Some more doctests from the book "Calcul mathématique avec Sage" #11672

mezzarobba · 2011-08-09T19:59:51Z

The attached patch adds to the Sage testsuite most examples appearing Chapters 6 and 8 (Polynomials, Polynomial Systems) of the French book Calcul mathématique avec Sage. See #9395 for some background.

All tests pass with sage 5.5.

CC: @malb @sagetrac-Bouillaguet

Component: doctest coverage

Author: Marc Mezzarobba

Reviewer: Martin Albrecht, Charles Bouillaguet

Merged: sage-5.7.beta2

Issue created by migration from https://trac.sagemath.org/ticket/11672

zimmermann6 · 2011-08-24T19:36:50Z

comment:2

Martin, please could you review this? This will help our book to be more stable with future
versions of Sage. Thank you in advance (as a coauthor of the book, I'm quite reluctant to
review this).

Paul

malb · 2011-08-24T21:50:05Z

comment:3

Sure, I can take a look:

Please rename the patch to have the ".patch" suffix.
There might be an issue with the UTF-8, but we should try and wait if anybody complaints.
Do you really want to include an autogenerated file without any manual post processing? ("This file was autogenerated from sagebook.tex with sagetex.sty")
Please add your full name to the author field here on Trac.
I get some numerical noise errors:

File "/mnt/usb1/scratch/malb/sage-4.7.2/devel/sage/sage/tests/french_book/mpoly.py", line 373:
    sage: [CDF['x'](p(y=ys[0][0])).roots() for p in J.gens()]
Expected:
    [[(-0.6 - 1.30624677741e-16*I, 1), (0.6 + 1.30624677741e-16*I, 1)],
    [(0.6 - 3.13499226579e-16*I, 1), (2.6 + 3.13499226579e-16*I, 1)]]
Got:
    [[(-0.6 - 1.30628991909e-16*I, 1), (0.6 + 1.30628991909e-16*I, 1)], 
    [(0.6 - 3.13509580582e-16*I, 1), (2.6 + 3.13509580582e-16*I, 1)]]

malb · 2011-08-24T21:50:05Z

Reviewer: Martin Albrecht

zimmermann6 · 2011-08-25T10:15:13Z

comment:4

Martin, on which platform do you get numerical noise errors? With Sage 4.7 on a 64-bit Core 2,
I get no difference.

Paul

malb · 2011-08-26T12:40:24Z

comment:5

This was on sage.math (sorry, should have mentioned).

sagetrac-Bouillaguet · 2013-01-12T09:02:35Z

comment:6

I will try to make this go through

zimmermann6 · 2013-01-12T11:32:51Z

comment:7

thanks Charles!

Paul

mezzarobba · 2013-01-18T13:14:03Z

Author: Marc Mezzarobba

mezzarobba · 2013-01-18T13:16:52Z

comment:9

Charles: Thanks!

Here is a new version of the patch, updated to the last draft of the book (which contains what should hopefully be the final version of the chapters in question...) and to Sage 5.5.

sagetrac-Bouillaguet · 2013-01-18T16:57:21Z

comment:10

Looks good to me !

sagetrac-Bouillaguet · 2013-01-18T16:57:21Z

Changed reviewer from Martin Albrecht to Martin Albrecht, Charles Bouillaguet

jdemeyer · 2013-01-19T13:59:32Z

comment:11

On sage.math (Linux x86_64):

sage -t  -force_lib devel/sage/sage/tests/french_book/mpoly.py
**********************************************************************
File "/release/merger/sage-5.7.beta0/devel/sage-main/sage/tests/french_book/mpoly.py", line 366:
    sage: [CDF['x'](p(y=ys[0][0])).roots() for p in J.gens()]
Expected:
    [[(-0.6 - 1.30624...e-16*I, 1), (0.6 + 1.30624...e-16*I, 1)],
    [(0.6 - 3.13499...e-16*I, 1), (2.6 + 3.13499...e-16*I, 1)]]
Got:
    [[(-0.6 - 1.30628991909e-16*I, 1), (0.6 + 1.30628991909e-16*I, 1)], [(0.6 - 3.13509580582e-16*I, 1), (2.6 + 3.13509580582e-16*I, 1)]]
**********************************************************************

mezzarobba · 2013-01-19T14:32:30Z

comment:12

I am unable to reproduce the failure you get on sage.math (though I am working on Linux x86_64 too), so I just reduced the number of digits taken into account in this test again.

sagetrac-Bouillaguet · 2013-01-20T10:28:57Z

comment:13

I confirm that I ran the tests before giving the earlier positive review. It did work fine on my core i7-3615QM CPU running OS X 10.7.5...

The new patch also gets a positive review (the tests pass).

jdemeyer · 2013-01-21T14:54:49Z

comment:14

On bsd (OS X 10.6 x86_64):

sage -t  --long -force_lib devel/sage/sage/tests/french_book/mpoly.py
**********************************************************************
File "/Users/buildbot/build/sage/bsd-1/bsd_full/build/sage-5.7.alpha1/devel/sage-main/sage/tests/french_book/mpoly.py", line 373:
    sage: J.variety(RDF)
Expected:
    [{y: 396340.89..., x: 26.61226...}]
Got:
    [{y: 396340.890167, x: -54.9445477048}]
**********************************************************************

On arando (Linux Ubuntu 12.04 i686):

sage -t  --long -force_lib devel/sage/sage/tests/french_book/mpoly.py
**********************************************************************
File "/var/lib/buildbot/build/sage/arando-1/arando_full/build/sage-5.7.alpha1/devel/sage-main/sage/tests/french_book/mpoly.py", line 373:
    sage: J.variety(RDF)
Expected:
    [{y: 396340.89..., x: 26.61226...}]
Got:
    [{y: 396340.890167, x: -46.7888621592}]
**********************************************************************

zimmermann6 · 2013-01-21T15:46:11Z

comment:15

I wonder why we get different results for x. If all computations are based on IEEE 754, we should get the same (wrong) value. Is it possible to know which components of Sage are used for J.variety(RDF) on each platform? On mine I get:

sage: get_systems('J.variety(RDF)')                          
['MPFI', 'Singular', 'numpy', 'ginac']

Since MPFI is based on MPFR, MPFI should be architecture independent, but I wonder if the same applies to Singular, numpy and ginac...

