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\DOC REAL_POLY_POW_CONV
\TYPE {REAL_POLY_POW_CONV : term -> thm}
\SYNOPSIS
Raise real polynomial to numeral power while retaining canonical form.
\DESCRIBE
For many purposes it is useful to retain polynomials in a canonical form. For
more information on the usual normal form in HOL Light, see the function
{REAL_POLY_CONV}, which converts a polynomial to normal form while proving the
equivalence of the original and normalized forms. The function
{REAL_POLY_POW_CONV} is a more delicate conversion that, given a term
{p1 pow n} where {p} is a real polynomial in normal form and {n} a numeral,
returns a theorem {|- p pow n = p'} where {p'} is in normal form.
\FAILURE
Fails if applied to a term that is not a real term raised to a numeral power.
If the subterm is not a polynomial in normal form, the overall normalization is
not guaranteed.
\EXAMPLE
{
# REAL_POLY_POW_CONV `(x + &1) pow 4`;;
val it : thm =
|- (x + &1) pow 4 = x pow 4 + &4 * x pow 3 + &6 * x pow 2 + &4 * x + &1
}
\USES
More delicate polynomial operations that simply the direct normalization with
{REAL_POLY_CONV}.
\SEEALSO
REAL_ARITH, REAL_POLY_ADD_CONV, REAL_POLY_CONV, REAL_POLY_MUL_CONV,
REAL_POLY_NEG_CONV, REAL_POLY_SUB_CONV, REAL_RING.
\ENDDOC
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