Opened 8 years ago
Closed 7 years ago
#17151 closed enhancement (fixed)
symbolic Laguerre / associated Laguerre polynomials
Reported by:  rws  Owned by:  

Priority:  major  Milestone:  sage6.8 
Component:  symbolics  Keywords:  special, function, holonomic, orthogonal 
Cc:  Merged in:  
Authors:  Ralf Stephan  Reviewers:  Marc Mezzarobba 
Report Upstream:  N/A  Work issues:  
Branch:  f0d809f (Commits, GitHub, GitLab)  Commit:  f0d809ffdc8d1342aabbc12c95bb5d5c15b1648b 
Dependencies:  #17953  Stopgaps: 
Description (last modified by )
Not only is laguerre(n,x)
not symbolic, a naive implementation is already 2x as fast at n=100
and 10x at n=1000
:
R.<x> = PolynomialRing(QQ, 'x') def lag(n): return R([binomial(n,k)*(1)^k/factorial(k) for k in xrange(n+1)])
Change History (36)
comment:1 Changed 8 years ago by
 Description modified (diff)
comment:2 Changed 8 years ago by
 Branch set to u/rws/symbolic_laguerre___associated_laguerre_polynomials
comment:3 Changed 8 years ago by
 Commit set to 1626a8b208a1c2641d05cf8c76d9df86714fb4f0
 Status changed from new to needs_review
comment:4 Changed 8 years ago by
comment:5 Changed 8 years ago by
 Commit changed from 1626a8b208a1c2641d05cf8c76d9df86714fb4f0 to f727de55a3d6ea92be9c70606f57f81795b4c73a
Branch pushed to git repo; I updated commit sha1. New commits:
f727de5  17151: reduce evalf logic further; fix merge conflict

comment:6 Changed 7 years ago by
 Status changed from needs_review to needs_work
For some reason this branch is red.
comment:7 Changed 7 years ago by
 Commit changed from f727de55a3d6ea92be9c70606f57f81795b4c73a to 6d05ac6987afb4423a6978888e5566b9730fa793
Branch pushed to git repo; I updated commit sha1. New commits:
6d05ac6  Merge branch 'develop' into t/17151/symbolic_laguerre___associated_laguerre_polynomials

