Opened 9 years ago
Closed 9 years ago
#6465 closed defect (fixed)
Derivative D acts wrongly on symbolic integration
Reported by: | gmhossain | Owned by: | |
---|---|---|---|
Priority: | critical | Milestone: | sage-4.3.3 |
Component: | symbolics | Keywords: | |
Cc: | Merged in: | sage-4.3.3.alpha1 | |
Authors: | Burcin Erocal, Golam Mortuza Hossain | Reviewers: | Tim Dumol, Karl-Dieter Crisman, Ross Kyprianou, Minh Van Nguyen |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
In new symbolics, derivative operator does not know how to act on symbolic integration.
sage: f(x) = function('f',x) sage: g = integrate(f(x),x) sage: g.diff(x) D[0](integrate)(f(x), x)*D[0](f)(x) + D[1](integrate)(f(x), x)
Patches:
- Both patches should be applied in order (spkg is already included in sage-4.1.1).
Apart from solving this bug it introduces couple of new features (by moving it into new symbolics' SFunction sub-class)
(1) Stricter syntax:
http://groups.google.com/group/sage-devel/browse_thread/thread/3e98841311653d7a
(2) Numerical approximation using .n() method
(3) Updated "integrate?" docstring
(4) Graceful handling of situations where integration is specified w.r.t. an expression
http://groups.google.com/group/sage-devel/browse_thread/thread/cd9f91338635ada9
(4) Behind the scene it provides a framework to hook up easily new integration algorithm written within sage.
Attachments (9)
Change History (31)
Changed 9 years ago by
comment:1 Changed 9 years ago by
attachment:trac_6465-chain_rule.patch adds support for disabling chain rule for symbolic functions. It depends on the new pynac package here:
http://sage.math.washington.edu/home/burcin/pynac/pynac-0.1.8.p2.spkg
comment:2 Changed 9 years ago by
- Description modified (diff)
- Summary changed from Derivative D acts wrongly on symbolic integration to [with patch, needs review] Derivative D acts wrongly on symbolic integration
comment:3 Changed 9 years ago by
There need to be deprecation warnings for things like
sage: integral(sin(x), pi, 2*pi) sage: integral(sin(x)^3
comment:4 Changed 9 years ago by
- Reviewers set to Tim Dumol
- Summary changed from [with patch, needs review] Derivative D acts wrongly on symbolic integration to [with patch, needs work] Derivative D acts wrongly on symbolic integration
The sudden API change probably merits a deprecation warning, as kcrisman said. Also:
Doctest failure:
sage -t -long devel/sage/sage/libs/ginac/decl.pxi [0.1 s] sage -t -long devel/sage/sage/misc/functional.py ********************************************************************** File "/opt/sage-bin/devel/sage-deriv/sage/misc/functional.py", line 412: sage: integral(exp(-x), (x, 1, oo)) Expected: e^(-1) Got: gamma_incomplete(1, 1) ********************************************************************** 1 items had failures: 1 of 15 in __main__.example_25 ***Test Failed*** 1 failures. For whitespace errors, see the file /opt/sage-bin/tmp/.doctest_functional.py [9.3 s]
comment:5 Changed 9 years ago by
That may be due to the Maxima upgrade - has it been patched elsewhere? Just FYI, I'm not certain on this.
comment:6 Changed 9 years ago by
- Report Upstream set to N/A
This patch needs to be rebased on #6816. The doctest failure persists, but gamma_incomplete(1, 1) is equivalent to e^{(-1) anyways. }
comment:7 follow-up: ↓ 8 Changed 9 years ago by
- Milestone set to sage-4.3.1
- Summary changed from [with patch, needs work] Derivative D acts wrongly on symbolic integration to Derivative D acts wrongly on symbolic integration
comment:8 in reply to: ↑ 7 Changed 9 years ago by
The problem with
gamma_incomplete
might be related to/fixed by #7748.
Yes, I think so, as Maxima 5.20.1 now returns this for both integrate(exp(-x),x,1,inf) and integrate(1/%e^{x,x,1,inf). Note that }
sage: gamma_inc(1,1) 0.367...
rather than 1/e at this point, so it really is the symbolic piece, not just having translation from Maxima, that would be important.
comment:9 Changed 9 years ago by
I uploaded new versions of the two old patches, rebased to 4.3.1.rc0, and a referee patch. I consider this ready now, though someone needs to review my changes.
