Hi Doug!

I thought of this solution already, but it didn't want to work. Maple sometimes decided to give me the output, and two minutes later it decided to give me a spinning ball of death.

But something is fishy with this anyway. In my opinion the output maple is giving me for a simple solve command is wrong! Maybe you can tell me if I am doing something wrong here:

All I wanted to do is this:

> fb := proc (H, Sigma) options operator, arrow; -(1-H^2)*(2*Sigma^2+(1/2+(3/2)*w)*(1-Sigma^2)-H*Sigma), -(2-2*Sigma^2-(1/2+(3/2)*w)*(1-Sigma^2))*H*Sigma-(1-H^2)*(1-Sigma^2)-(1/2)*(3-3*Sigma^2)*(-w+1)*beta end proc;

print(`output redirected...`); # input placeholder

(H, Sigma) ->

/ 2\ / 2 /1 3 \ / 2\ \

-\1 - H / |2 Sigma + |- + - w| \1 - Sigma / - H Sigma|,

\ \2 2 / /

/ 2 /1 3 \ / 2\\

-|2 - 2 Sigma - |- + - w| \1 - Sigma /| H Sigma

\ \2 2 / /

/ 2\ / 2\ 1 / 2\

- \1 - H / \1 - Sigma / - - \3 - 3 Sigma / (-w + 1) beta

2

> `assuming`([solve({fb(H, Sigma)[1] = 0, fb(H, Sigma)[2] = 0}, [H, Sigma], useassumptions)], [H > 0]);

print(`output redirected...`); # input placeholder

/ /

| 1 |

piecewise|----------------------------------- \(3 beta w - 2

| 2

|-1 + 6 w - 9 w - 6 beta + 6 beta w

\

(1/2)\ [[

/ 2 \ | [[

- 3 beta) \1 - 6 w + 9 w + 6 beta - 6 beta w/ / < 0, [[H =

[[

[[

[[

/

1 |

- ----------------------------------- \(3 beta w - 2 - 3 beta)

2

-1 + 6 w - 9 w - 6 beta + 6 beta w

(1/2)\

/ 2 \ |

\1 - 6 w + 9 w + 6 beta - 6 beta w/ /,

]

1 + 3 w ]

Sigma = - -----------------------------------------],

(1/2)]

/ 2 \ ]

\1 - 6 w + 9 w + 6 beta - 6 beta w/ ]

[H = 1, Sigma = 1], [H = 1, Sigma = -1],

]

]

[H = 1, Sigma = -beta], [H = 2, Sigma = 1]], 0 <

]

]

]

/

1 |

----------------------------------- \(3 beta w - 2 - 3 beta)

2

-1 + 6 w - 9 w - 6 beta + 6 beta w

(1/2)\ [[

/ 2 \ | [[

\1 - 6 w + 9 w + 6 beta - 6 beta w/ /, [[H =

[[

[[

[[

/

1 |

----------------------------------- \(3 beta w - 2 - 3 beta)

2

-1 + 6 w - 9 w - 6 beta + 6 beta w

(1/2)\

/ 2 \ |

\1 - 6 w + 9 w + 6 beta - 6 beta w/ /,

]

1 + 3 w ]

Sigma = -----------------------------------------],

(1/2)]

/ 2 \ ]

\1 - 6 w + 9 w + 6 beta - 6 beta w/ ]

[H = 1, Sigma = 1], [H = 1, Sigma = -1],

] \

] |

[H = 1, Sigma = -beta], [H = 2, Sigma = 1]], []|

] |

] |

] /

And in my opinion this output is wrong in the following sense: When looking at the equations one sees by naked eye that (1,±1), (2,1) and (1,-beta) are solutions in any case. But they aren't listed in the last case! Further I think I once took a closer look on the first case, and found that it is a contradiction on its own, as in this case H and Sigma of the first solution get complex, but H is assumed to be >0. (But I didn't write the latter down properly, and can't remember for sure).

Do you have an idea whats going on here? -.^