20200401

== previous dependencies ==

==== Eq2png ====

The Perl script uses the Perl program eq2png

http://www-users.math.umd.edu/~olsson/eq2png/

to generate PNG files for each equation and each operator.

example use:

perl statement2png.pl

Common issue: error message "Can't locate XML/DOM.pm"

This can be isolated to eq2png by issuing the command

perl eq2png '$\int x^2 dx$' -o file.png

if this causes the error message, then install module

perl -MCPAN -e shell 'install XML::DOM'

==== mash.pl ====

Allows mathematica to be used from a shell

http://ai.eecs.umich.edu/people/dreeves/mash/

http://ai.eecs.umich.edu/people/dreeves/mash/mash.pl

20180512

Use Activity log to get a list of times and functions:

$ cat activity_log.dat | sed '/write_steps/d' | sed 's/ | <function /,/' | sed 's/ at .*//'

How many times was each function called?

$ cat activity_log.dat | sed '/write_steps/d' | sed 's/ | <function /,/' | sed 's/ at .*//' | cut -d',' -f2 | sort | uniq -c | sort -k1,1

Store unique functions to an array,

https://askubuntu.com/questions/439026/store-output-of-command-into-the-array/439038#439038

$ readarray -t ary_of_funcs <<< "$(cat activity_log.dat | sed '/write_steps/d' | sed 's/ | <function /,/' | cut -d',' -f2 | sort | uniq )"

$ printf -- "%s\n" "${ary_of_funcs[@]}"

20151107

# nothing up my sleeve - clean the destination directories

bin/clean_dev.sh

cp site/d3/d3.v3.min.js dev/site/

rm -rf output/

mkdir output

# user input

bin/interactive_user_prompt.py

mv dev/output/new_*.csv dev/

# or recycle existing

cp new_*.csv dev/

cp derivation_name.dat dev/output/

# set variables to pass to scripts

deriv_name_with_spaces=`cat dev/output/derivation_name.dat`

deriv_name_without_spaces=`cat dev/output/derivation_name.dat | sed 's/ /_/g'`

# create infrastructure

bin/create_picture_per_expression_from_expressionDB.py

bin/create_picture_per_feed_from_feedDB.py

bin/create_picture_per_derivation_from_connectionsDB.py "${deriv_name_with_spaces}"

bin/create_json_per_derivation_from_connectionsDB.py "${deriv_name_with_spaces}"

bin/create_d3js_html_per_derivation_for_local.sh dev/site/ json/ pictures/ ${deriv_name_without_spaces} local

# place results in appropriate directories for visualization

cp dev/output/*.json dev/site/json/

cp dev/output/*.png dev/site/pictures/

cp dev/images_expression_png/*.png dev/site/pictures/images_expression_png/

cp dev/images_feed_png/*.png dev/site/pictures/images_feed_png/

cp lib/images_infrule_png/*.png dev/site/pictures/images_infrule_png/

# visualize the results

open /Applications/Google\ Chrome.app --args --allow-file-access-from-files file:///Users/benpayne/version_controlled/proofofconcept/dev/site/${deriv_name_without_spaces}.html

20151105

now that I'm doing rapid prototyping, I need a development environment which is

separate from the projection environment.

--> added /dev/

bin/interactive_user_prompt.py

mv dev/output/new_*.csv dev/

bin/create_picture_per_expression_from_expressionDB.py

bin/create_picture_per_feed_from_feedDB.py

bin/create_picture_per_derivation_from_connectionsDB.py

bin/create_json_per_derivation_from_connectionsDB.py

bin/create_d3js_html_per_derivation.sh dev/output new_derivation_eipiplusone

cp dev/output/new_derivation_eipiplusone.html site/testing/

cp dev/output/*.json site/json/

cp dev/output/*.png site/pictures/

20151104

bin/interactive_user_prompt.py

mv eipiplusone/output/new_* eipiplusone/

bin/create_picture_per_expression_from_expressionDB.py

bin/create_picture_per_feed_from_feedDB.py

bin/create_picture_per_derivation_from_connectionsDB.py

open eipiplusone/output/new_derivation_with_labels.png

open eipiplusone/output/new_derivation_without_labels.png

bin/create_json_per_derivation_from_connectionsDB.py

bin/create_d3js_html_per_derivation.sh output new_derivation

cp output/new_derivation.html site/

cp eipiplusone/output/*.json site/json/

cp eipiplusone/output/*.png site/pictures/

20151102

cleaned up lots of inconsistencies

todo:

* create nodes and edges csv file is not yet working as desired

* end-to-end test of enter derivation to create json needs to be demonstrated

* link overview graph to each derivation

See also https://trello.com/b/kSZvdVg5/physics-derivation-graph

20150908

Physics derivation graph is hierarchical

Symbol, operators

Expressions, inference rules

Step

Derivation

Physics derivation graph

20150806

I recognized that derivations are distinct from identities and definitions.

What confused me is that validation of an identity is a derivation.

