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|| [[http://trac.sagemath.org/sage_trac/ticket/11364|11364]] || cyclic subspaces (aka Krylov subspaces) || with patch || ||

Converting Latex Documents to Sage Worksheets

Introduction

Latex documents can be translated to jsMath, the tool used to render mathematics in the Sage notebook. This project is about automating the conversion process so that authors can easily use a single command to convert a book-length Latex document to a collection of Sage worksheets. These could have embedded Sage input cells, possibly containing interacts, and the cross-referencing features of Latex would be preserved in the collection of Sage worksheets.
Rob Beezer, [email protected], rbeezer on #sage-devel IRC

Supported by

  • University Puget Sound Lantz Senior Fellowship (AY 2010-11)
  • National Science Foundation DUE-1022574 (2010-2013)

Conversion Software

Mercurial Repository @BitBucket
Clone using:

hg clone https://[email protected]/rbeezer/tex2sws/

Linear Algebra Patches

This table tracks patches meant to support the teaching of introductory linear algebra and the enhancement of Beezer's "A First Course in Linear Algebra."

Some tickets below that are available for review can be seen building and passing tests at the Sage PatchBot. Failures can be due to improper listing of necessary prerequisites, or builds not caught up with latest alpha version, so do not necessarily mean a ticket is not ready for review.

Items in RED are urgently needed because they are used in textbook additions.

Ticket

Description

Status

Acknowledgements

8071

trivial matrix kernels over non-fields

4.4.alpha0

Martin Albrecht

10362

vector constructor documentation

4.6.1.alpha3

Andrey Novoseltsev

10422

documentation fix on new_matrix constructor

4.6.1.alpha3

Benjamin Jones

10189

additions to all-ones matrix constructor

4.6.2.alpha0

Karl-Dieter Crisman, Robert Miller

10364

zero_vector constructor, vector constructor error-checking

4.6.2.alpha0

Andrey Novoseltsev

10424

matrix augment accepts a vector

4.6.2.alpha0

Joris Vankerschaver, Robert Bradshaw

10625

generic Smith form fails on integer matrices

4.6.2.alpha2

Author: David Loeffler

4492

block matrix constructor

4.6.2.alpha3

Author: Willem Jan Palenstijn

8948

latex printing for vectors

4.6.2.alpha3

Author: Jason Grout

10454

add .is_singular()

