointer();
1849 if (this->has_children())
1850 for (
unsigned int c = 0; c < this->n_children(); ++c)
1851 this->child(c)->recursively_clear_user_pointer();
1856template <
int spacedim>
1866template <
int spacedim>
1876template <
int spacedim>
1887template <
int spacedim>
1893 if (this->has_children())
1894 for (
unsigned int c = 0; c < this->n_children(); ++c)
1895 this->child(c)->recursively_set_user_index(p);
1900template <
int spacedim>
1906 if (this->has_children())
1907 for (
unsigned int c = 0; c < this->n_children(); ++c)
1908 this->child(c)->recursively_clear_user_index();
1921 return (this->vertex(0)[0] <= p[0]) && (p[0] <= this->vertex(1)[0]);
1954 static const int direction[4] = {-1, 1, 1, -1};
1955 for (
unsigned int f = 0; f < 4; ++f)
1979 if ((-face[1] * to_p[0] + face[0] * to_p[1]) < 0)
2010 const unsigned int dim = 3;
2011 const unsigned int spacedim = 3;
2015 for (
unsigned int v = 1; v < this->n_vertices(); ++v)
2016 for (
unsigned int d = 0; d < dim; ++d)
2018 maxp[d] =
std::max(maxp[d], this->vertex(v)[d]);
2019 minp[d] =
std::min(minp[d], this->vertex(v)[d]);
2024 for (
unsigned int d = 0; d < dim; ++d)
2025 if ((p[d] < minp[d]) || (p[d] > maxp[d]))
2040 .
template get_default_linear_mapping<dim, spacedim>()
2041 .transform_real_to_unit_cell(cell_iterator, p)));
2054template <
int dim,
int spacedim>
2060 ExcMessage(
"The current iterator points to an inactive cell. "
2061 "You cannot convert it to an iterator to an active cell."));
2063 ExcMessage(
"The triangulation associated with the iterator does not "
2064 "match that of the DoFHandler."));
2075template <
int dim,
int spacedim>
2081 ExcMessage(
"The triangulation associated with the iterator does not "
2082 "match that of the DoFHandler."));
2097template <
int dim,
int spacedim>
2098template <
int dim_,
int spacedim_>
2107 this->reference_cell()
2108 .template get_default_linear_mapping<dim_, spacedim_>()
2109 .transform_real_to_unit_cell(cell_iterator, p);
2120 return point_inside_codim<1, 2>(p);
2128 return point_inside_codim<1, 3>(p);
2138 return point_inside_codim<2, 3>(p);
2143template <
int dim,
int spacedim>
2147 for (
const auto face : this->face_indices())
2148 if (at_boundary(face))
2156template <
int dim,
int spacedim>
2161 return this->tria->levels[this->present_level]
2162 ->cells.boundary_or_material_id[this->present_index]
2168template <
int dim,
int spacedim>
2175 this->tria->levels[this->present_level]
2176 ->cells.boundary_or_material_id[this->present_index]
2177 .material_id = mat_id;
2182template <
int dim,
int spacedim>
2187 set_material_id(mat_id);
2189 if (this->has_children())
2190 for (
unsigned int c = 0; c < this->n_children(); ++c)
2191 this->child(c)->recursively_set_material_id(mat_id);
2196template <
int dim,
int spacedim>
2202 Assert(this->is_active(),
2203 ExcMessage(
"set_subdomain_id() can only be called on active cells!"));
2204 this->tria->levels[this->present_level]->subdomain_ids[this->present_index] =
2210template <
int dim,
int spacedim>
2216 this->tria->levels[this->present_level]
2217 ->level_subdomain_ids[this->present_index] = new_level_subdomain_id;
2221template <
int dim,
int spacedim>
2226 if constexpr (dim == spacedim)
2228 else if constexpr (dim == spacedim - 1)
2229 return this->tria->levels[this->present_level]
2230 ->direction_flags[this->present_index];
2234 ExcMessage(
"This function cannot be called if dim<spacedim-1."));
2241template <
int dim,
int spacedim>
