Hi Cary and John!
On 24 Okt., 04:41, John H Palmieri <[email protected]> wrote:
>...
> sage: R.<g17,g19> = PolynomialRing(QQ)
> sage: R.inject_variables()
Note that inject_variables is not needed, because g17 annd g19 are
defined by the previous line anyway.
> sage: p = (g17^2 - g19^2)/(g17 + g19)
> sage: type(p)
> <type 'sage.rings.fraction_field_element.FractionFieldElement'>
> sage: type(R(p))
> <type
> 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
There is a faster way in this special case.
Elements of the fraction field F of a ring R have methods
"numerator()" and "denominator()" that return elements of R. An
element of F is in R if and only if its denominator is one. For
example:
sage: R.<a,b,c> = ZZ[]
sage: p = R.random_element()
sage: q = p^2/p
sage: q.parent()
Fraction Field of Multivariate Polynomial Ring in a, b, c over Integer
Ring
sage: q.numerator().parent()
Multivariate Polynomial Ring in a, b, c over Integer Ring
sage: q.denominator()
1
The aim is now to return an element of R that is equal to q, if this
happens to be possible. As John said, this can be done by attempting
an explicit conversion, by R(q). But apparently, if the denominator is
one, it can also be done by simply returning the numerator.
The second solution is a lot faster:
sage: timeit('r=R(q)')
625 loops, best of 3: 520 µs per loop
sage: timeit('r=q.numerator() if q.denominator()==1 else R(q)')
625 loops, best of 3: 6.12 µs per loop
sage: p==q==R(q)==q.numerator() # verify that it is correct
True
Note the detail "... else R(q)" above. This is in order to get a
proper error raised, in case that q really does not fit into R.
By the way, I wonder why apparently there is no special case made for
fraction fields in the element constructor of R. Shouldn't there be a
ticket opened?
Best regards,
Simon
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