comment:8 Changed 7 years ago by
 Status changed from needs_work to needs_review
comment:9 Changed 7 years ago by
 Status changed from needs_review to needs_work
sage t long src/sage/symbolic/expression.pyx # 1 doctest failed sage t long src/sage/matrix/matrix2.pyx # 1 doctest failed sage t long src/sage/graphs/bipartite_graph.py # 1 doctest failed
comment:10 Changed 7 years ago by
 Branch changed from u/rws/symbolic_laguerre___associated_laguerre_polynomials to u/rws/17151
comment:11 Changed 7 years ago by
 Commit changed from 6d05ac6987afb4423a6978888e5566b9730fa793 to ea2ff9b11a520edd58b1db527ef41eed6b0e7f85
 Milestone changed from sage6.4 to sage6.6
 Status changed from needs_work to needs_review
comment:12 Changed 7 years ago by
sage: laguerre(9, 2.) 0.000000000000000
sage: laguerre(9, 2).n() 1566.22186244286
comment:13 followup: ↓ 18 Changed 7 years ago by
Are the three separate cases in _pol_laguerre()
necessary? Couldn't one just do something like
R = PolynomialRing(QQ, 'x') pol = R([binomial(n,k)*(1)**k/factorial(k) for k in xrange(n+1)]) return pol(x)
no matter what x
is?
comment:14 followup: ↓ 16 Changed 7 years ago by
sage: gen_laguerre(3, 1, x+1).expand() 1/6*x^3 + 3/2*x^2  5/2*x  1/6 sage: gen_laguerre(0, 1, x+1).expand() ... AttributeError: 'sage.rings.integer.Integer' object has no attribute 'expand'
comment:15 Changed 7 years ago by
 Status changed from needs_review to needs_work
Otherwise looks good to me overall...
comment:16 in reply to: ↑ 14 ; followup: ↓ 17 Changed 7 years ago by
Replying to mmezzarobba:
sage: gen_laguerre(0, 1, x+1).expand() ... AttributeError: 'sage.rings.integer.Integer' object has no attribute 'expand'
Well that is ZZ(1)
and cannot be expanded. I don't think we should return SR(1)
.
comment:17 in reply to: ↑ 16 Changed 7 years ago by
Replying to rws:
Replying to mmezzarobba:
sage: gen_laguerre(0, 1, x+1).expand() ... AttributeError: 'sage.rings.integer.Integer' object has no attribute 'expand'Well that is
ZZ(1)
and cannot be expanded. I don't think we should returnSR(1)
.
Why? Having similar calls to the same function return elements of different parents (or even values of different types) is rarely a good idea... That being said, I don't think we should return SR(1)
in all cases, but perhaps something like pushout(QQ, parent(x))
.
comment:18 in reply to: ↑ 13 ; followups: ↓ 20 ↓ 25 Changed 7 years ago by
Replying to mmezzarobba:
Are the three separate cases in
_pol_laguerre()
necessary? Couldn't one just do something likeR = PolynomialRing(QQ, 'x') pol = R([binomial(n,k)*(1)**k/factorial(k) for k in xrange(n+1)]) return pol(x)no matter what
x
is?
No, because (apart from speed reasons) the R([...]) construction is not available in all parents. However, when investigating this I found that the argument is coerced into SR
by the superclasses BuiltinFunction/Function
, so it must be unwrapped for the real parent. OTOH, for simplicity the branch with sum
would be a catchall. Let's see if going polynomial really is faster and, if not, do only summing for all parents.
comment:19 Changed 7 years ago by
 Commit changed from ea2ff9b11a520edd58b1db527ef41eed6b0e7f85 to 009c0289def83e6e3c2d0911bd44b275cf0d635a
comment:20 in reply to: ↑ 18 ; followup: ↓ 21 Changed 7 years ago by
 Status changed from needs_work to needs_review
Let's see if going polynomial really is faster and, if not, do only summing for all parents.
Here's the catch: Using R(...)
for polynomial creation makes for 5x speedup with L(1000,x)
and 10x with L(1000,x^2+x+1)
if x
is a polynomial generator vs. a symbol. OTOH, summing over monomials is faster with sum
and this is the only way to get a result for other rings.
I don't thing we should return
SR(1)
in all cases, but perhaps something likepushout(QQ, parent(x))
.
There is a problem: even if I return SR(ZZ(1))
, it gets converted back somewhere to Integer(1)
. This will have to be addressed in another ticket.
comment:21 in reply to: ↑ 20 Changed 7 years ago by
 Dependencies set to #17953
There is a problem: even if I return
SR(ZZ(1))
, it gets converted back somewhere toInteger(1)
. This will have to be addressed in another ticket.
See #17953.
comment:22 Changed 7 years ago by
 Branch changed from u/rws/17151 to u/rws/171511
comment:23 Changed 7 years ago by
 Commit changed from 009c0289def83e6e3c2d0911bd44b275cf0d635a to 351b5c69625489c7c12139436b193a3735fd429f
Squashed it all into one commit. Please note I'll rename OrthogonalPolynomial
to OrthogonalFunction
in the other ticket, so I depend on this being merged first. In the end the type problem required a one liner in #17953 and didn't require any forced result conversion to SR
.
New commits:
a99ad55  17151: symbolic Laguerre / associated Laguerre polynomials

f0fe6f4  17953: any symbolic function arg prevents forced result conversion to numeric