2244 const bool new_direction_flag)
const
2250 if constexpr (dim == spacedim)
2251 Assert(new_direction_flag ==
true,
2252 ExcMessage(
"If dim==spacedim, direction flags are always true and "
2253 "can not be set to anything else."));
2254 else if constexpr (dim == spacedim - 1)
2255 this->tria->levels[this->present_level]
2256 ->direction_flags[this->present_index] = new_direction_flag;
2258 Assert(new_direction_flag ==
true,
2259 ExcMessage(
"If dim<spacedim-1, then this function can be called "
2260 "only if the argument is 'true'."));
2265template <
int dim,
int spacedim>
2271 this->tria->levels[this->present_level]->parents[this->present_index / 2] =
2277template <
int dim,
int spacedim>
2286 return this->tria->levels[this->present_level]
2287 ->parents[this->present_index / 2];
2292template <
int dim,
int spacedim>
2295 const unsigned int active_cell_index)
const
2297 this->tria->levels[this->present_level]
2298 ->active_cell_indices[this->present_index] = active_cell_index;
2303template <
int dim,
int spacedim>
2308 this->tria->levels[this->present_level]
2309 ->global_active_cell_indices[this->present_index] = index;
2314template <
int dim,
int spacedim>
2319 this->tria->levels[this->present_level]
2320 ->global_level_cell_indices[this->present_index] = index;
2325template <
int dim,
int spacedim>
2332 this->present_level - 1,
2339template <
int dim,
int spacedim>
2344 if (this->has_children())
2345 for (
unsigned int c = 0; c < this->n_children(); ++c)
2346 this->child(c)->recursively_set_subdomain_id(new_subdomain_id);
2348 set_subdomain_id(new_subdomain_id);
2353template <
int dim,
int spacedim>
2356 const unsigned int i,
2363 this->tria->levels[this->present_level]
2365 .first = pointer->present_level;
2366 this->tria->levels[this->present_level]
2368 .second = pointer->present_index;
2372 this->tria->levels[this->present_level]
2375 this->tria->levels[this->present_level]
2383template <
int dim,
int spacedim>
2387 std::array<unsigned char, 30> id;
2390 const unsigned int n_child_indices = ptr.
level();
2392 while (ptr.
level() > 0)
2395 const unsigned int n_children = parent->n_children();
2398 unsigned char v =
static_cast<unsigned char>(-1);
2399 for (
unsigned int c = 0; c < n_children; ++c)
2401 if (parent->child_index(c) == ptr.
index())
2409 id[ptr.
level() - 1] = v;
2415 const unsigned int coarse_index = ptr.
index();
2417 return {this->tria->coarse_cell_index_to_coarse_cell_id(coarse_index),
2424template <
int dim,
int spacedim>
2427 const unsigned int neighbor)
const
2440 if ((dim == 1) && (spacedim == dim))
2444 this->neighbor(neighbor);
2459 const unsigned int this_face_index = face_index(neighbor);
2461 const unsigned int neighbor_guess =
2464 if (neighbor_guess < neighbor_cell->n_faces() &&
2465 neighbor_cell->face_index(neighbor_guess) == this_face_index)
2466 return neighbor_guess;
2473 for (
const unsigned int face_no : neighbor_cell->face_indices())
2474 if (neighbor_cell->face_index(face_no) == this_face_index)
2490template <
int dim,
int spacedim>
2493 const unsigned int face_no)
const
2495 const unsigned int n2 = neighbor_of_neighbor_internal(face_no);
2504template <
int dim,
int spacedim>
2507 const unsigned int face_no)
const
2509 return neighbor_of_neighbor_internal(face_no) ==
2515template <
int dim,
int spacedim>
2516std::pair<unsigned int, unsigned int>
2518 const unsigned int neighbor)
const
2523 Assert(neighbor_is_coarser(neighbor),
