Opened 6 years ago
Last modified 6 years ago
#21071 needs_work defect
substitution in denominator is skipped
Reported by:  Daniel Krenn  Owned by:  

Priority:  major  Milestone:  sage7.4 
Component:  symbolics  Keywords:  
Cc:  Travis Scrimshaw, Daniel Krenn  Merged in:  
Authors:  Ralf Stephan  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/rws/substitution_in_denominator_is_skipped (Commits, GitHub, GitLab)  Commit:  5e39b7b65f7f3ae6e778adacf9514f137c930900 
Dependencies:  #22102  Stopgaps: 
Description (last modified by )
The following comes very unexpected
sage: ((1+x^2)/x^2).subs({x^2: 42}) 43/x^2
The problem is the internal representation as
sage: ((1+x^2)/x^2).operands() [x^2 + 1, x^(2)]
Reported upstream as https://github.com/pynac/pynac/issues/186
Change History (17)
comment:1 Changed 6 years ago by
Description:  modified (diff) 

Report Upstream:  N/A → Reported upstream. Developers acknowledge bug. 
Summary:  substitution in denomintor is skipped → substitution in denominator is skipped 
comment:2 Changed 6 years ago by
comment:3 Changed 6 years ago by
Branch:  → u/rws/substitution_in_denominator_is_skipped 

comment:4 Changed 6 years ago by
Authors:  → Ralf Stephan 

Cc:  Travis Scrimshaw Daniel Krenn added 
Commit:  → 67f46511fb82b1c96182c212cb6112bceda240e0 
Milestone:  sage7.3 → sage7.4 
Report Upstream:  Reported upstream. Developers acknowledge bug. → N/A 
Remaining fail, hopefully the author(s) can see where they worked around this bug so that their workaround can be removed:
File "src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py", line 1717, in sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator.? Failed example: asy # long time Expected: (4/3*sqrt(3)*sqrt(r)/sqrt(pi) + 47/216*sqrt(3)/(sqrt(pi)*sqrt(r)), 1, 4/3*sqrt(3)*sqrt(r)/sqrt(pi) + 47/216*sqrt(3)/(sqrt(pi)*sqrt(r))) Got: (4/3*sqrt(3)*sqrt(r)/sqrt(pi) + 587/216*sqrt(3)/(sqrt(pi)*sqrt(r)), 1, 4/3*sqrt(3)*sqrt(r)/sqrt(pi) + 587/216*sqrt(3)/(sqrt(pi)*sqrt(r))) ********************************************************************** File "src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py", line 1720, in sage.rings.asymptotic.asymptotics_multivariate_generating_functions.FractionWithFactoredDenominator.? Failed example: F.relative_error(asy[0], alpha, [1, 2, 4, 8], asy[1]) # long time Expected: [((3, 3, 2), 0.9812164307, [1.515572606], [0.54458543...]), ((6, 6, 4), 1.576181132, [1.992989399], [0.26444185...]), ((12, 12, 8), 2.485286378, [2.712196351], [0.091301338...]), ((24, 24, 16), 3.700576827, [3.760447895], [0.016178847...])] Got: [((3, 3, 2), 0.9812164307, [3.958585166], [3.034364939]), ((6, 6, 4), 1.576181132, [3.720460147], [1.360426775]), ((12, 12, 8), 2.485286378, [3.933702631], [0.5827965202]), ((24, 24, 16), 3.700576827, [4.624183269], [0.2495844526])]
New commits:
67f4651  21071: substitution in denominator is skipped

comment:5 Changed 6 years ago by
Commit:  67f46511fb82b1c96182c212cb6112bceda240e0 → deeea0ac1ab28e246944059bbd576c554a6f4579 

Branch pushed to git repo; I updated commit sha1. New commits:
deeea0a  21071: refine algorithm, fixes fail

comment:6 Changed 6 years ago by
Status:  new → needs_review 

comment:7 Changed 6 years ago by
Commit:  deeea0ac1ab28e246944059bbd576c554a6f4579 → 5e39b7b65f7f3ae6e778adacf9514f137c930900 

