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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, - (ag - b) - 1, - (bg - c), - (cg - d) + 10, - (dg - e) - 22, - fg - 2, - (eg - 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 - 1.781741795058668I}, {g: -0.04961250951921104 + 1.781741795058668I}, {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

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,  - (ag (a*g - b) - 1, - (bg (b*g - c), - (cg (c*g - d) + 10, - (dg (d*g - e) - 22, - fg f*g - 2, - (eg (e*g - f) + 14], a,b,c,d,e,f,g, solution_dict=true)
[{g: sol[Eg]} for sol in sols]
sols]

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