2530 const int this_face_index = face_index(neighbor);
2532 this->neighbor(neighbor);
2547 const unsigned int face_no_guess =
2551 neighbor_cell->face(face_no_guess);
2553 if (face_guess->has_children())
2554 for (
unsigned int subface_no = 0;
2555 subface_no < face_guess->n_children();
2557 if (face_guess->child_index(subface_no) == this_face_index)
2558 return std::make_pair(face_no_guess, subface_no);
2564 for (
const unsigned int face_no : neighbor_cell->face_indices())
2566 if (face_no != face_no_guess)
2569 face = neighbor_cell->face(face_no);
2570 if (face->has_children())
2571 for (
unsigned int subface_no = 0;
2572 subface_no < face->n_children();
2574 if (face->child_index(subface_no) == this_face_index)
2575 return std::make_pair(face_no, subface_no);
2589 const int this_face_index = face_index(neighbor);
2591 this->neighbor(neighbor);
2599 const unsigned int face_no_guess =
2603 neighbor_cell->face(face_no_guess);
2605 if (face_guess->has_children())
2606 for (
unsigned int subface_no = 0;
2607 subface_no < face_guess->n_children();
2610 if (face_guess->child_index(subface_no) == this_face_index)
2614 return std::make_pair(face_no_guess,
2615 translate_subface_no(face_guess,
2618 if (face_guess->child(subface_no)->has_children())
2619 for (
unsigned int subsub_no = 0;
2620 subsub_no < face_guess->child(subface_no)->n_children();
2622 if (face_guess->child(subface_no)->child_index(subsub_no) ==
2627 return std::make_pair(face_no_guess,
2628 translate_subface_no(face_guess,
2635 for (
const unsigned int face_no : neighbor_cell->face_indices())
2637 if (face_no == face_no_guess)
2641 neighbor_cell->face(face_no);
2643 if (!face->has_children())
2646 for (
unsigned int subface_no = 0; subface_no < face->n_children();
2649 if (face->child_index(subface_no) == this_face_index)
2653 return std::make_pair(face_no,
2654 translate_subface_no(face,
2657 if (face->child(subface_no)->has_children())
2658 for (
unsigned int subsub_no = 0;
2659 subsub_no < face->child(subface_no)->n_children();
2661 if (face->child(subface_no)->child_index(subsub_no) ==
2666 return std::make_pair(face_no,
2667 translate_subface_no(face,
2691template <
int dim,
int spacedim>
2694 const unsigned int i_face)
const
2709 cell_iterator current_cell(*
this);
2710 if (this->tria->periodic_face_map.find(
2711 std::make_pair(current_cell, i_face)) !=
2712 this->tria->periodic_face_map.end())
2719template <
int dim,
int spacedim>
2733 cell_iterator current_cell(*
this);
2736 this->tria->periodic_face_map.find(std::make_pair(current_cell, i_face));
2739 Assert(my_face_pair != this->tria->periodic_face_map.end(),
2741 return my_face_pair->second.first.first;
2746template <
int dim,
int spacedim>
2749 const unsigned int i_face)
const
2751 if (!(this->face(i_face)->at_boundary()))
2752 return this->neighbor(i_face);
2753 else if (this->has_periodic_neighbor(i_face))
2754 return this->periodic_neighbor(i_face);
2758 return this->neighbor(i_face);
2763template <
int dim,
int spacedim>
2766 const unsigned int i_face,
2767 const unsigned int i_subface)
const
2783 cell_iterator my_it(*
this);
2786 this->tria->periodic_face_map.find(std::make_pair(my_it, i_face));
2791 Assert(my_face_pair != this->tria->periodic_face_map.end(),
2793 cell_iterator parent_nb_it = my_face_pair->second.first.first;
2794 unsigned int nb_face_num = my_face_pair->second.first.second;
2796 parent_nb_it->face(nb_face_num);
2803 const auto [orientation, rotation, flip] =
