simplify_full returns odd result from symbolic series input #17400

rwst · 2014-11-26T10:08:06Z

SR.series will lose the order term when passed to Maxima. Thus only the coefficients may be simplified, and this must be done in all simplify* functions.

sage: x=var('x')
sage: s=(1/(1-x)).series(x,6)
sage: s.coeffs()
[[x^5 + x^4 + x^3 + x^2 + x + Order(x^6) + 1, 0]]
sage: s.simplify_full().coeffs()
[[Order(x^6) + 1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [1, 5]]

See also the related #17399.

Originally found in http://ask.sagemath.org/question/24968/coefficients-in-polynomial-ring-over-symbolic-ring/

Also, series should simplify its terms on a per-term basis:

sage: var('x,y')
(x, y)
sage: ex=1/(1-x*y-x^2)
sage: ex.series(x,5)
1 + (y)*x + (y^2 + 1)*x^2 + ((y^2 + 1)*y + y)*x^3 + (((y^2 + 1)*y + y)*y + y^2 + 1)*x^4 + Order(x^5)

Compare with e.g. Pari:

? 1/(1-x*y-x^2) + O(x^5)
%1 = 1 + y*x + (y^2 + 1)*x^2 + (y^3 + 2*y)*x^3 + (y^4 + 3*y^2 + 1)*x^4 + O(x^5)

Both issues can be fixed by writing series simplification methods.

Depends on #17399
Depends on #17659

Component: symbolics

Author: Ralf Stephan

Branch/Commit: u/rws/17400-1 @ 22c947a

Issue created by migration from https://trac.sagemath.org/ticket/17400

The text was updated successfully, but these errors were encountered:

rwst · 2014-12-04T14:44:49Z

comment:3

Probably with symbolic series, only coefficients should be simplified in the simplify* functions.

rwst · 2015-01-13T16:52:53Z

comment:4

There are no power series objects in Maxima, just conversion to infinite sums, i.e. formal power series:

sage: maxima.powerseries(x^2+1/(1-x),x,0)
'sum(_SAGE_VAR_x^i2,i2,0,inf)+_SAGE_VAR_x^2
sage: maxima.powerseries(x^2+1/(1-x),x,0).sage()
x^2 + sum(x^i3, i3, 0, +Infinity)

The Taylor series objects have an order parameter on creation, but this does not get output or translated to Sage:

sage: maxima.taylor(1+x+x^2+x^3,x,0,3)
1+_SAGE_VAR_x+_SAGE_VAR_x^2+_SAGE_VAR_x^3
sage: maxima.taylor(1+x+x^2+x^3,x,0,3).sage()
x^3 + x^2 + x + 1

so there is no way around it that SR.series will lose the order term when passed to Maxima. Thus only the coefficients may be simplified, and this must be done in or called from all simplify* functions.

rwst · 2015-01-13T17:08:11Z

comment:5

The following functions call Maxima, have a meaning /wrt series, and therefore need to be modified:
simplify, simplify_trig, simplify_rectform, simplify_rational, simplify_log, expand_log, expand_trig.

rwst · 2015-01-23T17:37:30Z

Branch: u/rws/simplify_full_returns_odd_result_from_symbolic_series_input

rwst · 2015-01-23T17:39:20Z

Commit: 2660235

rwst · 2015-01-23T17:39:20Z

comment:8

Proof of concept.

New commits:

`a4d2084`	`17659: make symbolic series subclass of Expression`
`ed003f0`	`16203: make imports more specific to prevent import loops`
`32ae67c`	`17399: do not let maxima handle ex.series coefficients`
`99820cf`	`17399: roll back previous commit to allow merge of 17428`
`168b659`	`Merge branch 'u/rws/coefficients_of_symbolic_expressions_revamp' of trac.sagemath.org:sage into t/17399/fix_coefficients_for_symbolic_series`
`6cd5286`	`17399: handle series in ex.coefficients()`
`0b9914f`	`17399: remove whitespace changes`
`2e74911`	`Merge commit '0b9914f8b6cd4cb0f885f0550bfd375d80495a71' of trac.sagemath.org:sage into t/17400/simplify_full_returns_odd_result_from_symbolic_series_input`
`2660235`	`17400: implement series.simplify_full()`

rwst · 2015-01-23T17:39:20Z

Dependencies: #17399, #17659

rwst · 2015-01-25T15:40:52Z

Changed branch from u/rws/simplify_full_returns_odd_result_from_symbolic_series_input to public/17400

rwst · 2015-01-25T15:42:15Z

Changed commit from 2660235 to 2643553

rwst · 2015-01-25T15:42:15Z

comment:10

Squashed it all into one commit.

New commits:

`2643553`	`17400: merge 17659, add simplify/expand methods for SymbolicSeries`

rwst · 2015-01-25T15:42:15Z

Author: Ralf Stephan

rwst · 2015-03-05T14:23:25Z

Changed branch from public/17400 to u/rws/17400

rwst · 2015-03-05T14:24:06Z

comment:12

Squashed it all into one commit.