4.6.2.alpha3

Robert Bradshaw

10471

conjugate-transpose of a matrix

4.6.2.alpha3

Robert Bradshaw

10500

documentation: matrix row/column linear combinations

4.6.2.alpha3

Alyson Deines

10535

column-oriented matrix constructor

4.6.2.alpha3

Dan Drake

10537

dictionary input to vector constructor

4.6.2.alpha3

Dima Pasechnik

10626

route sparse integer matrices to specialized Smith form

4.6.2.alpha3

David Loeffler

10627

matrix pretty-printing

4.6.2.alpha3

Author: Ivan Andrus

10028

improved error messages for non-invertible matrices

4.6.2.alpha4

Author: Andre Apitzsch

10541

row and column matrix from vector, deprecate transpose

4.6.2.alpha4

Volker Braun, Marco Streng

10543

echelon form over QQ is mutable

4.6.2.alpha4

Tom Coates

10604

diagonal matrix constructor rewrite

4.6.2.alpha4

Joint with: Dan Drake

9796

diagonal elements of a matrix

4.6.2.rc0

Tom Coates

10714

rows/columns of sparse matrices with zero rows/columns

4.6.2.rc0

Jason Grout

10568

speed-up scalar multiples of sparse matrices

4.7.alpha1

Author: Maarten Derickx

10426

matrix row and column swapping, returns new matrix

4.7.alpha2

Alain Filbois

10763

matrix multiplication speedup

4.7.alpha2

Author: Simon King

10477

random vector constructor

4.7.alpha3

Felix Lawrence

10536

vector conjugation

4.7.alpha3

Felix Lawrence

10545

outer product of vectors

4.7.alpha3

Felix Lawrence, John Palmieri

10595

vector constructor fails with empty list

4.7.alpha3

Joint: J. Palmieri, Review: D.Pasechnik

10977

document vector constructor

4.7.alpha3

Martin Raum

4983

fix subdivision attribute

4.7.alpha4

Author: John Palmieri

10470

listing infinite vector space just hangs

4.7.alpha4

John Palmieri

10683

Hermitian inner product, doctests

4.7.alpha4

Karl-Dieter Crisman

10737

extended echelon form

4.7.alpha4

John Palmieri

10752

make matrix pivots immutable

4.7.alpha4

Author: John Palmieri

10863

is_unitary() for matrices

4.7.alpha4

Martin Raum

10876

constructor for elementary matrices

4.7.alpha4

Karl-Dieter Crisman

10974

overhaul matrix stack, augment

4.7.alpha4

Keshav Kini

11004

make subdivisions optional on tensor product

4.7.alpha4

John Palmieri

11112

algebraic closure of CDF

4.7.alpha4

Mike Hansen

10987

subspace decomposition, check optional

4.7.alpha5

Author: Martin Raum

10794

QR matrix decomposition over exact rings

4.7.alpha5

Simon Spicer

11114

is_diagonalizable() for matrices

4.7.1.alpha0

Dan Drake

11027

Schur matrix decomposition

positive review

Martin Raum, John Palmieri

10944

similarity check for matrices

positive review

Dan Drake

7852

solve systems over CDF

with patch

8094

properties for matrices

with patch

Harald Schilly, Jason Grout

10746

refactor matrix kernels

with patches

10791

fix and upgrade Gram-Schmidt

with patches, dep. 10683, 10794

Martin Raum

10795

QR double dense matrix decomposition upgrade

with patch

10802

singular values for matrices over CDF

with patch

Martin Raum

10839

LU decomposition for rectangular matrices

with patch

10848

is_hermitian() for matrices

with patch

11104

is_normal() for matrices

with patch

11259

LU decomposition for exact matrices

with patch

11306

upgrade is_unitary() for RDF/CDF

with patch, dep. #11027, #10848, #11277

11356

companion matrix constructor

with patch

11364

cyclic subspaces (aka Krylov subspaces)

with patch

10837

matrix and vector norms, condition number over CDF

needs work - numerical

Simon Spicer

4932

remove solve-left-LU

needs work

7392

rank for matrices over CDF

new

8046

add double dense matrix file to documentation

needs work

10465

adjoint meta-ticket

information, dep. 10471, 8094, 10501

10501

deprecate adjoint in favor of adjugate

needs work

10544

LLL reduced bases for right kernels

new

10765

obliterate sage/matrix/misc.pyx

orphaned

11274

Cholesky decomposition over rationals

new

11286

speed up solve_right()

new

Group Theory Patches

Ticket

Description

Status

Acknowledgements

7244

dicyclic groups

4.2.1.alpha0

David Joyner

7305

Higman-Sims graph

4.2.1.rc0

Nathann Cohen

7555

Cayley tables, operation tables

4.4.alpha0

Nicolas M. Thiery, Jason Grout

10685

all subgroups of a permutation group

4.6.2.alpha4

Dima Pasechnik

10722

all cosets of a permutation group

4.6.2.alpha4

Dima Pasechnik

10871

intersections of permutation groups

4.7.alpha3

Dima Pasechnik

10911

inverse of permutation group elements

4.7.alpha3

Robert Bradshaw

10920

conjugates of permutation groups

4.7.alpha3

Dima Pasechnik

10921

commutator subgroup for permutation groups

4.7.alpha3

Dima Pasechnik, David Joyner

10334

permutation group cleanup

4.7.1.alpha1

Author: Mike Hansen

11289

random poset generation (docs, error checks)

positive review

Franco Saliola

11292

inputs to lattice meet and join

positive review

Anne Schilling, Franco Saliola

11293

all relations of a poset

positive review

Franco Saliola

9773

finitely-generated abelian groups

needs work

Examples

To view a worksheet, click on the "worksheet" link, then in the resulting page find the big blue download box and use your browser's function to copy the link there. Then open your notebook, click the "Upload" link near the upper-left and then paste in the link into the URL field (the second one).

