Opened 4 years ago
Last modified 22 months ago
#18396 new enhancement
Handle substitutions of partial sums and products
Reported by: | vdelecroix | Owned by: | |
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Priority: | major | Milestone: | sage-6.7 |
Component: | symbolics | Keywords: | |
Cc: | mjo, mmezzarobba | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Sage is not able to identify partial sum in a substitution
sage: var('x,y') sage: f = x + x^2 + x^4 sage: f.subs(x^2 == y) # one term is fine x^4 + x + y sage: f.subs(x + x^2 == y) # partial sum does not work x^4 + x^2 + x sage: f.subs(x + x^2 + x^4 == y) # whole sum is fine y
Similarly with products
sage: f = x * cos(x) * sin(x) sage: f.subs( cos(x) * sin(x) == y) x*cos(x)*sin(x)
As mentioned in the doc, this is the same behavior as in Maple but differ from Mathematica. We should be clearer on the semantic of substitute
and potentially implement partial sum and product substitutions.
See also #10049 and http://ask.sagemath.org/question/25972/substitute-xy-by-u/ (with related ticket #17879)
Change History (6)
comment:1 Changed 4 years ago by
- Description modified (diff)
comment:2 follow-up: ↓ 3 Changed 4 years ago by
comment:3 in reply to: ↑ 2 Changed 4 years ago by
Replying to nbruin:
I'm not so sure we have to do more than document it. Obviously you cannot expect substitutions to happen on any "equal" subexpression, since that concept isn't well-defined.
I do not want to substitute "equal" subexpression but only identical ones. And doing so, I want to consider 'a+c' as a unit of 'a+b+c+d' and 'a*c' as a unit in 'a*b*c*d'. This is perhaps not desirable though.
The thing is:
x+x^2
isn't a syntactical subunit ofx + x^2 + x^4
for the internal representation, which is roughly('+',x,('^',x,2))
versus('+',x,('^',x,2),('^',x,4))
I know, and this is precisely the purpose of the ticket.
You'll have to decide how much tricks are worthwhile to implement before you just add the relation
y-(x^2+x)
and ask for elimination of x via groebner bases.
Note that x + y - (u + v)
does not exist. But I agree that there is an ambiguous +/-
issue (as far as the ticket description is concerned).
comment:4 Changed 4 years ago by
- Description modified (diff)
comment:5 Changed 22 months ago by
However, even the whole matching
does not work consistently. See https://github.com/pynac/pynac/issues/269
comment:6 Changed 22 months ago by
- Description modified (diff)
I'm not so sure we have to do more than document it. Obviously you cannot expect substitutions to happen on any "equal" subexpression, since that concept isn't well-defined.
The thing is:
x+x^2
isn't a syntactical subunit ofx + x^2 + x^4
for the internal representation, which is roughly('+',x,('^',x,2))
versus('+',x,('^',x,2),('^',x,4))
You'll have to decide how much tricks are worthwhile to implement before you just add the relation
y-(x^2+x)
and ask for elimination of x via groebner bases.