Opened 11 years ago
Closed 11 years ago
#6636 closed enhancement (fixed)
[with patch, positive review] Simplification of factorials and binomial coefficients is not very good
Reported by: | jbandlow | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-4.1.2 |
Component: | symbolics | Keywords: | symbolics, factorials, binomial coefficients |
Cc: | jbandlow, burcin, mhansen | Merged in: | Sage 4.1.2.alpha2 |
Authors: | Karl-Dieter Crisman | Reviewers: | Mike Hansen |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Maple can simplify all but the first of the following examples:
%maple print(simplify(binomial(n,2)+binomial(n+1,2))); print(simplify(factorial(n)/factorial(n-2)/2 + factorial(n+1)/factorial(n-1)/2)); print(simplify(factorial(n+1)/factorial(n))); print(simplify(binomial(n,k)*factorial(k)*factorial(n-k)));
returns
binomial(n,2)+binomial(n+1,2) n^2 n+1 n!
Sage can simplify only the first:
var('n,k') print (binomial(n,2) + binomial(n+1,2)).simplify_full() print (factorial(n)/factorial(n-2)/2 + factorial(n+1)/factorial(n)/2).simplify_full() print (factorial(n+1)/factorial(n)).simplify_full() print (binomial(n,k)*factorial(k)*factorial(n-k)).simplify_full()
returns
n^2 1/2*(factorial(n - 2)*factorial(n + 1) + factorial(n)^2)/(factorial(n - 2)*factorial(n)) factorial(n + 1)/factorial(n) Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/jason/.sage/sage_notebook/worksheets/admin/10/code/49.py", line 11, in <module> exec compile(ur'print (binomial(n,k)*factorial(k)*factorial(n-k)).simplify_full()' + '\n', '', 'single') File "", line 1, in <module> File "expression.pyx", line 4837, in sage.symbolic.expression.Expression.simplify_full (sage/symbolic/expression.cpp:19979) File "expression.pyx", line 4864, in sage.symbolic.expression.Expression.simplify_trig (sage/symbolic/expression.cpp:20076) File "expression.pyx", line 418, in sage.symbolic.expression.Expression._maxima_ (sage/symbolic/expression.cpp:3415) File "sage_object.pyx", line 364, in sage.structure.sage_object.SageObject._interface_ (sage/structure/sage_object.c:3384) File "sage_object.pyx", line 451, in sage.structure.sage_object.SageObject._maxima_init_ (sage/structure/sage_object.c:5065) File "expression.pyx", line 443, in sage.symbolic.expression.Expression._interface_init_ (sage/symbolic/expression.cpp:3544) File "/home/jason/sage-4.0/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__ return self.arithmetic(ex, operator) File "/home/jason/sage-4.0/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 497, in arithmetic args = ["(%s)"%self(op) for op in ex.operands()] File "/home/jason/sage-4.0/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 206, in __call__ operator = ex.operator() File "expression.pyx", line 3088, in sage.symbolic.expression.Expression.operator (sage/symbolic/expression.cpp:15127) RuntimeError: cannot find SFunction in table
Attachments (1)
Change History (9)
comment:1 Changed 11 years ago by
- Cc burcin added
comment:2 Changed 11 years ago by
comment:3 Changed 11 years ago by
- Summary changed from Simplification of factorials and binomial coefficients is not very good to [with patch, needs review] Simplification of factorials and binomial coefficients is not very good
The following patch should fix all of the issues on this ticket - Maxima has quite a bit of simplifying capability, but prefers to leave things unsimplified for further processing, as a rule. See examples for what now works. I have also changed simplify_full() to take this in, and hope that simplification of binomials and factorials first is best. This needs the patch at #6197 to function properly, since otherwise binomial isn't recognized by sage as something it can pass to Maxima.
comment:4 Changed 11 years ago by
- Cc mhansen added
This has been slightly changed because the doctest fix here actually belonged in #6197. Otherwise still ready for review!
comment:5 follow-up: ↓ 6 Changed 11 years ago by
- Reviewers set to Mike Hansen
- Summary changed from [with patch, needs review] Simplification of factorials and binomial coefficients is not very good to [with patch, positive review] Simplification of factorials and binomial coefficients is not very good
Looks good to me.
We might want to improve simplify_full so that we don't have 4 round trips to Maxima (convert to maxima, run all of the simplification commands on the MaximaElement?, and then finally convert back to an Expression.)
comment:6 in reply to: ↑ 5 Changed 11 years ago by
We might want to improve simplify_full so that we don't have 4 round trips to Maxima (convert to maxima, run all of the simplification commands on the MaximaElement?, and then finally convert back to an Expression.)
That makes a lot of sense. Once this is merged, do you mind opening a ticket on that?
comment:7 Changed 11 years ago by
Sure thing.
comment:8 Changed 11 years ago by
- Merged in set to Sage 4.1.2.alpha2
- Resolution set to fixed
- Status changed from new to closed
A related discussion on sage-devel is http://groups.google.com/group/sage-devel/browse_thread/thread/58db110fc55b11e5.
The lack of simplification is a bug, or at least very poorly exposed functionality, in Maxima. One would think that simplify would include this... but instead one needs to expose Maxima's *minfactorial*:
This should not be hard to add to simplify_full, though.
Also note that the last issue is addressed by #6197.