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2018-10-09 01:33:29 +0100 | commented question | Ideal.variety() when working with symbolic rings Secretly I know that the value for every constant will be a positive number. And, while there may be lots of possible (x9,x10,x11) triples that satisfy the equations, the only ones that are "physically meaningful" are those with all three values between 0 and 1 (inclusive), possibly irrational. The fact that I cannot find any physically meaningful solutions after taking the Groebner basis and doing the rootfinding myself is what alerted me to a problem. I'm not sure if these physically-motivated assumptions of mine are at the root of my confusion. |

2018-10-09 01:33:19 +0100 | commented question | Ideal.variety() when working with symbolic rings I suppose the problem may be that there are no solutions that are valid over all possible values of the constants? Here's an example of there existing a solution if we substitute 1.0 (or 0.5) for all the constants: The solution is {1/3,1/3,1/3} |

2018-10-09 01:32:51 +0100 | commented question | Ideal.variety() when working with symbolic rings copying my comments to tmoteil here: A less trivial problem looks like this: When I do this, I get an empty list as the result. |

2018-10-08 22:08:32 +0100 | commented answer | Ideal.variety() when working with symbolic rings Secretly I know that the value for every constant will be a positive number. And, while there may be lots of possible (x9,x10,x11) triples that satisfy the equations, the only ones that are "physically meaningful" are those with all three values between 0 and 1 (inclusive), possibly irrational. The fact that I cannot find any physically meaningful solutions after taking the Groebner basis and doing the rootfinding myself is what alerted me to a problem. I'm not sure if these physically-motivated assumptions of mine are at the root of my confusion. |

2018-10-08 22:03:47 +0100 | commented answer | Ideal.variety() when working with symbolic rings I suppose the problem may be that there are no solutions that are valid over all possible values of the constants? Here's an example of there existing a solution if we substitute 1.0 (or 0.5) for all the constants: The solution is {1/3,1/3,1/3} |

2018-10-08 21:59:14 +0100 | commented answer | Ideal.variety() when working with symbolic rings I haven't yet adapted the very large chemical networks to this framework, but a less trivial problem looks like this: When I do this, I get an empty list as the result. |

2018-10-08 19:41:03 +0100 | asked a question | Ideal.variety() when working with symbolic rings I have a system of multivariate polynomials I would like to solve (the equations come from chemical reaction networks). I have many symbolic constants, but I've managed to generate a Groebner basis with the following code (using a toy example with solutions {{x: x0, y:0},{x: 0,y: x0}): In practice, I get many resulting equations which are extremely long, and it is numerically challenging to sequentially find the roots of these polynomials (in downstream code, I will get values for the constant parameters and then need to return solutions to these equations on the fly). Using the Is this expected behavior? When I try I would be happy to convert the |

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2018-10-02 00:37:39 +0100 | asked a question | Solving Groebner Basis of an ideal that includes parameters with order=lex yields non triangular equations From this reference, it seems that a Groebner basis with respect to lexicographic order should yield a 'triangular system': www This yields four equations (rather than 3) which do not seem to exhibit this triangular property (first three equations mention all three variables x9,x10,x11, and the last one involves both x9 and x10). Do I have a misunderstanding about what to expect from Sage's output? Or is there a test to see if my system of equations is pathological in some way? If I ignore the fact that variables x1...x8 are parameters, I am surprised to get a basis of three equations which is also not triangularizable with respect to x9,x10,x11. |

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