351b5c6  Merge branch 'u/rws/inconsistency_in_returned_type_of_builtinfunction_result' of trac.sagemath.org:sage into tmp1

comment:24 Changed 7 years ago by
 Milestone changed from sage6.6 to sage6.7
Passes all patchbot tests.
comment:25 in reply to: ↑ 18 ; followups: ↓ 28 ↓ 34 Changed 7 years ago by
Replying to rws:
Replying to mmezzarobba:
Are the three separate cases in
_pol_laguerre()
necessary? Couldn't one just do something likeR = PolynomialRing(QQ, 'x') pol = R([binomial(n,k)*(1)**k/factorial(k) for k in xrange(n+1)]) return pol(x)no matter what
x
is?No, because (apart from speed reasons) the R([...]) construction is not available in all parents.
I don't understand what you mean, sorry: I just tried the exact code that I suggested, and it works on all examples in the docstring, except that the result comes out in Horner form (which we could perhaps change if nothing else depends on it or somehow get or get around otherwise). What parents do you have in mind?
comment:26 followup: ↓ 29 Changed 7 years ago by
I also don't like that
sage: laguerre(3, polygen(QQ)).parent() Symbolic Ring
while for instance
sage: chebyshev_T(3, polygen(QQ)).parent() Univariate Polynomial Ring in x over Rational Field sage: pow(polygen(QQ), 3).parent() Univariate Polynomial Ring in x over Rational Field
comment:27 Changed 7 years ago by
Not a bug, but would be nice to have: the implementation doesn't seem to know that L(n, 0) = 1 and more generally L(n, α, 0) = binomial(n+α,n).
comment:28 in reply to: ↑ 25 Changed 7 years ago by
 Status changed from needs_review to needs_work
comment:29 in reply to: ↑ 26 Changed 7 years ago by
Replying to mmezzarobba:
I also don't like that
sage: laguerre(3, polygen(QQ)).parent() Symbolic Ring
Equivalently to #16813 this behaviour can only be changed when we have #18832. EDIT: pow
is not a BuiltinFunction
and chebyshev_T
uses its own __call__
which is frowned upon. I would advise to not make this ticket dependent on the feature you suggest but to open a followup ticket.
comment:30 Changed 7 years ago by
 Branch changed from u/rws/171511 to u/rws/171512
comment:31 Changed 7 years ago by
 Commit changed from 351b5c69625489c7c12139436b193a3735fd429f to 6631c77809f8e1025105508232ef2615f363e358
 Milestone changed from sage6.7 to sage6.8
 Status changed from needs_work to needs_review
With the new branch all other comments were addressed.
New commits:
6631c77  17151: symbolic Laguerre / associated Laguerre polynomials

comment:32 Changed 7 years ago by
 Status changed from needs_review to needs_work
needs rebase, does not apply
comment:33 Changed 7 years ago by
 Branch changed from u/rws/171512 to public/ticket/17151
 Commit changed from 6631c77809f8e1025105508232ef2615f363e358 to f0d809ffdc8d1342aabbc12c95bb5d5c15b1648b
 Status changed from needs_work to needs_review
comment:34 in reply to: ↑ 25 Changed 7 years ago by
 Reviewers set to Marc Mezzarobba
 Status changed from needs_review to positive_review
As explained in one of my previous comments, I still don't understand why you don't like the idea of using QQ['x']
to compute the coefficients in _pol_laguerre()
(especially since #18282 has been merged and the problem with symbolic results being computed in Horner form no longer exists). But that's something that can be fixed later and this ticket has languished long enough already.
Thanks for working on it!
comment:35 Changed 7 years ago by
Thanks for the review.
comment:36 Changed 7 years ago by
 Branch changed from public/ticket/17151 to f0d809ffdc8d1342aabbc12c95bb5d5c15b1648b
 Resolution set to fixed
 Status changed from positive_review to closed
New commits:
Simplify numerical evaluation of BuiltinFunctions
Merge remotetracking branches 'origin/u/jdemeyer/ticket/17131' and 'origin/u/jdemeyer/ticket/17133' into ticket/17130
Merge branch 'u/jdemeyer/ticket/17130' of trac.sagemath.org:sage into t/17151/symbolic_laguerre___associated_laguerre_polynomials
17151: skeleton impl.
17151: implement symbolic Laguerre pol.
17151: implement laguerre(n,x)
17151: implement gen_laguerre