## 300 Reputation

12 years, 108 days

## Not correct...

@ Kitonum, your command is not correct with the equation x^4 -(3*m+2)*x^2 + 3*m+1 = 0.

## Thanks...

Thank for your answer. I am sorry about my question. I see, I asked many quetions, but, there are problems I can not solve them by myself, therefore I posted at here.  Please forgive me and help me.

## Thanks...

Thank for your answer. I am sorry about my question. I see, I asked many quetions, but, there are problems I can not solve them by myself, therefore I posted at here.  Please forgive me and help me.

## How many solutions?...

Thank you very much. How to get all solution?

## How many solutions?...

Thank you very much. How to get all solution?

## Thank you very much...

Thank you very much

## Thank you very much...

Thank you very much

## I tried...

I tried

restart;

L:=[]:

k:=10:

for x1 from -k to k  do

for y1 from -k to k  do

for x2 from -k to k  do

for y2 from -k to k  do

for x3 from -k to k  do

for y3 from -k to k do

G:=[1,1]:

H:=[3,3]:

if x1+x2+x3=3*G[1] and y1+y2+y3=3*G[2] and (H[1]-x1)*(x3-x2) +(H[2]-y1)*(y3-y2) = 0 and (H[1]-x2)*(x2-x1) +(H[2]-y2)*(y2-y1)=0 and (x2-x1)*(y3-y1) +(x3-x1)*(y2-y1) <>0 then

L:=[op(L), [[x1,y1], [x2,y2], [x3,y3]]] fi;

od: od: od: od: od: od:

nops(L);  L;

## I tried...

I tried

restart;

L:=[]:

k:=10:

for x1 from -k to k  do

for y1 from -k to k  do

for x2 from -k to k  do

for y2 from -k to k  do

for x3 from -k to k  do

for y3 from -k to k do

G:=[1,1]:

H:=[3,3]:

if x1+x2+x3=3*G[1] and y1+y2+y3=3*G[2] and (H[1]-x1)*(x3-x2) +(H[2]-y1)*(y3-y2) = 0 and (H[1]-x2)*(x2-x1) +(H[2]-y2)*(y2-y1)=0 and (x2-x1)*(y3-y1) +(x3-x1)*(y2-y1) <>0 then

L:=[op(L), [[x1,y1], [x2,y2], [x3,y3]]] fi;

od: od: od: od: od: od:

nops(L);  L;

## It works...

> restart:

with(geom3d):

point(A,1/3,5/7,8/5):

point(B,-1/2,2/5, -1/8):

point(C,1,-1,-4):

plane(P,[A,B,C],[x,y,z]):

n:=NormalVector(P);

cdn:=ilcm(op(denom~(n)));

n:=cdn*n;

k:=igcd(n[1],n[2],n[3]):

if n[1]<>0 then

sign(n[1])*cdn/k*sort(Equation(P))

elif n[2] <> 0 then sign(n[2])*cdn/k*sort(Equation(P))

else sign(n[3])*cdn/k*sort(Equation(P))

end;

## It works...

> restart:

with(geom3d):

point(A,1/3,5/7,8/5):

point(B,-1/2,2/5, -1/8):

point(C,1,-1,-4):

plane(P,[A,B,C],[x,y,z]):

n:=NormalVector(P);

cdn:=ilcm(op(denom~(n)));

n:=cdn*n;

k:=igcd(n[1],n[2],n[3]):

if n[1]<>0 then

sign(n[1])*cdn/k*sort(Equation(P))

elif n[2] <> 0 then sign(n[2])*cdn/k*sort(Equation(P))

else sign(n[3])*cdn/k*sort(Equation(P))

end;

## Repair...

I see, the line r:=convert(domain, list); should be repair r:=convert(Domain, list);

## Repair...

I see, the line r:=convert(domain, list); should be repair r:=convert(Domain, list);

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