Unfortunately attachment:trac_6465-chain_rule.take2.patch depends on the next version of pynac. I will release that real soon now. :)
The patches should be applied in this order:
- attachment:trac_6465-chain_rule.take2.patch
- attachment:trac_6465-moves-integration-into-sfunction-subclass.take2.patch
- attachment:trac_6465-integral.patch
They probably depend on other tickets. ATM, my queue contains: #7822, #6961, #7876, #7363, #7955, #7957, #7916 related to symbolics.
comment:10 Changed 9 years ago by
- Status changed from needs_work to needs_review
comment:11 Changed 9 years ago by
There is a reject on sage/symbolic/random_tests.py with the last patch.
comment:12 Changed 9 years ago by
See #6559 for the correct order of patches to avoid the reject.
comment:13 Changed 9 years ago by
I've applied every one of Burcin's patches I could find, and get only one type of doctest failure with all of them (when applied in the right order). So so far so good! Unfortunately, I can't review any of them for two reasons - my understanding of C++/Pynac is not reliable enough to do a good job, and there are so many failures until one applies all the patches that it's hard to separate out what's what.
The reason I say that here is that I do get a significant failure, in a few different files, for the _tderivative_ method, though the actual failure occurs as a RuntimeError? in line 216 of sage/misc/derivative.pyx (with no error message, more's the pity). For instance, in line 99 of sage/symbolic/integration/integral.py,
sage: f = function('f'); a,b = var('a,b') sage: h = indefinite_integral(f(x), x) sage: h.diff(x) RuntimeError
I hope this helps track it down.
comment:14 follow-up: ↓ 15 Changed 9 years ago by
Can you download the package file again and install it?
I forgot to include a patch when I first put the release together. I fixed the spkg file once I realized the problem, assuming no one looked at it yet. You must have downloaded in that period.
Sorry for the inconvenience and many thanks for trying these patches out.
comment:15 in reply to: ↑ 14 Changed 9 years ago by
- Reviewers changed from Tim Dumol to Tim Dumol, Karl-Dieter Crisman
- Status changed from needs_review to needs_work
Replying to burcin:
Can you download the package file again and install it?
I forgot to include a patch when I first put the release together. I fixed the spkg file once I realized the problem, assuming no one looked at it yet. You must have downloaded in that period.
I now get
sage: h.diff(x) f(x)
However, I now get some errors after applying all patches up to and including this set. Some should also be marked # optional - requires Internet (the mathematica_free ones). They all seem to be related to some extra keyword being passed to the DeprecatedSFunction constructor.
sage -t "devel/sage/sage/symbolic/integration/integration.py" ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 29: sage: from sage.symbolic.integration.integration import _maxima_integrator Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_1[2]>", line 1, in <module> from sage.symbolic.integration.integration import _maxima_integrator###line 29: sage: from sage.symbolic.integration.integration import _maxima_integrator File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 316, in <module> integral = SymbolicIntegration() File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 152, in __init__ SFunction.__init__(self, "integrate", *args, **kwds) File "function.pyx", line 1059, in sage.symbolic.function.DeprecatedSFunction.__init__ (sage/symbolic/function.cpp:8588) TypeError: __init__() got an unexpected keyword argument 'built_in_function' ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 30: sage: _maxima_integrator(sin(x), x) Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_1[3]>", line 1, in <module> _maxima_integrator(sin(x), x)###line 30: sage: _maxima_integrator(sin(x), x) NameError: name '_maxima_integrator' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 33: sage: _maxima_integrator(f(x), x) Expected: Traceback (most recent call last): ... NotImplementedError: Maxima failed to integrate Got: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_1[5]>", line 1, in <module> _maxima_integrator(f(x), x)###line 33: sage: _maxima_integrator(f(x), x) NameError: name '_maxima_integrator' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 293: sage: from sage.symbolic.integration.integration import integral Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_10[2]>", line 1, in <module> from sage.symbolic.integration.integration import integral###line 293: sage: from sage.symbolic.integration.integration import integral File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 316, in <module> integral = SymbolicIntegration() File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 152, in __init__ SFunction.