#include <stdio.h>

#define PGA2D

#define U N

#ifdef GA2D
enum { E1 = 1, E2, E12, N };
int grade[] = { 0, 1, 1, 2 };

int elt[N][N] = {
	//       E1    E2   E12
	{  U,    E1,   E2,  E12 },
/*E1*/	{ E1,     U,  E12,   E2 },
/*E2*/	{ E2,  -E12,    U,  -E1 },
/*E12*/	{ E12,  -E2,   E1,   -U },
};
#endif

#ifdef GA3D
enum {  E1 = 1, E2, E3, E12, E31, E23, E123, N };
int grade[] = {  0, 1, 1, 1, 2, 2, 2, 3, };
int elt[N][N] = {
	{      U,     E1,     E2,     E3,    E12,    E31,    E23,   E123,  },
	{     E1,      U,    E12,   -E31,     E2,    -E3,   E123,    E23,  },
	{     E2,   -E12,      U,    E23,    -E1,   E123,     E3,    E31,  },
	{     E3,    E31,   -E23,      U,   E123,     E1,    -E2,    E12,  },
	{    E12,    -E2,     E1,   E123,     -U,    E23,   -E31,    -E3,  },
	{    E31,     E3,   E123,    -E1,   -E23,     -U,    E12,    -E2,  },
	{    E23,   E123,    -E3,     E2,    E31,   -E12,     -U,    -E1,  },
	{   E123,    E23,    E31,    E12,    -E3,    -E2,    -E1,     -U,  },
};
#endif

#ifdef PGA2D
enum { E0 = 1, E1, E2, E01, E20, E12, E012, N };
int grade[] = { 0, 1, 1, 1, 2, 2, 2, 3 };
int dualsign[] = {  1, 1, 1, 1, 1, 1, 1, 1, };
int elt[N][N] = {
	//          E0     E1     E2    E01    E20    E12   E012
	{     U,    E0,    E1,    E2,   E01,   E20,   E12,  E012 },
/*E0*/	{    E0,     0,   E01,  -E20,     0,     0,  E012,     0 },
/*E1*/	{    E1,  -E01,     U,   E12,   -E0,  E012,    E2,   E20 },
/*E2*/	{    E2,   E20,  -E12,     U,  E012,    E0,   -E1,   E01 },
/*E01*/	{   E01,     0,    E0,  E012,     0,     0,  -E20,     0 },
/*E20*/	{   E20,     0,  E012,   -E0,     0,     0,   E01,     0 },
/*E12*/	{   E12,  E012,   -E2,    E1,   E20,  -E01,    -U,   -E0 },
/*E012*/{  E012,     0,   E20,   E01,     0,     0,   -E0,     0 },
};
#endif