Branch pushed to git repo; I updated commit sha1. New commits:
5e39b7b  Merge branch 'develop' into t/21071/substitution_in_denominator_is_skipped

comment:8 Changed 6 years ago by
I'm not completely sure I agree with this:
sage: eq.substitute(a=x, x=1)  x + 1 == sin(1/x) + x + 1 == sin(1)
On the LHS, you simplify x
then a
(or simultaneously where one substitution does not affect the other), whereas on the RHS, you currently do a
, then x
(with the new x
from the a
). So I see this as an inconsistency. IMO, they should be done simultaneously, and the RHS should be sin(1/x)
.
comment:9 Changed 6 years ago by
I agree, but the inconsistency already exists in develop:
sage: sin(x/a).subs({1/x : 1, a : x, x : 1}) sin(1)
(EDIT: simplified)
comment:10 Changed 6 years ago by
However, the following shows that it is not due to sequential application but premature evaluation (x/x > 1
).
sage: sin(x/a).subs({a^1:x^1,x^1:pi}) sin(1)
comment:11 Changed 6 years ago by
Quoting from http://www.ginac.de/reference/basic_8cpp_source.html#l00606, it looks like this is pretty fundamental:
606 ex basic::subs(const exmap & m, unsigned options) const 607 { 608 size_t num = nops(); 609 if (num) { 610 611 // Substitute in subexpressions 612 for (size_t i=0; i<num; i++) { 613 const ex & orig_op = op(i); 614 const ex & subsed_op = orig_op.subs(m, options); 615 if (!are_ex_trivially_equal(orig_op, subsed_op)) { 616 617 // Something changed, clone the object 618 basic *copy = duplicate(); 619 copy>clearflag(status_flags::hash_calculated  status_flags::expanded); 620 621 // Substitute the changed operand 622 copy>let_op(i++) = subsed_op; 623 624 // Substitute the other operands 625 for (; i<num; i++) 626 copy>let_op(i) = op(i).subs(m, options); 627 628 // Perform substitutions on the new object as a whole 629 return copy>subs_one_level(m, options); 630 } 631 } 632 } 633 634 // Nothing changed or no subexpressions 635 return subs_one_level(m, options); 636 }
The problem is that substitutions are done on the subexpressions and *then* on the entire expression. So, we have:
sage: (x/a).subs({a:x,x:1}) 1/x sage: (x/a).subs({a:x,x:1,1/x:17}) 17
I'm pretty sure this is because of line 629. This is not because of premature evaluation (which, as you show, can also be an issue)
comment:12 Changed 6 years ago by
Dependencies:  → #22102 

I would like to solve this outside Pynac via an intermediate substitution step. It would depend on #22102.
comment:13 Changed 6 years ago by
There is an ambiguity. What is the expected result of
sage: f = piecewise([((0,2), x), ([2,0], x)] sage: (x+f).subs(x==1) piecewise(x>1 on (0, 2), x>1 on [2, 0]; x) + 1 or 2?
Plot expects this to be 2
.
comment:14 Changed 6 years ago by
I think subs
should do nothing inside piecewise
and only evaluate if the main variable is substituted. If one wishes to change the piece definition one should use another method that is still to be implemented, like e.g. substitute_piece
. Otherwise I don't see how to untangle this issue.
comment:15 Changed 6 years ago by
Status:  needs_review → needs_work 

comment:16 Changed 6 years ago by
I think what it should do is return the constant function 3 as this would be in line with how subs
works on general functions/expressions:
sage: f(x) = x^2 sage: f.subs(x=2) x > 4 sage: f x > x^2 sage: (f+2).subs(x=2) x > 6 sage: (f(x)+2).subs(x=2) 6
comment:17 Changed 6 years ago by
Substitution in computer algebra systems doesn't tend to be semantically defined. It's an operation on syntax trees. So I think piecewise functions can be treated in two ways:
Either you regard them as "atomic" objects. Then substitution doesn't do anything within them. That's not unreasonable. A piecewise function cannot be evaluated at a symbolic input either ...
Or you regard them as a syntax tree (probably a list of (a,b,expression) tuples or so) and you do a substitution on that (hopefully raising an error when the substitution leads to something illegal).
Note that there is the walkaround of substituting twice, i.e. as given followed by a substitution of the inverse pattern with the inverse replacement, e.g.,
((1+x^2)/(x^2)).subs({x^2: 42}).subs({x^2: 1/42})