# implicit curve (CAS) , how to get some points on curve ?

jean-pierre Ortolland shared this question 4 years ago

Hi

#implicit Elliptic curve and CAS

elcG:y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5

#how to get the numerical values ​​of x of the curve in y={5,4,3,2,1,0,-1,-2,-3,-4,-5}

#this below does not work

C = Sequence(Solve({y^2 + x*y + 3*y = x^3 + 2x^2 + 4*x + 5, y = Y},{x, y}),Y,-5,5,1)

how to get the 11 points (not the 11 straight line equations !)

1

merci Noel

PointList(L_1) extrait bien la liste de point,

cela fait bien la liste de points mais les points ne sont pas visible sur mon graphe !

1

oui j'avais essayé comme d'habitude quand j'avais ce probleme mais rien n'y faisait.

dans ton fichier c'est ok merci beaucoup

I re-Write my code in a simplest and more rigorous way.

```#implicit Elliptic curve # in Input CAS window
elcG:y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5
L_1:=PointList(Sequence(Solve({elcG(x,y), y = Y},{x, y}),Y,-5,5,1))
# in input cmd
SetColor(L_1, red )```

1

I do not understand this point {(0, 0)} in the list ???, maybe it's a bug ?

{{(0.48933, -5)}, {(-0.12889, -4)}, {(-0.82931, -3)}, {(-1.36388, -2)}, {(-1.60382, -1)}, {(0, 0)}, {(-1.52596, 0)}, {(-0.43016, 1)}, {(1, 2)}, {(1.73628, 3)}, {(2.31006, 4)}, {(2.80497, 5)}}

2

```#implicit Elliptic curve # in Input CAS window
elcG:y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5
L_1:=PointList(Sequence(Solve({elcG(x,y), y = Y},{x, y}),Y,-5,5,1))

```

not true. define the equation in first cell of CAS

the right syntax is PointList(Sequence(Solve({elcG, y = Y},{x, y}),Y,-5,5,1))

can be a bug or wrong syntax. type elcG(x,y) in CAS for testing

I think the bug is the answer to Solve({elcG, y = 3},{x, y}) when elcG is defined in input bar

see the attached, a little change does the work

Files: foro.ggb
1

thank you mathmagic