2806 unsigned int sub_neighbor_num =
2813 nb_parent_face_it->refinement_case());
2814 return parent_nb_it->child(sub_neighbor_num);
2819template <
int dim,
int spacedim>
2820std::pair<unsigned int, unsigned int>
2822 const unsigned int i_face)
const
2838 const int my_face_index = this->face_index(i_face);
2839 cell_iterator my_it(*
this);
2842 this->tria->periodic_face_map.find(std::make_pair(my_it, i_face));
2847 Assert(my_face_pair != this->tria->periodic_face_map.end(),
2849 cell_iterator nb_it = my_face_pair->second.first.first;
2850 unsigned int face_num_of_nb = my_face_pair->second.first.second;
2853 this->tria->periodic_face_map.find(std::make_pair(nb_it, face_num_of_nb));
2859 Assert(nb_face_pair != this->tria->periodic_face_map.end(),
2861 cell_iterator p_nb_of_p_nb = nb_face_pair->second.first.first;
2863 p_nb_of_p_nb->face(nb_face_pair->second.first.second);
2864 for (
unsigned int i_subface = 0; i_subface < parent_face_it->n_children();
2866 if (parent_face_it->child_index(i_subface) == my_face_index)
2867 return std::make_pair(face_num_of_nb, i_subface);
2880template <
int dim,
int spacedim>
2883 const unsigned int i_face)
const
2885 return periodic_neighbor(i_face)->index();
2890template <
int dim,
int spacedim>
2893 const unsigned int i_face)
const
2895 return periodic_neighbor(i_face)->level();
2900template <
int dim,
int spacedim>
2903 const unsigned int i_face)
const
2905 return periodic_neighbor_face_no(i_face);
2910template <
int dim,
int spacedim>
2913 const unsigned int i_face)
const
2925 cell_iterator my_it(*
this);
2928 this->tria->periodic_face_map.find(std::make_pair(my_it, i_face));
2934 Assert(my_face_pair != this->tria->periodic_face_map.end(),
2936 return my_face_pair->second.first.second;
2941template <
int dim,
int spacedim>
2944 const unsigned int i_face)
const
2965 cell_iterator my_it(*
this);
2968 this->tria->periodic_face_map.find(std::make_pair(my_it, i_face));
2973 Assert(my_face_pair != this->tria->periodic_face_map.end(),
2976 cell_iterator nb_it = my_face_pair->second.first.first;
2977 unsigned int face_num_of_nb = my_face_pair->second.first.second;
2980 this->tria->periodic_face_map.find(std::make_pair(nb_it, face_num_of_nb));
2986 Assert(nb_face_pair != this->tria->periodic_face_map.end(),
2988 const unsigned int my_level = this->
level();
2989 const unsigned int neighbor_level = nb_face_pair->second.first.first->level();
2991 return my_level > neighbor_level;
2996template <
int dim,
int spacedim>
3003 return (neighbor_index(i) == -1);
3008template <
int dim,
int spacedim>
3013 return at_boundary();
3016 for (
unsigned int l = 0; l < this->n_lines(); ++l)
3017 if (this->line(l)->at_boundary())
3026template <
int dim,
int spacedim>
3029 const unsigned int face,
3030 const unsigned int subface)
const
3032 Assert(!this->has_children(),
3033 ExcMessage(
"The present cell must not have children!"));
3034 Assert(!this->at_boundary(face),
3035 ExcMessage(
"The present cell must have a valid neighbor!"));
3036 Assert(this->neighbor(face)->has_children() ==
true,
3037 ExcMessage(
"The neighbor must have children!"));
3045 const auto neighbor_cell = this->neighbor(face);
3048 Assert(neighbor_cell->refinement_case() ==
3054 const unsigned int neighbor_face =
3055 this->neighbor_of_neighbor(face);
3060 const unsigned int neighbor_subface =
3061 (!(this->line_orientation(face)) !=
3062 !(neighbor_cell->line_orientation(neighbor_face))) ?
