等分する(2)

この記事の続き。式を整理する。

ちょっと書き換えて

    • Eqdiv(n)_{k}=\sqrt{\frac{n+1}{n}}(\sqrt{\frac{n-k}{n-k+1}}e_{k}-\sum_{i=0}^{k-1}(\sqrt{\frac{1}{(n-i)(n+1-i)}}e_i)),k=0,1,2,...,n
    • さらにjavaで確かめてみよう
public static double[][] eqdiv(int n){
		double[][] ret = new double[n][n-1];
		for(int i=0;i<ret.length;i++){
			if(i<n-1){
				ret[i][i]=Math.sqrt((double)(n)/(double)(n-1))*
				Math.sqrt((double)(n-i-1)/(double)(n-i));
			}
			
			for(int j=0;j<i;j++){
				ret[i][j]=-Math.sqrt((double)(n)/(double)(n-1))*
				Math.sqrt(1/(double)((n-1-j)*(n-j)));
			}
		}
		return ret;
	}
    • 19次元、20分割の場合。行が、20分割のベクトル、列は、19次元を張る格子単位ベクトルの成分。各行について、格子単位ベクトル成分の自乗を足し合わせると1になる(分割ベクトルが単位ベクトルであることを示している)。また、各列を足し合わせると0になる(全分割ベクトルは「放射状」に「均等」に広がっていて、全部足すと、ゼロベクトルとなることを示している)。
0.9999999999999998	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	0.9986139979479091	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	0.9970717360268645	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	0.9953452035868788	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	0.9933992677987827	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	0.991189255566704	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	0.9886574781098639	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	0.9857281161802883	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	0.982299486257503	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	0.9782319760890369	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	0.973328526784575	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	0.9673016668133487	0.0	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	0.959714869937393	0.0	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	-0.13710212427677043	0.9498713802919552	0.0	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	-0.13710212427677043	-0.15831189671532586	0.9365858115816939	0.0	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	-0.13710212427677043	-0.15831189671532586	-0.18731716231633877	0.917662935482247	0.0	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	-0.13710212427677043	-0.15831189671532586	-0.18731716231633877	-0.22941573387056174	0.8885233166386384	0.0	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	-0.13710212427677043	-0.15831189671532586	-0.18731716231633877	-0.22941573387056174	-0.29617443887954614	0.8377078165833909	0.0	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	-0.13710212427677043	-0.15831189671532586	-0.18731716231633877	-0.22941573387056174	-0.29617443887954614	-0.41885390829169544	0.7254762501100116	
-0.05263157894736842	-0.0554785554415505	-0.058651278589815566	-0.06220907522417993	-0.06622661785325218	-0.07079923254047886	-0.0760505752392203	-0.08214400968169068	-0.08929995329613663	-0.09782319760890368	-0.108147614087175	-0.12091270835166859	-0.13710212427677043	-0.15831189671532586	-0.18731716231633877	-0.22941573387056174	-0.29617443887954614	-0.41885390829169544	-0.7254762501100116