#ifdef PGA3D
enum {  E0 = 1, E1, E2, E3, E01, E02, E03, E12, E31, E23, E021, E013, E032, E123, E0123, N };
int grade[] = {  0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, };
int dualsign[] = {  1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, };
int elt[N][N] = {
	{      U,     E0,     E1,     E2,     E3,    E01,    E02,    E03,    E12,    E31,    E23,   E021,   E013,   E032,   E123,  E0123,  },
	{     E0,      0,    E01,    E02,    E03,      0,      0,      0,  -E021,  -E013,  -E032,      0,      0,      0,  E0123,      0,  },
	{     E1,   -E01,      U,    E12,   -E31,    -E0,   E021,  -E013,     E2,    -E3,   E123,    E02,   -E03,  E0123,    E23,   E032,  },
	{     E2,   -E02,   -E12,      U,    E23,  -E021,    -E0,   E032,    -E1,   E123,     E3,   -E01,  E0123,    E03,    E31,   E013,  },
	{     E3,   -E03,    E31,   -E23,      U,   E013,  -E032,    -E0,   E123,     E1,    -E2,  E0123,    E01,   -E02,    E12,   E021,  },
	{    E01,      0,     E0,  -E021,   E013,      0,      0,      0,    E02,   -E03,  E0123,      0,      0,      0,  -E032,      0,  },
	{    E02,      0,   E021,     E0,  -E032,      0,      0,      0,   -E01,  E0123,    E03,      0,      0,      0,  -E013,      0,  },
	{    E03,      0,  -E013,   E032,     E0,      0,      0,      0,  E0123,    E01,   -E02,      0,      0,      0,  -E021,      0,  },
	{    E12,  -E021,    -E2,     E1,   E123,   -E02,    E01,  E0123,     -U,    E23,   -E31,     E0,   E032,  -E013,    -E3,   -E03,  },
	{    E31,  -E013,     E3,   E123,    -E1,    E03,  E0123,   -E01,   -E23,     -U,    E12,  -E032,     E0,   E021,    -E2,   -E02,  },
	{    E23,  -E032,   E123,    -E3,     E2,  E0123,   -E03,    E02,    E31,   -E12,     -U,   E013,  -E021,     E0,    -E1,   -E01,  },
	{   E021,      0,    E02,   -E01, -E0123,      0,      0,      0,     E0,   E032,  -E013,      0,      0,      0,    E03,      0,  },
	{   E013,      0,   -E03, -E0123,    E01,      0,      0,      0,  -E032,     E0,   E021,      0,      0,      0,    E02,      0,  },
	{   E032,      0, -E0123,    E03,   -E02,      0,      0,      0,   E013,  -E021,     E0,      0,      0,      0,    E01,      0,  },
	{   E123, -E0123,    E23,    E31,    E12,   E032,   E013,   E021,    -E3,    -E2,    -E1,   -E03,   -E02,   -E01,     -U,     E0,  },
	{  E0123,      0,  -E032,  -E013,  -E021,      0,      0,      0,   -E03,   -E02,   -E01,      0,      0,      0,    -E0,      0,  },
};
#endif

int
gen(int i, int j, int k)
{
	if(i == 0) i = U;	// fix because we can't have negative 0
	if(elt[j][k] != i && -elt[j][k] != i) return 0;		// only generate elements we're interested in
	// non-zero result
	if(elt[j][k] != 0)
		return printf(" %c l.e[%d]*r.e[%d]",
				elt[j][k] > 0 ? '+' : '-',
				j, k);
	return 0;
}

int
gendual(int i, int j, int k)
{
	if(i == 0) i = U;	// fix because we can't have negative 0
	if(elt[j][k] != i && -elt[j][k] != i) return 0;		// only generate elements we're interested in
	// non-zero result
	if(elt[j][k] != 0) {
		int s = elt[j][k] * dualsign[N-j-1] * dualsign[N-k-1];
		return printf(" %c l.e[%d]*r.e[%d]",
				s > 0 ? '+' : '-',
				N-j-1, N-k-1);
	}
	return 0;
}

int
main()
{
	int i, j, k, gr;
	int n;

	printf("	geometric\n");
	for(i = 0; i < N; i++){
		n = 0;
		printf("v.e[%d] =", i);
		for(j = 0; j < N; j++)
		for(k = 0; k < N; k++) {
			n += gen(i, j, k);
		}
		printf("%s;\n", n ? "" : " 0.0f");
	}

	printf("	meet\n");
	for(i = 0; i < N; i++){
		printf("v.e[%d] =", i);
		n = 0;
		for(j = 0; j < N; j++)
		for(k = 0; k < N; k++) {
			gr = grade[j]+grade[k];
			if(grade[i] != gr) continue;

			n += gen(i, j, k);
		}
		printf("%s;\n", n ? "" : " 0.0f");
	}

	printf("	join\n");
	for(i = 0; i < N; i++){
		printf("v.e[%d] = %c(", N-1-i, dualsign[N-1-i] < 0 ? '-' : '+');
		n = 0;
		for(j = 0; j < N; j++)
		for(k = 0; k < N; k++) {
			gr = grade[j]+grade[k];
			if(grade[i] != gr) continue;

			n += gendual(i, j, k);
		}
		printf("%s);\n", n ? "" : " 0.0f");
	}

	printf("	dot\n");
	for(i = 0; i < N; i++){
		printf("v.e[%d] =", i);
		n = 0;
		for(j = 0; j < N; j++)
		for(k = 0; k < N; k++) {

			gr = grade[j]-grade[k];
			if(gr < 0) gr = -gr;
			if(grade[i] != gr) continue;

			n += gen(i, j, k);
		}
		printf("%s;\n", n ? "" : " 0.0f");
	}

	return 0;
}