Note: If your version of Sage is 4.3.2 or older then some examples may not render quite right. See way below for how to edit older configurations.

  • Sage-Enhancing an Abstract Algebra Textbook (Updated: 2011/04/22)
    • Tom Judson's free open-source Abstract Algebra; Theory and Applications

    • Live Sage code for each chapter (except 7, 8, 12, 13 will be done later - especially 13)
    • Requires Sage 4.7.alpha3 or newer (or else some commands will not run properly)
    • 259 Sage examples, input/output for each tested on Sage 4.7.alpha3
    • Upload the zip file using the notebook's "Upload Worksheet" function - the notebook will do the unzipping
    • In the notebook, skip table-of-contents section, click on actual sections to bring up content
    • SageTeX can be used to render faithful PDF from the same source

    • Alpha quality: Worksheet Zip File

  • Sage-Enhancing a Linear Algebra Textbook (Updated: 2011/02/28)
    • Rob Beezer's A First Course in Linear Algebra

    • Live Sage code for first five chapters of eight (Chapters SLE, V, M, VS, D)
    • "Read-Only" - some content is temporarily missing, Sage commands use new unofficial patches for linear algebra, some formatting needs improvements
    • Upload the zip file using the notebook's "Upload Worksheet" function - the notebook will do the unzipping
    • In the notebook, skip front matter sections, click on actual sections to bring up content
    • SageTeX is used to render faithful PDF from the same source

    • Worksheet Zip File

    • PDF Version (old)

  • Abstract Algebra Worksheets (2011/04/18)
  • An Entire Mathematics Textbook (2010/08/27)
  • Approximating Polynomial Worksheet (2010/02/20)
    • A classroom worksheet, with interacts
    • Nice mix of mathematics and live demonstrations
    • PDF could do something better with interacts (hide code, show screenshot?)
    • Latex source

    • PDF

    • Worksheet

  • SageTeX integration (Robert Marik, 2010/02/20)
    • Slightly modified version of the example.tex file from the SageTeX distribution

    • All but three graphics coming through, understandably
    • Missing 3D tachyon graphic is just a path problem and is fixable
    • Might be able to do something better with the sagesilent environment such as inserting a %hide at the start of the block

    • To re-create this, run the following sequence of commands:
      pdflatex example.tex
      sage example.sage
      htlatex example.tex "/path/to/tex4ht-sage.cfg" " -cunihtf -utf8"
      tex2sws
    • Latex source

    • PDF

    • Worksheet

    • For fixed tex4ht-sage.cfg, tex2sws.py which allows to insert 3D graphics and vertex labels see this link.

  • A Whole-Book Experiment (2010/02/07)

    This is all of Beezer's First Course in Linear Algebra as a linked collection of Sage worksheets. It runs about 900 pages when printed, but as a tar archive is around 700K.

    • See note below about jsMath configuration and matrix formatting.
    • No Sage content yet - see other experiments for demonstrations.
    • Installation: To rig worksheet numbers, and thus have cross-worksheet linking work properly, it is necessary to create a pristine user and insert the worksheets properly into the notebook storage area. In the following, you must use the new user "linear", but password and notebook location can be adjusted. But the notebook location needs to end with ".sagenb".
      $ sage
      sage: from sagenb.notebook.notebook import Notebook
      sage: nb=Notebook("/tmp/fcla.sagenb")
      sage: nb.add_user('linear', 'algebra', '', account_type='user', force=True)
      sage: exit
      $ cd /tmp/fcla.sagenb/home
      $ tar -xvf /path/to/fcla-worksheets.tar.bz2
      $ sage
      sage: notebook(directory="/tmp/fcla.sagenb")
    • You will possibly be asked to create an admin password, just do it.
    • Even if you see the right worksheets, sign-out right away.
    • Sign-in as the user "linear" with password "algebra".
    • Now you should be able to view the worksheets.
    • Tar Archive of FCLA Worksheets

  • tikz graphics migration (2010/02/03, Updated: 2010/02/20)

    • tikz graphics in latex source passing through to the worksheet
    • combinatorial graphs in Sage creating tikz source, also included
    • worksheet has graphics as SVG, live cells, graph editor
    • Not all browsers render SVG? Tested in Firefox
    • Latex source, some generated by Sage

