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Alex Flint
Alex Flint
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I am attempting to find all real solutions of a system of 12 polynomial equations in 12 unknowns. The equations each have total degree 6 and contain up to 1700 terms. I am only interested in real solutions. The equations were derived as the gradients of a sum-of-squares cost function, which I am attempting to find all global optima of. I believe there are a finite number of real solutions but I have not confirmed this yet. I have floating point coefficients and I'm looking for numerical solutions (as opposed to symbolic solutions).

Which software packages (and which functions specifically) are generally most promising to solve such a problem?

I am aware of various functions in Maple, Matlab, and Mathematica that can solve systems of polynomial equations but there are a large number of options in each software package and I'm interested in advice on where I should be looking first for problems of this scale.

A numerical dump of the cost function is here: bit.ly/1qA2kOp.

https://raw.githubusercontent.com/alexflint/polygamy/master/out/epipolar_accel_bezier3/cost.txt

I am attempting to find all real solutions of a system of 12 polynomial equations in 12 unknowns. The equations each have total degree 6 and contain up to 1700 terms. I am only interested in real solutions. The equations were derived as the gradients of a sum-of-squares cost function, which I am attempting to find all global optima of. I believe there are a finite number of real solutions but I have not confirmed this yet. I have floating point coefficients and I'm looking for numerical solutions (as opposed to symbolic solutions).

Which software packages (and which functions specifically) are generally most promising to solve such a problem?

I am aware of various functions in Maple, Matlab, and Mathematica that can solve systems of polynomial equations but there are a large number of options in each software package and I'm interested in advice on where I should be looking first for problems of this scale.

A numerical dump of the cost function is here: bit.ly/1qA2kOp.

I am attempting to find all real solutions of a system of 12 polynomial equations in 12 unknowns. The equations each have total degree 6 and contain up to 1700 terms. I am only interested in real solutions. The equations were derived as the gradients of a sum-of-squares cost function, which I am attempting to find all global optima of. I believe there are a finite number of real solutions but I have not confirmed this yet. I have floating point coefficients and I'm looking for numerical solutions (as opposed to symbolic solutions).

Which software packages (and which functions specifically) are generally most promising to solve such a problem?

I am aware of various functions in Maple, Matlab, and Mathematica that can solve systems of polynomial equations but there are a large number of options in each software package and I'm interested in advice on where I should be looking first for problems of this scale.

A numerical dump of the cost function is here:

https://raw.githubusercontent.com/alexflint/polygamy/master/out/epipolar_accel_bezier3/cost.txt

Notice added Draw attention by Alex Flint
Bounty Started worth 50 reputation by Alex Flint
Changed tags. -- I think this is rather a numerics question than an algebraic geometry question.
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Stefan Kohl ♦
Stefan Kohl ♦
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Alex Flint
Alex Flint
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Software tools for medium-scale systems of polynomial equations

I am attempting to find all real solutions of a system of 12 polynomial equations in 12 unknowns. The equations each have total degree 6 and contain up to 1700 terms. I am only interested in real solutions. The equations were derived as the gradients of a sum-of-squares cost function, which I am attempting to find all global optima of. I believe there are a finite number of real solutions but I have not confirmed this yet. I have floating point coefficients and I'm looking for numerical solutions (as opposed to symbolic solutions).

Which software packages (and which functions specifically) are generally most promising to solve such a problem?

I am aware of various functions in Maple, Matlab, and Mathematica that can solve systems of polynomial equations but there are a large number of options in each software package and I'm interested in advice on where I should be looking first for problems of this scale.

A numerical dump of the cost function is here: bit.ly/1qA2kOp.