# Revision history [back]

### Limitation of solve?

I am using (or trying to use) the solve function to solve a system of 10 nonlinear equations in 10 variables. However, solve simply outputs the 10 equations after some time computing. Is this running into a limit of the solve function, or is there some other way to economize my input to make it more solve-function-friendly? Would it help to know the algorithm which solve uses?

### Limitation of solve?

I am using (or trying to use) the solve function to solve a system of 10 nonlinear equations in 10 variables. However, solve simply outputs the 10 equations after some time computing. Is this running into a limit of the solve function, or is there some other way to economize my input to make it more solve-function-friendly? Would it help to know the algorithm which solve uses?

EDIT: At a suggestion from niles, I am putting up the equations that I am solving. I have a version that is simplified, but it is not a problem to solve. In the equations below it is legal to set any combination of the variables equal to zero, and the resulting solutions will be a subset of the solution set of the full collection of equations.

var('a b c d e f g h i j')

eq1 = a == a2 + ba + 2ac + 2ad + 2ae + 2af + ga + ha + ia + ja + b2 + db + gb + bc + dc + gc

eq2 = b == cb + 2be + hb + bd + cd

eq3 = c == c*2 + 2ec + hc + bf + cf

eq4 = d == fb + d2 + 2ed + fd

eq5 = e == e**2

eq6 = f == fc + ic + 2fe + df + f*2

eq7 = g == ib + jb + 2gd + 2hd + id + jd + 2ge + ag + bg + cg + fg + g*2 + 2hg + ig + jg + ah + bh + ai

eq8 = h == 2he + ch + h2 + bi + c*i

eq9 = i == 2ie + fh + ih + di + fi

eq10 = j == 2je + gf + hf + jf + 2jh + gi + hi + i2 + ji + aj + bj + cj + dj + fj + gj + i*j + j2

For those who are curious, the simplified version is this set of equations with a, b, c, g, h, i, j == 0.

If there is anything more that anybody would like to know about these equations or where I am getting them from, just say so in a comment.

### Limitation of solve?

I am using (or trying to use) the solve function to solve a system of 10 nonlinear equations in 10 variables. However, solve simply outputs the 10 equations after some time computing. Is this running into a limit of the solve function, or is there some other way to economize my input to make it more solve-function-friendly? Would it help to know the algorithm which solve uses?

EDIT: At a suggestion from niles, I am putting up the equations that I am solving. I have a version that is simplified, but it is not a problem to solve. In the equations below it is legal to set any combination of the variables equal to zero, and the resulting solutions will be a subset of the solution set of the full collection of equations.

var('a b c d e f g h i j')

eq1 = a == a^2 + ba + 2a2 + ba c + 2ac d + 2ad e + 2ae + 2f + ga + ha + ia + ja + b^2 + db + gb + bc + dc + gc

eq2 = b == cb + 2be + hb + bd + cd

eq3 = c == c^2 + 2ec + hc + bf + c*f

eq4 = d == fb + d^2 + 2ed + fd

eq5 = e == e^2

eq6 = f == fc + ic + 2fe + d*f + f^2

eq7 = g == ib + jb + 2gd + 2hd + id + jd + 2ge + ag + bg + cg + fg + g^2 + 2hg + ig + jg + ah + bh + a*i

eq8 = h == 2he + ch + h^2 + bi + c*i

eq9 = i == 2ie + fh + ih + di + fi

eq10 = j == 2je + gf + ga + ha + ia + ja + b2 hf + jf + 2jh + gi + hi + i^2 + ji + aj + bj + cj + db + gb + bc + dc + gc

eq2 = b == cb + 2be + hb + bd + cd

eq3 = c == c*2 + 2ec + hc + bf + cf

eq4 = d == fb + d2 + 2ed + fd

eq5 = e == e**2

eq6 = f == fc + ic + 2fe + df + f*2

eq7 = g == ib + jb + 2gd + 2hd + id + jd + 2ge + ag + bg + cg + fg + g*2 + 2hg + ig + jg + ah + bh + ai

eq8 = h == 2he + ch + h2 + bi + c*i

eq9 = i == 2ie + fh + ih + di + fi

eq10 = j == 2je + gf + hf + jf + 2jh + gi + hi + i2 + ji + aj + bj + cj + dj + fj + gj + i*j + j2j^2

For those who are curious, the simplified version is this set of equations with a, b, c, g, h, i, j == 0.

If there is anything more that anybody would like to know about these equations or where I am getting them from, just say so in a comment.

### Limitation of solve?

I am using (or trying to use) the solve function to solve a system of 10 nonlinear equations in 10 variables. However, solve simply outputs the 10 equations after some time computing. Is this running into a limit of the solve function, or is there some other way to economize my input to make it more solve-function-friendly? Would it help to know the algorithm which solve uses?

EDIT: At a suggestion from niles, I am putting up the equations that I am solving. I have a version that is simplified, but it is not a problem to solve. In the equations below it is legal to set any combination of the variables equal to zero, and the resulting solutions will be a subset of the solution set of the full collection of equations.

var('a b c d e f g h i j') j')

eq1 = a == a^2 + ba + 2ab*a + 2*a*c + 2*a*d + 2*a*e + 2*a*f + g*a + h*a + i*a + j*a + b^2 + d*b + g*b + b*c + d*c + g*c

eq2 = b == c*b + 2*b*e + h*b + b*d + c*d

eq3 = c + 2a== c^2 + 2*e*c + h*c + b*f + c*f

eq4 = d + 2a== f*b + d^2 + 2*e*d + f*d

eq5 = e + 2a== e^2

eq6 = f + ga + ha + ia + ja + b^2 + db + gb + bc + dc + gc eq2 = b == cb + 2be + hb + bd + cd eq3 = c == c^2 + 2ec + hc + bf + c*f eq4 = d == fb + d^2 + 2ed + fd eq5 = e == e^2 eq6 = f == fc + ic + 2fe == f*c + i*c + 2*f*e + d*f + f^2 f^2

eq7 = g == ib + jb + 2gd + 2hd + id + jd + 2ge + ag + bg + cg + fg i*b + j*b + 2*g*d + 2*h*d + i*d + j*d + 2*g*e + a*g + b*g + c*g + f*g + g^2 + 2hg + ig + jg + a2*h*g + i*g + j*g + a*h + b*h + a*i

eq8 = h + bh + a*i eq8 = h == 2he + ch == 2*h*e + c*h + h^2 + bb*i + c*i

eq9 = i + c*i eq9 = i == 2ie + fh + ih + di + fi == 2*i*e + f*h + i*h + d*i + f*i

eq10 = j == 2je + gf + hf + jf + 2jh + gi + hi 2*j*e + g*f + h*f + j*f + 2*j*h + g*i + h*i + i^2 + ji + aj + bj + cj + dj + fj + gj j*i + a*j + b*j + c*j + d*j + f*j + g*j + i*j + j^2j^2


For those who are curious, the simplified version is this set of equations with a, b, c, g, h, i, j == 0.

If there is anything more that anybody would like to know about these equations or where I am getting them from, just say so in a comment.