Nice example, Yann.
> Is the following helping?
> sage: var('x a b c d')
> (x, a, b, c, d)
To Vasu: Notice that it's important that x is a symbolic variable
here, not a polynomial indeterminate.
> sage: M=matrix(SR,2,[x^a, x^b, x^c, x^d])
If you tried this with your R.<x> definition, you would get
TypeError: non-integral exponents not supported
instead of this nice answer.
> sage: M
> [x^a x^b]
> [x^c x^d]
> sage: M.det()
> x^d*x^a - x^c*x^b
This is because x^(1/2) makes sense as a symbolic element, but not as
a polynomial thing, and the polynomial ring has no way of knowing that
your a,b,c,d are nonnegative integers. My guess is that "assume()"-
ing that would not be recognized by the polynomial ring either.
- kcrisman
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