1 | initial version |

My system has three equations and three unknowns, which I want to transform into a series of three 1-D root finding problems.

For this to be possible, the system must have a finite number of solutions, but your system has an infinite number of solutions.

is there a test to see if my system of equations is pathological in some way?

You can compute `I.dimension()`

. For 0-dimensional ideals (like the Scholarpedia example), the output will be more like what you expect.

2 | No.2 Revision |

My system has three equations and three unknowns, which I want to transform into a series of three 1-D root finding problems.

For this to be ~~possible, ~~possible the system must have a finite number of solutions, but your system has an infinite number of solutions.

is there a test to see if my system of equations is pathological in some way?

You can compute `I.dimension()`

. (By the way, this uses the Gröbner basis.) For 0-dimensional ideals (like the Scholarpedia ~~example), ~~example) there are finitely many solutions over $\mathbb{C}$, and the output will be more like what you expect.

3 | No.3 Revision |

My system has three equations and three unknowns, which I want to transform into a series of three 1-D root finding problems.

For this to be possible the system must have a finite number of solutions, but your system has an infinite number of solutions.

is there a test to see if my system of equations is pathological in some way?

You can compute `I.dimension()`

. (By the way, this uses the Gröbner basis.) For 0-dimensional ideals in $\mathbb{Q}[x_1,\ldots,x_n]$ (like the Scholarpedia example) there are finitely many solutions over $\mathbb{C}$, and the output will be ~~more like ~~what you expect.

4 | No.4 Revision |

For this to be possible the system must have a finite number of solutions, but your system has an infinite number of solutions.

is there a test to see if my system of equations is pathological in some way?

You can compute `I.dimension()`

. (By the way, this uses the Gröbner basis.) For 0-dimensional ideals in $\mathbb{Q}[x_1,\ldots,x_n]$ (like the Scholarpedia example) there are finitely many solutions over $\mathbb{C}$, and the output will be what you expect.

You can also call `I.variety(ring=R)`

to solve the system of equations, which will give a warning if the ideal is not 0-dimensional.

5 | No.5 Revision |

For this to be possible the system must have a finite number of solutions, but your system has an infinite number of solutions.

is there a test to see if my system of equations is pathological in some way?

You can compute `I.dimension()`

. (By the way, this uses the Gröbner basis.) For 0-dimensional ideals in $\mathbb{Q}[x_1,\ldots,x_n]$ (like the Scholarpedia example) there are finitely many solutions over $\mathbb{C}$, and the output will be what you expect.

You can also call `I.variety(ring=R)`

to solve the system of ~~equations, ~~equations over `R`

(e.g. `CC`

or `RR`

for approximate solutions;`AA`

or `QQbar`

for exact solutions), which will give a warning if the ideal is not 0-dimensional.

6 | No.6 Revision |

is there a test to see if my system of equations is pathological in some way?

You can compute `I.dimension()`

. (By the way, this uses the Gröbner basis.) For 0-dimensional ideals in $\mathbb{Q}[x_1,\ldots,x_n]$ (like the Scholarpedia example) there are finitely many solutions over $\mathbb{C}$, and the output will be what you expect.

You can also call `I.variety(ring=R)`

to solve the system of equations over `R`

(e.g. `CC`

or `RR`

for approximate ~~solutions;~~solutions, `AA`

or `QQbar`

for exact solutions), which will give ~~a warning ~~an error if the ideal is not 0-dimensional.

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