Opened 11 years ago

Last modified 6 years ago

#9424 closed defect

FP evaluation of symbolic sums fails — at Version 14

Reported by: burcin Owned by: burcin
Priority: major Milestone: sage-6.8
Component: symbolics Keywords:
Cc: whuss, kcrisman, eviatarbach Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by rws)

Symbolics sums returned from maxima cannot be numerically evaluated, since they don't define an _evalf_() method.

This was reported by dirkd on sage-support:

Why is evaluating this expression problematical?

y1(x)=x^2;y2(x)=5-x;
a0=1;an=3;Delta=(an-a0)/n;p(k)=a0+(k-1/2)*Delta;
I(n)=sum(abs(y2(p(k))-y1(p(k)))*Delta,k,1,n);
N(I(10))

SAGE respons:
<snipped traceback>
  File "expression.pyx", line 3797, in
sage.symbolic.expression.Expression.n (sage/symbolic/expression.cpp:
17022)
TypeError: cannot evaluate symbolic expression numerically

Here is the thread:

http://groups.google.com/group/sage-support/t/615b15ca638c9652

See also #15346

Change History (14)

comment:1 Changed 11 years ago by whuss

  • Cc whuss added

comment:2 Changed 11 years ago by kcrisman

  • Cc kcrisman added

comment:3 Changed 9 years ago by eviatarbach

  • Cc eviatarbach added

comment:4 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:5 Changed 8 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:6 Changed 8 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:7 Changed 7 years ago by rws

  • Milestone changed from sage-6.3 to sage-duplicate/invalid/wontfix
  • Status changed from new to needs_review

Your problem is threefold: 1. you use n both as sum endpoint and variable, 2. Sage sum is only intended with symbolic endpoints, and 3. the need to use Python summation may require defining a Python function instead of a Sage symbolic function:

sage: sum?
...
Warning: This function only works with symbolic expressions. To sum any
     other objects like list elements or function return values,
     please use python summation...

sage: I(n)=sum(abs(y2(p(k))-y1(p(k)))*Delta,k,1,n);
sage: I
n |--> 2*sum(abs(-4*k^2 - 3*(2*k - 1)*n + 3*n^2 + 4*k - 1), k, 1, n)/n^3

sage: def I(n):
....:     return (2*sum(abs(-4*k^2 - 3*(2*k - 1)*n + 3*n^2 + 4*k - 1) for k in range(1,n+1))/n^3)
....: 
sage: I(10)
1301/250
sage: [I(i) for i in range(1,11)]
[2, 5, 46/9, 5, 26/5, 277/54, 254/49, 665/128, 418/81, 1301/250]

comment:8 Changed 7 years ago by kcrisman

  • Milestone changed from sage-duplicate/invalid/wontfix to sage-6.3
  • Type changed from defect to enhancement

I don't think any of these invalidate the ticket; the point is to extend the behavior. Why is 1. a problem? This seems like it should be a nice function to me. See Burcin's reply in the thread:

> If I leave out the N( )-operator on the last line the block evaluates
> to
> 
> 
> 1/500*sum(abs(-4*k^2 - 56*k + 329), k, 1, 10)
> 
> which can be evaluated in a new inputbox. Why not in one step?
The result returned from maxima uses a symbolic function object created
on the fly. This is quite different from the sum() function
available on the command line, and unfortunately, it doesn't define a
numerical evaluation function, _evalf_().

Burcin knows this code very well, so I would be surprised if he misdiagnosed this. But I figure maybe changing to enhancement will appease everyone :)

comment:9 Changed 7 years ago by nbruin

Burcin is spot-on:

sage: S=(I(10).operands()[0].operator()); S
sum
sage: type(S)
<class 'sage.symbolic.function_factory.NewSymbolicFunction'>

(Note the "New", not "BuiltIn?" or similar. It's a completely generic placeholder) we just need a symbolic function hooked up that can do some mildly intelligent evaluation when asked for it.

Incidentally, we can just map back to maxima and do the right thing there:

sage: maxima_calculus(I(10))
('sum(abs(4*_SAGE_VAR_k^2+56*_SAGE_VAR_k-329),_SAGE_VAR_k,1,10))/500
sage: SR(maxima_calculus(I(10)).simplify_sum())
1301/250

(I haven't checked if it's correct). You can see why the "simplify_sum" is required: the newly created "sum" function in SR is linked to the inert "'sum".

comment:10 Changed 7 years ago by rws

  • Status changed from needs_review to needs_work

comment:11 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:12 follow-up: Changed 7 years ago by kcrisman

A relevant ask.sagemath question.

Another one.

Maybe it's time we fixed this.

comment:13 in reply to: ↑ 12 Changed 7 years ago by rws

  • Description modified (diff)
  • Summary changed from numerical evaluation of symbolic sums to FP evaluation of symbolic sums fails

Replying to kcrisman:

Maybe it's time we fixed this.

It is not clear if forcing people to use N() and getting a float, even if there is an integer simplification of the sum, is the right thing to do. Granted, the error thrown on N(I(10)) is a bug, and this ticket is about it. Here is a minimal example:

sage: (k,n) = var('k,n')
sage: f(n)=sum(abs(-k*k+n),k,1,n)
sage: f(n=8)
sum(abs(-k^2 + 8), k, 1, 8)
sage: N(f(8))

However, I would expect f(n=8).simplify() or .expand() to give me the result 162, and this is #17422

comment:14 Changed 7 years ago by rws

  • Description modified (diff)
  • Type changed from enhancement to defect
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