3066 const unsigned int neighbor_child_index =
3067 neighbor_cell->reference_cell().child_cell_on_face(
3068 neighbor_face, neighbor_subface);
3070 neighbor_cell->child(neighbor_child_index);
3074 Assert(sub_neighbor->refinement_case() ==
3078 return sub_neighbor;
3082 const unsigned int neighbor_neighbor =
3083 this->neighbor_of_neighbor(face);
3084 const unsigned int neighbor_child_index =
3086 this->neighbor(face)->refinement_case(),
3091 this->neighbor(face)->child(neighbor_child_index);
3097 while (sub_neighbor->has_children())
3100 sub_neighbor->refinement_case(),
3101 neighbor_neighbor) ==
3106 sub_neighbor->refinement_case(), neighbor_neighbor, 0));
3109 return sub_neighbor;
3177 mother_face = this->face(face);
3178 const unsigned int total_children =
3179 mother_face->n_active_descendants();
3184 unsigned int neighbor_neighbor;
3187 this->neighbor(face);
3191 mother_face->refinement_case();
3192 if (mother_face_ref_case ==
3201 neighbor_neighbor = this->neighbor_of_neighbor(face);
3205 const unsigned int neighbor_child_index =
3207 neighbor->refinement_case(),
3210 neighbor->face_orientation(neighbor_neighbor),
3211 neighbor->face_flip(neighbor_neighbor),
3212 neighbor->face_rotation(neighbor_neighbor));
3213 neighbor_child = neighbor->child(neighbor_child_index);
3217 Assert((this->face(face)->child(subface) ==
3218 neighbor_child->face(neighbor_neighbor)),
3228 unsigned int first_child_to_find;
3229 unsigned int neighbor_child_index;
3230 if (total_children == 2)
3231 first_child_to_find = subface;
3234 first_child_to_find = subface / 2;
3235 if (total_children == 3 && subface == 1 &&
3236 !mother_face->child(0)->has_children())
3237 first_child_to_find = 1;
3239 if (neighbor_is_coarser(face))
3241 std::pair<unsigned int, unsigned int> indices =
3242 neighbor_of_coarser_neighbor(face);
3243 neighbor_neighbor = indices.first;
3288 unsigned int iso_subface;
3289 if (neighbor->face(neighbor_neighbor)
3291 iso_subface = 2 * first_child_to_find + indices.second;
3294 Assert(neighbor->face(neighbor_neighbor)
3295 ->refinement_case() ==
3299 first_child_to_find + 2 * indices.second;
3301 neighbor_child_index =
3303 neighbor->refinement_case(),
3306 neighbor->face_orientation(neighbor_neighbor),
3307 neighbor->face_flip(neighbor_neighbor),
3308 neighbor->face_rotation(neighbor_neighbor));
3312 neighbor_neighbor = neighbor_of_neighbor(face);
3313 neighbor_child_index =
3315 neighbor->refinement_case(),
3317 first_child_to_find,
3318 neighbor->face_orientation(neighbor_neighbor),
3319 neighbor->face_flip(neighbor_neighbor),
3320 neighbor->face_rotation(neighbor_neighbor),
3321 mother_face_ref_case);
3324 neighbor_child = neighbor->child(neighbor_child_index);
3330 neighbor_child->has_children() &&
3332 neighbor_child->refinement_case(), neighbor_neighbor) ==
3334 neighbor_child = neighbor_child->child(
3336 neighbor_child->refinement_case(),
3346 if (total_children == 3)
3348 if (mother_face->child(0)->has_children())
3351 neighbor_child = neighbor_child->child(
3353 neighbor_child->refinement_case(),
3356 neighbor_child->face_orientation(
3358 neighbor_child->face_flip(neighbor_neighbor),
3359 neighbor_child->face_rotation(
3361 mother_face->child(0)->refinement_case()));
3365 Assert(mother_face->child(1)->has_children(),
3368 neighbor_child = neighbor_child->child(
3370 neighbor_child->refinement_case(),
3373 neighbor_child->face_orientation(
3375 neighbor_child->face_flip(neighbor_neighbor),
3376 neighbor_child->face_rotation(
3378 mother_face->child(1)->refinement_case()));
3381 else if (total_children == 4)
3383 neighbor_child = neighbor_child->child(
3385 neighbor_child->refinement_case(),
3388 neighbor_child->face_orientation(neighbor_neighbor),
3389 neighbor_child->face_flip(neighbor_neighbor),
3390 neighbor_child->face_rotation(neighbor_neighbor),
3391 mother_face->child(subface / 2)->refinement_case()));
3399 while (neighbor_child->has_children())
3402 neighbor_child->refinement_case(), neighbor_neighbor, 0));
3408 switch (this->subface_case(face))
3413 requested = mother_face->child(subface);
3418 mother_face->child(subface / 2)->child(subface % 2);
3427 requested = mother_face->child(0)->child(subface);
3430 requested = mother_face->child(1);
3441 requested = mother_face->child(0);
3445 requested = mother_face->child(1)->child(subface - 1);
3455 Assert(requested == neighbor_child->face(neighbor_neighbor),
3459 return neighbor_child;
3476template <
int structdim,
int dim,
int spacedim>
3485template <
int structdim,
int dim,
int spacedim>
3494template <
int structdim,
int dim,
int spacedim>
3503#include "tria_accessor.inst"