> >  > 1. There is no way to get a symbolic interpolated polynomial de novo
> >  > without going through polynomial rings, e.g. all these steps:
> >  >
> >  > pts = [(1,2),(2,3),(3,2),(4,3),(5,2),(6,3)]
> >  > R.<x>=QQ[]
> >  > f = R.lagrange_polynomial(pts)
> >  > SR(f)
> >  >

Everything you're doing above can be "functionalized", so you need
only one line:
   SR(QQ['x'].lagrange_polynomial([ ... ])
Of course, usually, you would have or would like the points in a
variable anyway. I think the above is pretty short given the
specificity of what you're doing. I often use the "implicit"
construction of the polynomial ring in some function call as above.

- Johan

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