    • PDF, a faithful rendition

    • Worksheet, note SVG graphics, run code, experiment with graph editor

    • This experiment prompted by a mailing list discussion

  • Group Theory Primer (2010/01/28)
    Lots of simple Sage code, some simple mathematics, one interact (search for "@interact")
    Best working demo (though it lacks a title)
    Worksheet Source

  • Textbook Section Experiment (2010/01/30, updated 2010/02/07)
    This is a straight conversion of a math-heavy section from Beezer's linear algebra text.

    • See note above about jsMath and matrix formatting.
    • The original tex4ht output is at FCLA Section FS in jsMath which seems to render just fine for me.

    • There is no embedded Sage code here yet, but that will be easy to add.
    • Links go nowhere unless they are internal to this section.
    • Worksheet

  • Linked Worksheets (2010/01/30)
    A simple manufactured example of cross-worksheet linking.

    • Fire up Sage, then create a new, temporary notebook with the user "link"
      sage: from sagenb.notebook.notebook import Notebook
      sage: nb = Notebook('/tmp/test.sagenb')
      sage: nb.add_user('link', 'link', '', force=True)
      sage: nb.save()
      sage: exit
    • At system command-line extract archive (below) to create the worksheets with numbers 0 and 1 in link's space.
      $ cd /tmp/test.sagenb/home
      $ tar -xvf <path-to>/link-worksheets.tar.gz
    • Fire up Sage to start a notebook session in the temporary notebook:
      sage: notebook(directory="/tmp/test.sagenb")
    • You may need to create an admin password (do it).

      You may see the worksheets, but be logged in as admin.
      If needed, be certain to login as "link" with password "link."

    • Open worksheet 0, execute a cell or two, find link to worksheet 1.
    • Follow link to worksheet 1, execute some cells here too.
    • Archive (described above) Python generation script

tex4ht

This is a list of known configurations of tex4ht that seem to work:

  • "tex4ht is part of the standard mactex distribution" (Dana Ernst, 2010/01/29)
  • "TeXLive 2009 (separate from Ubuntu package manager) includes its own little package manager ('tlmgr') and I used that to install tex4ht" (Dan Drake, 2010/01/30)
  • Ubuntu/Kubuntu/Debian: (K)Ubuntu Karmic 2009/05/21, Debian stable 2008/07/01, Debian testing 2009/06/11
    From Jason B. Hill (2010/02/24)

    • "texlive-full" depends on tex4ht (and hence will install tex4ht) in Ubuntu/Xubuntu/Kubuntu 9.10.
    • "tex4ht" may also be installed directly from the standard Ubuntu repositories via apt/aptitude on top of the smaller "texlive-base/texlive-base-bin". This is also true for Debian stable.
    • In either case, tex4ht/htlatex/etc commands must be added manually at this point to Kile, or can be called directly from the terminal.

sws2tex, Example
Anybody want to try for the round-trip, Latex -> SWS -> Latex?

jsMath Safe Boxes Edit

For Sage versions prior to 4.3.3.alpha0 (sagenb prior to 0.7.5) it is necessary to slightly tweak the jsMath configuration in Sage. It is a one-character edit. You can still view the sections, but "reasons" given in math displays (generally in proofs) won't render right and you will see lots of "@a()" stuff. This was fixed in Trac 8202 for Sage 4.3.3. Check your version of Sage with sage --version.

The file to edit is

SAGE_ROOT/local/lib/python/site-packages/sagenb-0.6-py2.6.egg/sagenb/data/sage/js/jsMath.js

where you might have to adjust the numbering on the sagenb package. Then at line 97 (or thereabouts) make the following change

jsMath.safeHBoxes=1 --> jsMath.safeHBoxes=0

Also, these examples have a bit of a formatting problem for larger matrices (more than two rows) on my setup, but I'm uncertain if that is my problem or more general. A report, either way, would be appreciated if you look at these.

The 20% Defying Categorization

devel/LatexToWorksheet (last edited 2011-12-14 03:50:48 by rbeezer)