I'm pretty interested in solving the following kind of problem using Sage: ``Let R be a polynomial ring in, say, x,y,z as variables over a field k. I'd like to find field-elements a,b,c such that
a(x^2+y^2)+b(xy+zx)+c(xyz)==0, if they exist (I know they do)''
so that Sage returns (a,b,c)=(0,0,0). That seems to be an easy matter if one can traduce the polynomial identity into a vector space identity. I proved to be unable to do so.
I've to say that my polynomial identities are quite more cumbersome and include up to 7 variables so working them by-hand is almost impossible in a finite ammount of time or patience.
Here is some code which "linearizes" your problem:
The result is a vector space which gives you all of your solutions. Your example
shows that (0,0,0) is the only answer. Another example:
posted May 27 '12Mike Hansen
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Asked: May 27 '12
Seen: 87 times
Last updated: May 27 '12
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