New commits:

`73cd5bf`	`17400: symbolic series simplification methods`

rwst · 2015-03-05T14:24:06Z

Changed commit from 2643553 to 73cd5bf

rwst · 2015-04-20T15:50:15Z

comment:13

Pending because #17659 is pending.

rwst · 2016-02-05T07:53:28Z

Changed branch from u/rws/17400 to u/rws/17400-1

vbraun · 2016-02-23T22:39:19Z

comment:15

Still pending?

New commits:

`611f93b`	`Merge branch 'u/rws/17400' of trac.sagemath.org:sage into tmp05`

vbraun · 2016-02-23T22:39:19Z

Changed commit from 73cd5bf to 611f93b

rwst · 2016-02-24T06:17:14Z

comment:16

No, you're right. Maybe there are conflicts with #17402.

vbraun · 2016-03-05T22:58:34Z

comment:17

Merge conflict, possibly with #20088

nbruin · 2016-03-06T05:37:00Z

comment:18

Replying to @rwst:

There are no power series objects in Maxima,
[...]
The Taylor series objects have an order parameter on creation, but this does not get output or translated to Sage

So there are power series-type object in maxima. We could just access those then and use them to translate back-and-forth. It's a bit of a question how much functionality maxima has for it and whether maxima itself works with them faithfully.

The internal representation seems to be a bit complicated:

sage: P=maxima_calculus.taylor(exp(x),x,0,5)
sage: P
1+_SAGE_VAR_x+_SAGE_VAR_x^2/2+_SAGE_VAR_x^3/6+_SAGE_VAR_x^4/24+_SAGE_VAR_x^5/120
sage: P.ecl()
<ECL: ((MRAT SIMP (((MEXPT SIMP) $%E |$_SAGE_VAR_x|) |$_SAGE_VAR_x|)
  (#:|%e^_SAGE_VAR_x2396| #:|_SAGE_VAR_x2397|)
  ((|$_SAGE_VAR_x| ((5 . 1)) 0 NIL #:|_SAGE_VAR_x2397| . 2)) TRUNC)
 PS (#:|_SAGE_VAR_x2397| . 2) ((5 . 1)) ((0 . 1) 1 . 1) ((1 . 1) 1 . 1)
 ((2 . 1) 1 . 2) ((3 . 1) 1 . 6) ((4 . 1) 1 . 24) ((5 . 1) 1 . 120))>

but fundamentally everything is there to create/peel apart these objects.

(note that it would be a bit harder to work with these objects via the expect-interface to maxima)

A basic explanation of the MRAT format is here: http://def.fe.up.pt/pipermail/maxima-discuss/2005/010416.html

EDIT: never mind, this isn't suitable for power series. This whole "TRUNC" property is very fickle (and it doesn't carry proper order information). It disappears with very trivial arithmetic already.

sagetrac-git · 2016-08-03T13:14:08Z

Changed commit from 611f93b to e3907ec

sagetrac-git · 2016-08-03T13:14:08Z

Branch pushed to git repo; I updated commit sha1. New commits:

`e3907ec`	`Merge branch 'develop' into t/17400/17400-1`

sagetrac-git · 2016-09-22T07:02:55Z

Branch pushed to git repo; I updated commit sha1. New commits:

`895d900`	`Merge branch 'develop' into t/17400/17400-1`
`22c947a`	`17400: adapt doctest to changed simplify behaviour`

sagetrac-git · 2016-09-22T07:02:55Z

Changed commit from e3907ec to 22c947a

rwst · 2017-11-28T07:03:54Z

comment:22

Two doctests failing, see patchbot.

Fixes #20846 (but not the related #17400). URL: #35001 Reported by: Marc Mezzarobba Reviewer(s): Frédéric Chapoton

rwst added this to the sage-6.5 milestone Nov 26, 2014

rwst added c: symbolics labels Nov 26, 2014

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rwst modified the milestones: sage-6.5, sage-6.6 Mar 5, 2015

rwst removed this from the sage-6.6 milestone Apr 20, 2015

rwst added the pending label Apr 20, 2015

rwst added this to the sage-7.1 milestone Feb 24, 2016

rwst removed the pending label Feb 24, 2016

vbraun added s: needs work and removed s: needs review labels Mar 5, 2016

rwst added s: needs review and removed s: needs work labels Aug 3, 2016

rwst modified the milestones: sage-7.1, sage-7.4 Aug 3, 2016

rwst added s: needs work and removed s: needs review labels Nov 28, 2017

mkoeppe removed this from the sage-7.4 milestone Dec 29, 2022

rwst mentioned this issue Jan 30, 2016

make symbolic series subclass of Expression #17659

Closed

This was referenced Dec 29, 2022

Maxima does not handle symbolic series #20846

Closed

add doctest for #20846 #35001

Merged

vbraun pushed a commit that referenced this issue Feb 24, 2023

gh-35001: add doctest for #20846

67f8e43

Fixes #20846 (but not the related #17400). URL: #35001 Reported by: Marc Mezzarobba Reviewer(s): Frédéric Chapoton

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simplify_full returns odd result from symbolic series input #17400

simplify_full returns odd result from symbolic series input #17400

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