Paul

mezzarobba · 2013-01-21T16:20:53Z

Attachment: trac_11672_doctests_from_french_book.patch.gz

New version (last draft of the book, Sage 5.5)

mezzarobba · 2013-01-21T16:21:09Z

comment:16

Paul: Could it be that whatever is used is compiled using extended precision on some platforms? Another strange thing, though, is that

sage: J.variety(Reals(p))
[{y: -1.00000001350726, x: -1929.60019649825}, {y: -0.999999986492719, x: 1929.62017010095}, {y: 396340.890166545, x: 10.3009522157620}]

finds 3 solutions for p as low as 39...

Anyway, this test doesn't make much sense, I shouldn't have included this test in the first place. Here is a new version of the patch without that test. I took the opportunity to ignore the last few significant digits in another numerical result that might change a bit in the future.

zimmermann6 · 2013-01-21T16:30:40Z

comment:18

Paul: Could it be that whatever is used is compiled using extended precision on some platforms?

yes, or with a different rounding precision. Anyway, it might be worth tracking down this issue. Jeroen, is there a way to trace the calls to the different Sage components (MPFI, Singular, numpy, ginac)?

Paul

sagetrac-Bouillaguet · 2013-01-21T16:44:11Z

comment:19

Replying to @mezzarobba:

Paul: Could it be that whatever is used is compiled using extended precision on some platforms? Another strange thing, though, is that
sage: J.variety(Reals(p))
[{y: -1.00000001350726, x: -1929.60019649825}, {y: -0.999999986492719, x: 1929.62017010095}, {y: 396340.890166545, x: 10.3009522157620}]
finds 3 solutions for p as low as 39...

Anyway, this test doesn't make much sense, I shouldn't have included this test in the first place. Here is a new version of the patch without that test. I took the opportunity to ignore the last few significant digits in another numerical result that might change a bit in the future.

Well, the test obviously indicate that there is a problem somewhere, and I tend to believe that we should keep the test and track the problem.

Either your computation is ill-conditioned, and the test should be removed from Sage (and probably also from the book), or there is a component of sage that misbehaves. We should understand what the situation is, and act accordingly. These tests have been there for 1.5 years, so we are not in a hurry. Maybe we could compare intermediate results on different machines?

jdemeyer · 2013-01-21T19:34:00Z

comment:20

Replying to @zimmermann6:

Jeroen, is there a way to trace the calls to the different Sage components (MPFI, Singular, numpy, ginac)?

I don't think so. You could of course use gdb and set suitable breakpoints...

mezzarobba · 2013-01-21T19:43:22Z

comment:21

Replying to @sagetrac-Bouillaguet:

Either your computation is ill-conditioned, and the test should be removed from Sage (and probably also from the book), or there is a component of sage that misbehaves. We should understand what the situation is, and act accordingly.

Sorry for the lack of context. Yes, the computation is ill-conditioned, that's deliberate (see http://purple.lateralis.org/sagebook-r1014.pdf, p. 210-211), and all three results above are completely wrong (the correct result is x=6.305...).

As Paul noted, in an ideal world, this code should nontheless yield the same result everywhere, so it might have made sense to test that the result didn't change over time. But there are a number of reasonable explanations for what we observe, and (as far as I can tell) in Sage, floating-point results are usually interpreted as mere approximations that should agree with the correct answer "up to some numerical noise" rather than well-defined exact results. So I am in favor of dropping this testcase—unless the policy is that machine-precision floating-point computations should yield exactly the same result on all platforms.

(Of course, this doesn't mean we shouldn't try to understand exactly what is going on!)

jdemeyer · 2013-01-21T19:49:30Z

comment:22

Or, add

J.variety(RDF)    # random

zimmermann6 · 2013-01-21T20:41:05Z

comment:23

I have created #13980 to keep track of the numerical noise issue, so that we can make progress on this
ticket independently.

Paul

mezzarobba · 2013-01-21T21:12:29Z

comment:24

Replying to @jdemeyer:

Or, add J.variety(RDF) # random

Is that better? (Given that many examples from the book are already excluded from the tests for various reasons.) Please tell me if you would like me to update the test file.

jdemeyer · 2013-01-21T21:16:10Z

comment:25

It was only a suggestion, do as you wish.

jdemeyer · 2013-01-30T07:34:57Z

Merged: sage-5.7.beta2

mezzarobba added this to the sage-5.6 milestone Aug 9, 2011

mezzarobba added t: tests labels Aug 9, 2011

mezzarobba assigned sagetrac-mvngu Aug 9, 2011

mezzarobba added the s: needs review label Aug 10, 2011

malb added s: needs work and removed s: needs review labels Aug 24, 2011

mezzarobba added p: minor / 4 and removed p: major / 3 labels Jan 18, 2013

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zimmermann6 mentioned this issue Dec 29, 2022

numerical noise in variety(RDF) #13980

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Some more doctests from the book "Calcul mathématique avec Sage" #11672

Some more doctests from the book "Calcul mathématique avec Sage" #11672

mezzarobba commented Aug 9, 2011

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Some more doctests from the book "Calcul mathématique avec Sage" #11672

Some more doctests from the book "Calcul mathématique avec Sage" #11672

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