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ecm_add_ff, ecm_sub_ff, ecm_chsgn_ff

ecm_add_ff(p1,p2,ec)
ecm_sub_ff(p1,p2,ec)
ecm_chsgn_ff(p1)
:: 楕円曲線上の点の加算, 減算, 逆元
return
ベクトルまたは 0
p1,p2
長さ 3 のベクトルまたは 0
ec
長さ 2 のベクトル
[0] setmod_ff(1125899906842679)$
[1] EC=newvect(2,[ptolmp(1),ptolmp(1)])$
[2] Pt1=newvect(3,[1,-412127497938252,1])$
[3] Pt2=newvect(3,[6,-252647084363045,1])$
[4] Pt3=ecm_add_ff(Pt1,Pt2,EC);
[ 560137044461222 184453736165476 125 ]
[5] F=y^2-(x^3+EC[0]*x+EC[1])$
[6] subst(F,x,Pt3[0]/Pt3[2],y,Pt3[1]/Pt3[2]);
0
[7] ecm_add_ff(Pt3,ecm_chsgn_ff(Pt3),EC);
0
[8] D=ecm_sub_ff(Pt3,Pt2,EC);
[ 886545905133065 119584559149586 886545905133065 ]
[9] D[0]/D[2]==Pt1[0]/Pt1[2];
1
[10] D[1]/D[2]==Pt1[1]/Pt1[2];
1
参照
section setmod_ff


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