#14496: unify the three implementations of gaussian q-binomial coefficients
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Reporter: chapoton | Owner: tbd
Type: task | Status: new
Priority: major | Milestone: sage-5.10
Component: PLEASE CHANGE | Keywords: gaussian binomial
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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In sage 5.8, one can find the gaussian q-binomial coefficients in (at
least) '''three''' places :
- sage.combinat.sf.kfpoly.q_bin
- sage.combinat.q_analogues.q_binomial
- sage.rings.arith.gaussian_binomial
The syntax is not quite the same for q_bin as for the two others.
Some timings:
{{{
sage: timeit("sage.combinat.sf.kfpoly.q_bin(7,5)")
625 loops, best of 3: 819 µs per loop
sage: timeit("sage.combinat.q_analogues.q_binomial(12,5)")
625 loops, best of 3: 1.12 ms per loop
sage: timeit("sage.rings.arith.gaussian_binomial(12,5)")
625 loops, best of 3: 294 µs per loop
}}}
The parents :
{{{
sage: sage.combinat.sf.kfpoly.q_bin(7,5).parent()
Fraction Field of Univariate Polynomial Ring in t over Integer Ring
sage: sage.combinat.q_analogues.q_binomial(12,5).parent()
Univariate Polynomial Ring in q over Integer Ring
sage: sage.rings.arith.gaussian_binomial(12,5).parent()
Fraction Field of Univariate Polynomial Ring in q over Integer Ring
}}}
The behaviour with an added integer parameter
{{{
sage: sage.combinat.sf.kfpoly.q_bin(7,5,2)
114429029715
sage: sage.combinat.q_analogues.q_binomial(12,5,2)
DOES NOT WORK
sage: sage.rings.arith.gaussian_binomial(12,5,2)
114429029715
}}}
The behaviour with a polynomial parameter
{{{
sage: w=polygen(ZZ,'w')
sage: sage.combinat.sf.kfpoly.q_bin(4,2,w)
w^8 + w^7 + 2*w^6 + 2*w^5 + 3*w^4 + 2*w^3 + 2*w^2 + w + 1
sage: sage.combinat.q_analogues.q_binomial(6,2,w)
w^8 + w^7 + 2*w^6 + 2*w^5 + 3*w^4 + 2*w^3 + 2*w^2 + w + 1
sage: sage.rings.arith.gaussian_binomial(6,2,w)
w^8 + w^7 + 2*w^6 + 2*w^5 + 3*w^4 + 2*w^3 + 2*w^2 + w + 1
sage: sage.combinat.sf.kfpoly.q_bin(4,2,w).parent()
Univariate Polynomial Ring in w over Integer Ring
sage: sage.combinat.q_analogues.q_binomial(6,2,w).parent()
Univariate Polynomial Ring in w over Integer Ring
sage: sage.rings.arith.gaussian_binomial(6,2,w).parent()
Fraction Field of Univariate Polynomial Ring in w over Integer Ring
}}}
Maybe it would be better to have a single function ?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14496>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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