### `ecm_add_ff`, `ecm_sub_ff`, `ecm_chsgn_ff`

ecm_sub_ff(p1,p2,ec)
ecm_chsgn_ff(p1)
:: Addition, Subtraction and additive inverse for points on an elliptic curve.
return
vector or 0
p1,p2
vector of length 3 or 0
ec
vector of length 2
• Let p1, p2 be points on the elliptic curve represented by ec over the current base field. ecm_add_ff(p1,p2,ec), ecm_sub_ff(p1,p2,ec) and ecm_chsgn_ff(p1) returns p1+p2, p1-p2 and -p1 respectively.
• If the current base field is a prime field of odd order, then ec represents y^2=x^3+ec[0]x+ec[1]. If the characteristic of the current base field is 2, then ec represents y^2+xy=x^3+ec[0]x^2+ec[1].
• The point at infinity is represented by 0.
• If an argument denoting a point is a vector of length 3, then it is the projective coordinate. In such a case the third coordinate must not be 0.
• If the result is a vector of length 3, then the third coordinate is not equal to 0 but not necessarily 1. To get the result by the affine coordinate, the first and the second coordinates should be divided by the third coordinate.
• The check whether the arguments are on the curve is omitted.
```[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])\$
[ 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
section `setmod_ff`