Re: question on correct mathematical construct to hold coordinates

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Mon, Jul 21, 2025 at 12:33:53PM -0700, American Citizen wrote:
> Hello all:
> 
> My experiment with trying to use number fields failed to keep accurate
> accounting of rationality, upon rotations of coordinates has failed, most
> likely due to my lack of knowledge of what polynomials are legitimate or not
> for initializing the field. For example nfinit(x^2-1/2) didn't work too well
> for me.

What you can do is:
- multiply (!) all the polynomials you need to take the roots of.
- call nfsplitting on the product to get a polynomila defining a common field.
- for each polynomials call nfisincl to get the roots of the polynomial
  in the common field.

? V=[x^2-1/2,x^2-5/3];
? P=nfsplitting(vecprod(V))
%15 = x^4-16*x^2+49
? R=[Mod(nfisincl(v,P),P)|v<-V]
%16 = [[Mod(-1/14*x^3+9/14*x,x^4-16*x^2+49),Mod(1/14*x^3-9/14*x,x^4-16*x^2+49)],[Mod(-1/3*x^2+8/3,x^4-16*x^2+49),Mod(1/3*x^2-8/3,x^4-16*x^2+49)]]

Cheers,
Bill.