# Why, in any system of equations, does Sage give repeated solutions only once?

For example, the following system of equations has two roots equal to one:

```
var('a,b,c,d,e,f,g,x')
sols = solve([(a - g) + 2, - (a*g - b) - 1, - (b*g - c), - (c*g - d) + 10, - (d*g - e) - 22, - f*g - 2, - (e*g - f) + 14], a,b,c,d,e,f,g, solution_dict=true)
[{g: sol[Eg]} for sol in sols]
```

Six, instead of seven, solutions are provided by Sage, because repeated root 1 is presented only once:

```
[{g: -1.825113562621674},
{g: -0.04961250951921104 - 1.781741795058668*I},
{g: -0.04961250951921104 + 1.781741795058668*I},
{g: 0.2000320307495195},
{g: 1.724306472919419},
{g: 1}]
```

If you don't know which is the repeated root and you want to know which is it, how to do it, because with the use of multiplicities, or f.root, you cannot know

Solving via

`SR`

's`solve`

isn'texact: given :The solutions do not check :

A better (checkable) solution is to use the ring of polynomials of

`QQbar`

:Then the results can be checked :

But I have no idea about your multiplicity problem for now...

Thank you Emmanuel, this is a good response to my question, but really what I am looking for is a solution like that of the answer below

@georgeafr : @rburing is right. He was faster|smarter than me... My remark was

not(even tentatively) an answer to your question...