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Solving Large Overdetermined Systems


My equation system consists (at the moment - by taking
all linear combinations, the cubics surely can be pruned too)
of 18 quadratics and 360 cubics in 15 variables.
Solve[] is out of question, for NSolve[] it's still
too large (not mentioning that there are some
1-parametric solutions), so I turned to FindRoot[] -
one found "random" solution would already be very revealing.
But alas, FindRoot[] needs #eq=#var. Bummer. (Of course I
can take 15 random equations and plug the solution back
in, but the probability of 378 zeroes is zero...)

Any other idea what I could try?
-- 
Hauke Reddmann <:-EX8    fc3a501 at uni-hamburg.de
    Er-a svo gott     sem gott kveða 
    öl alda sonum,     því að færra veit 
    er fleira drekkur     síns til geðs gumi.


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