__init__(self, "integrate", *args, **kwds) File "function.pyx", line 1059, in sage.symbolic.function.DeprecatedSFunction.__init__ (sage/symbolic/function.cpp:8588) TypeError: __init__() got an unexpected keyword argument 'built_in_function' ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 294: sage: _ilatex = integral._print_latex_ Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_10[3]>", line 1, in <module> _ilatex = integral._print_latex_###line 294: sage: _ilatex = integral._print_latex_ AttributeError: 'function' object has no attribute '_print_latex_' ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 298: sage: _ilatex(f(x),x) Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_10[6]>", line 1, in <module> _ilatex(f(x),x)###line 298: sage: _ilatex(f(x),x) NameError: name '_ilatex' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 300: sage: _ilatex(f(x),x,a,b) Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_10[7]>", line 1, in <module> _ilatex(f(x),x,a,b)###line 300: sage: _ilatex(f(x),x,a,b) NameError: name '_ilatex' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 51: sage: from sage.symbolic.integration.integration import _sympy_integrator Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_2[2]>", line 1, in <module> from sage.symbolic.integration.integration import _sympy_integrator###line 51: sage: from sage.symbolic.integration.integration import _sympy_integrator File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 316, in <module> integral = SymbolicIntegration() File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 152, in __init__ SFunction.__init__(self, "integrate", *args, **kwds) File "function.pyx", line 1059, in sage.symbolic.function.DeprecatedSFunction.__init__ (sage/symbolic/function.cpp:8588) TypeError: __init__() got an unexpected keyword argument 'built_in_function' ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 52: sage: _sympy_integrator(sin(x), x) Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_2[3]>", line 1, in <module> _sympy_integrator(sin(x), x)###line 52: sage: _sympy_integrator(sin(x), x) NameError: name '_sympy_integrator' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 55: sage: _sympy_integrator(f(x), x) Expected: Traceback (most recent call last): ... NotImplementedError: Sympy failed to integrate Got: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_2[5]>", line 1, in <module> _sympy_integrator(f(x), x)###line 55: sage: _sympy_integrator(f(x), x) NameError: name '_sympy_integrator' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 76: sage: from sage.symbolic.integration.integration import _mathematica_free_integrator Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_3[2]>", line 1, in <module> from sage.symbolic.integration.integration import _mathematica_free_integrator###line 76: sage: from sage.symbolic.integration.integration import _mathematica_free_integrator File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 316, in <module> integral = SymbolicIntegration() File "/Users/.../sage-4.3.1/local/lib/python/site-packages/sage/symbolic/integration/integration.py", line 152, in __init__ SFunction.__init__(self, "integrate", *args, **kwds) File "function.pyx", line 1059, in sage.symbolic.function.DeprecatedSFunction.__init__ (sage/symbolic/function.cpp:8588) TypeError: __init__() got an unexpected keyword argument 'built_in_function' ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 77: sage: _mathematica_free_integrator(sin(x), x) Exception raised: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_3[3]>", line 1, in <module> _mathematica_free_integrator(sin(x), x)###line 77: sage: _mathematica_free_integrator(sin(x), x) NameError: name '_mathematica_free_integrator' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 80: sage: _mathematica_free_integrator(f(x), x) Expected: Traceback (most recent call last): ... NotImplementedError: mathematica_free failed to integrate Got: Traceback (most recent call last): File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/Users/.../sage-4.3.1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_3[5]>", line 1, in <module> _mathematica_free_integrator(f(x), x)###line 80: sage: _mathematica_free_integrator(f(x), x) NameError: name '_mathematica_free_integrator' is not defined ********************************************************************** File "/Users/.../sage-4.3.1/devel/sage/sage/symbolic/integration/integration.py", line 241: sage: h.n() Expected: 0.472399177268953 Got: 0.47239917726895253 ********************************************************************** 5 items had failures: 3 of 6 in __main__.example_1 4 of 9 in __main__.example_10 3 of 6 in __main__.example_2 3 of 6 in __main__.example_3 1 of 4 in __main__.example_8 ***Test Failed*** 14 failures. [6.5 s]
Sorry for the inconvenience and many thanks for trying these patches out.
