#6949 closed enhancement (fixed)
add symbolic max and min functions
Reported by: | burcin | Owned by: | burcin |
---|---|---|---|
Priority: | major | Milestone: | sage-4.4.2 |
Component: | symbolics | Keywords: | |
Cc: | jason | Merged in: | sage-4.4.2.alpha0 |
Authors: | Burcin Erocal | Reviewers: | Laurent Fousse |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Matt Riesler wrote on sage-support:
Is it possible to have max behave as you would expect with a symbolic expression, i.e. wait until you evaluate it or restrict the domain to check what is the maximum of the two or more values.
Then kcrisman:
Might there be a way to do something that doesn't conflict with the builtin max function in the same way as the (nearly reviewed) #3587 seems to avoid conflict with the builtin sum function? This would be pretty useful, as currently: sage: var('x,y') (x, y) sage: max(x,y) x sage: f(x)=1+x;g(x)=2-x sage: max(f,g) x |--> x + 1 which last result is... debatable.
Here is a the thread, which has a simple minded implementation for symbolic max:
http://groups.google.com/group/sage-support/browse_thread/thread/aead15de586984d8
We should make sure the symbolic implementations don't slow down the current builtin python max()
and min()
too much. If they do, these functions should still be available under a different name.
Attachments (3)
Change History (14)
comment:1 Changed 12 years ago by
- Report Upstream set to N/A
comment:2 Changed 12 years ago by
- Status changed from new to needs_review
attachment:trac_6949-symbolic_min_max.patch provides basic implementations of max_symbolic()
and min_symbolic()
functions that work as expected when the input contains symbolic expressions.
The symbolic versions are significantly slower than Python's builtin min()
and max()
, so replacing the builtin functions with these is not possible at this point.
Changed 12 years ago by
comment:3 Changed 12 years ago by
- Owner changed from (none) to burcin
I updated attachment:trac_6949-symbolic_min_max.patch to fix a minor doctest error in sage/symbolic/ring.pyx.
comment:4 Changed 12 years ago by
- Cc jason added
comment:5 Changed 12 years ago by
- Status changed from needs_review to needs_work
I applied the patch on top of 4.3.5:
sage: f(x) = max_symbolic(sin(x), cos(x)) sage: f(0) 1 sage: f x |--> max(sin(x), cos(x)) sage: f(1) max(sin(1), cos(1))
So far, so good. But:
sage: N(f(1)) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) /opt/sage-4.3.5/<ipython console> in <module>() /opt/sage-4.3.5/local/lib/python2.6/site-packages/sage/misc/functional.pyc in numerical_approx(x, prec, digits) 1161 prec = int((digits+1) * 3.32192) + 1 1162 try: -> 1163 return x.numerical_approx(prec) 1164 except AttributeError: 1165 from sage.rings.complex_double import is_ComplexDoubleElement /opt/sage-4.3.5/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:17043)() TypeError: cannot evaluate symbolic expression numerically
comment:6 Changed 12 years ago by
- Status changed from needs_work to needs_review
Thanks for the review.
The new patch attachment:trac_6949-symbolic_min_max.take2.patch replaces the previous one, and implements _evalf_()
methods for numeric evaluation. I also created a base class with the common code from __call__()
and _eval_()
methods.
Can you take another look?
comment:7 Changed 12 years ago by
Thanks for the updated patch. I applied it on top of 4.4. I can verify the previously reported problem for numerical evaluation works. I have however a new problem:
sage: f(x) = max_symbolic(sin(x), cos(x)) sage: N(integral(f, x, 0, 1)) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) /opt/sage-4.4/<ipython console> in <module>() /opt/sage-4.4/local/lib/python2.6/site-packages/sage/misc/functional.pyc in numerical_approx(x, prec, digits) 1163 prec = int((digits+1) * 3.32192) + 1 1164 try: -> 1165 return x.numerical_approx(prec) 1166 except AttributeError: 1167 from sage.rings.complex_double import is_ComplexDoubleElement /opt/sage-4.4/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:16928)() /opt/sage-4.4/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._convert (sage/symbolic/expression.cpp:4677)() /opt/sage-4.4/local/lib/python2.6/site-packages/sage/functions/min_max.pyc in _evalf_(self, *args, **kwds) 155 TypeError: cannot evaluate symbolic expression numerically 156 """ --> 157 return max_symbolic(args) 158 159 max_symbolic = MaxSymbolic() /opt/sage-4.4/local/lib/python2.6/site-packages/sage/functions/min_max.pyc in __call__(self, *args, **kwds) 79 return args 80 ---> 81 return BuiltinFunction.__call__(self, *args, **kwds) 82 83 class MaxSymbolic(MinMax_base): /opt/sage-4.4/local/lib/python2.6/site-packages/sage/symbolic/function.so in sage.symbolic.function.Function.__call__ (sage/symbolic/function.cpp:4359)() /opt/sage-4.4/local/lib/python2.6/site-packages/sage/functions/min_max.pyc in _eval_(self, *args) 136 ValueError: number of arguments must be > 0 137 """ --> 138 return self.eval_helper(max_symbolic, builtin_max, None, args) 139 140 def _evalf_(self, *args, **kwds): /opt/sage-4.4/local/lib/python2.6/site-packages/sage/functions/min_max.pyc in eval_helper(self, this_f, builtin_f, initial_val, args) 51 52 symb_args.append(res) ---> 53 return this_f(*symb_args) 54 55 def __call__(self, *args, **kwds): /opt/sage-4.4/local/lib/python2.6/site-packages/sage/functions/min_max.pyc in __call__(self, *args, **kwds) 79 return args 80 ---> 81 return BuiltinFunction.__call__(self, *args, **kwds) 82 83 class MaxSymbolic(MinMax_base): /opt/sage-4.4/local/lib/python2.6/site-packages/sage/symbolic/function.so in sage.symbolic.function.Function.__call__ (sage/symbolic/function.cpp:4192)() TypeError: cannot coerce arguments: no canonical coercion from <type 'NoneType'> to Symbolic Ring
I don't know if the problem is with integrate or max_symbolic.
comment:8 Changed 12 years ago by
Thanks a lot for testing this. I uploaded a new patch in attachment:trac_6949-symbolic_min_max.take3.patch which should cover many corner cases not handled properly before. The aim is to make {max,min}_symbolic()
behave almost identical to the builtin min()
and max()
.
Can you try and break it again? :)
comment:9 Changed 12 years ago by
- Status changed from needs_review to positive_review
Applied on top of 4.4.1 this time. I could not break it with my tests, and I also checked -testall, -coverage etc. as per the patch review guidelines. So that would be a positive review. Thanks!
comment:10 Changed 12 years ago by
- Merged in set to sage-4.4.2.alpha0
- Resolution set to fixed
- Reviewers set to Laurent Fousse
- Status changed from positive_review to closed
comment:11 Changed 10 years ago by
See #13857 for adding this to the reference manual, which somehow never happened but would be worthy considering how many emails we still get about this situation.
see also #8508