Comment #11 on issue 2895 by [email protected]: minpoly hangs on this
expresion
http://code.google.com/p/sympy/issues/detail?id=2895
Every algebraic number has a minimal polynomial (algebraic number is
defined as a root of a polynomial with rational coefficients). Algebraic
numbers form a field, so sums, products, and integer powers of algebraic
numbers are again algebraic. Rational powers will work as well, since one
could just raise the power of each term in the polynomial that the base
expression satisfies by the denominator (e.g., sqrt(2) + sqrt(3) satisfies
x**4 - 10*x**2 + 1, so sqrt(sqrt(2) + sqrt(3)) satisfies x**8 - 10*x**4 + 1.
And note the distinction between satisfying a polynomial and that
polynomial being the minimal polynomial. Every algebraic number satisfies
many polynomials, but only one monic polynomial of minimal degree. That
minimal polynomial will divide every other polynomial that the number
satisfies, so finding it is just a matter of searching the irreducible
factors.
--
You received this message because this project is configured to send all
issue notifications to this address.
You may adjust your notification preferences at:
https://code.google.com/hosting/settings
--
You received this message because you are subscribed to the Google Groups
"sympy-issues" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sympy-issues?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