No problem. Although I strongly disagree with the removal of indefinite integration longterm without explicit variable, overall this set of changes will be a big improvement. I am sorry again I cannot review much of the C++ related stuff, or the Pynac changes, though I am glad they are now up on [|pynac.sagemath.org] !
comment:16 Changed 9 years ago by
- Status changed from needs_work to needs_review
attachment:trac_6465-integral.patch renames the file sage/symbolic/integration/integration.py
to sage/symbolic/integration/integral.py
. Are you sure you applied the patches correctly? Since these are git style diffs using hg import
or hg qimport
is recommended.
I applied the whole batch of symbolics patches associated to pynac-0.11 to 4.3.2.alpha0, and tested the sage/{symbolic,calculus,functions} directories. The only doctest failure I got was in sage/symbolic/integration/external.py
. attachment:trac_6465-integral.take2.patch removes this dubious test.
The patches that need to be applied from this ticket are now:
comment:17 Changed 9 years ago by
After testing on a 32-bit Debian box, I uploaded attachment:trac_6465-integral.take3.patch to replace attachment:trac_6465-integral.take2.patch. The only difference is the ...
used for the trailing digits of the numerical integral on line 188 of sage/symbolic/integration/integral.py
.
The patches that need to be applied are:
comment:18 Changed 9 years ago by
Oops, the last patch to be applied is attachment:trac_6465-integral.take3.patch! That was a typo in the list above.
comment:19 Changed 9 years ago by
I rebased the patches to 4.3.2. Patches to be applied are now:
comment:20 Changed 9 years ago by
- Reviewers changed from Tim Dumol, Karl-Dieter Crisman to Tim Dumol, Karl-Dieter Crisman, Ross Kyprianou
The patch solves the stated problem without loss of functionality (at least in the tests below). +1 for positive review.
sage: f(x) = function('f',x) sage: g = integrate(f(x),x) sage: g.diff(x) f(x) sage: integrate(f(x),x).diff(x) f(x) sage: h(x,y) = function('h',x,y) sage: kx = integrate(h(x,y),x) sage: kx integrate(h(x, y), x) sage: kx.diff(x) h(x, y) sage: kxy = integrate( integrate(h(x,y),x), y) sage: kxy integrate(integrate(h(x, y), x), y) sage: kxy.diff(y).diff(x) h(x, y) sage: kxy.diff(x).diff(y) h(x, y) sage: kxy.diff(x) integrate(h(x, y), y) sage: integrate(1/(2*x+1)^2, x, 0, 1) 1/3 sage: loads(dumps(integrate(1/(2*x+1)^2, x, 0, 1))) == 1/3 True sage: integrate(1/(2*x+1)^2, x, 0.0, 1.0) 0.333333333333 sage: integrate(1/(2*x+1)^2, x, 0, 1.0) 0.333333333333 sage: integrate(1/(2*x+1)^2, x, CC(0), 1.0) 0.333333333333 sage: integrate(x/(1+x^2),x) 1/2*log(x^2 + 1) sage: integrate(tan(x),x) log(sec(x))
There is one issue (that is not necessarily a part of this ticket). I may be wrong but I'm reasonably sure that in general that integrate( integrate(h(x,y),x), y).diff(y).diff(x) <> integrate( integrate(h(x,y),x), y).diff(x).diff(y) But the following seems to imply it is (both are equal to h(x, y) )
sage: kxy = integrate( integrate(h(x,y),x), y) sage: kxy integrate(integrate(h(x, y), x), y) sage: kxy.diff(y).diff(x) h(x, y) sage: kxy.diff(x).diff(y) h(x, y)
comment:21 Changed 9 years ago by
- Reviewers changed from Tim Dumol, Karl-Dieter Crisman, Ross Kyprianou to Tim Dumol, Karl-Dieter Crisman, Ross Kyprianou, Minh Van Nguyen
- Status changed from needs_review to positive_review
The rebase looks good. See #6961 for the order in which to apply patches.
comment:22 Changed 9 years ago by
- Merged in set to sage-4.3.3.alpha1
- Resolution set to fixed
- Status changed from positive_review to closed
support disabling chain rule for symbolic functions