// sym3x110620.c
// 次数 29 までの対称式を x+y+z, xy+xz+yz, xyz の多項式に表す
// TeX ファイルとして出力する

#include <stdio.h>

#define N 30
#define N2 15
#define N3 10

FILE *fp;

int main()
{
	int a[N][N2][N2+1][N3+1];
	int d, p, q, i, j, k, t, E, F, G;
	fp = fopen("sym3.tex","w");
	fputs("\\documentclass[12pt]{jarticle}\n\n\\begin{document}\n\n", fp);
	for (d=0; d<N; d++) {
		for (q=0; q<N2; q++) {
			for (j=-1; j<N2; j++) {
				for (k=-1; k<N3; k++)  a[d][q][j+1][k+1] = 0;
			}
		}
	}
	a[0][0][0+1][0+1] = 1; a[1][0][0+1][0+1] = 1;
	a[2][0][0+1][0+1] = 1; a[2][0][1+1][0+1] = -2; a[2][1][1+1][0+1] = 1;
	for (d=3; d<N; d++) {
		for (p=(d+1)/2; p<=d; p++) {
			q = d-p;
			fprintf(fp, "$s(%d,%d,0) = ", p, q);
			if (q == 0) E = 0;
			else if (q == 1 && d == 3) E = 3;
			else if (q ==1) E = 2;
			else if (q == 2 && d == 4) E = 2;
			else E = 1;
			if (2*q == d-2) F = 2;
			else if (2*q < d-2) F = 1;
			else F = 0;
			if (2*q == d) G =1; else G = 0;
			for (j=0; 2*j<=d; j++) {
				for (k=0; 2*j+3*k<=d; k++)  {
					i = d-2*j-3*k;
					t = a[d-1-G][q-G][j-G+1][k+1] - F*a[d][q+1][j+1][k+1]
						- E*a[d-3][q-1-G][j+1][k-1+1];
					if (t != 0) {
						if (t > 1) fprintf(fp, "+%d", t);
						else if (t == 1) fprintf(fp, "+");
						else if (t < -1) fprintf(fp, "-%d", -t);
						else if (t == -1) fprintf(fp, "-");
						if (i > 1) fprintf(fp, "(x+y+z)^{%d}", i);
						else if (i == 1) fprintf(fp, "(x+y+z)");
						if (j > 1) fprintf(fp, "(xy+yz+zx)^{%d}", j);
						else if (j == 1)fprintf(fp, "(xy+yz+zx)");
						if (k > 1) fprintf(fp, "(xyz)^%d", k);
						else if (k == 1) fprintf(fp, "(xyz)");
					}
					a[d][q][j+1][k+1] = t;
				}
			}
			fputs("$\n\n\\vspace{2mm}\n", fp);
		}
	}
	fputs("\\end{document}", fp);
	fclose(fp);
	return 0;
}