F=m*a is not an identity

Euler equation is an identity.

http://www.purplemath.com/modules/proving.htm

identity: only manipulate one side of the equation, whereas in a derivation both sides are manipulated

set of identities:

https://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities

20150618

contacted jibe, jon seaton, and wojech

https://www.physicsforums.com/threads/physics-equation-map.4269/

20150519

Now I have two tasks:

* non-overlapping node labels, a la

http://bl.ocks.org/MoritzStefaner/1377729

* hierarchical graph -- interactive via URLs

http://stackoverflow.com/questions/20575026/how-to-make-labels-and-nodes-in-d3-forced-layout-clickable-to-navigate-to-a-url?lq=1

http://stackoverflow.com/questions/13104681/hyperlinks-in-d3-js-objects

Both are presentation issues. I think the hierarchical graph is more important as it is the "zoom"

20150515

got quadratic equation in d3js!

Visualization needs non-overlapping labels, see

http://bl.ocks.org/MoritzStefaner/1377729

20150513

The translation from the static .xml based graphs to .json for d3js is not a simple regex.

The .json needs to include the picture dimensions.

My next task is to parse edges based JSON input rather than relying on the data structure native to d3js

{source: nodes[0], target: nodes[1]},

{source: nodes[1], target: nodes[2]},

See https://github.com/mbostock/d3/wiki/Force-Layout

"these attributes may be specified as a numeric index rather than a direct link, such that the nodes and links can be read-in from a JSON file"

...

"The source and target attributes on incoming links are only replaced with the corresponding entries in nodes if these attributes are numbers"

http://bl.ocks.org/mbostock/4062045

20150305

I created a project on webprotege for the physics derivation graph

http://webprotege.stanford.edu/#Edit:projectId=c816e793-12eb-4bfd-a4c7-3db0ba44b34c

The project is populated with data from

https://github.com/allofphysicsgraph/proofofconcept/wiki/Inference-Rules

and

https://github.com/allofphysicsgraph/proofofconcept/wiki/Operators

I then exported the data from webprotege as "OWL/XML" and got a ".owx" file

http://bhpayne.github.io/physics_derivation_graph/physics_derivation_graph.owx

I can plot the graph in

http://vowl.visualdataweb.org/webvowl/index.html#iri=http://bhpayne.github.io/physics_derivation_graph/physics_derivation_graph.owx

That same file input doesn't work on my instance

http://bhpayne.github.io/physics_derivation_graph/webvowl_0.3.3/index.html?#iri=http://bhpayne.github.io/physics_derivation_graph/physics_derivation_graph.owx

My next step is to determine how what I've done so far (developing

structure) relates to putting content into OWL. The content is

mathematical, so the format will likely be MathML.

20150304

Started a page for myself on

https://bhpayne.github.io/

Good news: github.io supports HTML5

https://haxiomic.github.io/GPU-Fluid-Experiments/html5/?q=Medium

20150304

Seems like the main hurdle will be converting XML to the RDF triple paradigm.

(expression) (is composed of) (operators)

(operators) (are) (symbols or math)

Problem is that some inference rules take feeds, rather than simply relate one expression to another

----------------

| expression 1 |

----------------

|

v

-------------------------- --------

\ multiply both sides by /--<--| feed |

------------------------ --------

|

v

----------------

| expression 2 |

----------------

Perhaps the triplets are

(expression) (is composed of) ({left-hand-side, relation, right-hand-side})

(left-hand-side) (is composed of) (symbols and operators)

(right-hand-side) (is composed of) (symbols and operators)

(relation operators) (is one of) ({=,<,>,!=,<=,>=})

(expression) (is acted upon by) (inference rule)

(inference rule) (takes) (feed)

(inference rule) (yields) (expression)

********************

Google search for

rdf physics derivation

yields no relevant results

The first return for

rdf physics equation

is

http://stackoverflow.com/questions/27860142/writing-scientific-hypothesis-in-rdf

It appears to be our friend jibe-b

http://stackoverflow.com/users/4087192/jeybee

*******************

Looking at the source code for the page

http://vowl.visualdataweb.org/webvowl/index.html#iri=http://jibe-b.github.io/ontology/physics-derivations-test

I am a bit confused -- I don't see where the graph is being loaded from.

******************

learning RDF

Good:

http://www.linkeddatatools.com/introducing-rdf

http://www.linkeddatatools.com/introducing-rdf-part-2

OK

http://www.w3schools.com/webservices/ws_rdf_example.asp

Out of date

http://www.rdfdata.org/

************************

http://protege.stanford.edu/

http://webprotege.stanford.edu/

20141207

what's the elevator pitch?

compile a database of all current known physics

showing how they correlate

the logic behind that correlation

showing how they are derived

examples of capturing lots of information concisely in an accessible form

* google maps

* wikipedia

20141207

syntax candidates: {ContentML, PresentationML, Latex, Mathematica, SymPy, abstract syntax tree}

In general, we need to evaluate

* ability to input

* ability to transform between representations

* ability to audit correctness

Not a problem:

* storage

consumer cares about:

* speed

* ease of use

* presentation

* accessibility - multi-device, multi-OS

* easy setup

A set of test cases for flexing the capability of syntax

1) polynomial

Latex: a x^2 + b x + c = 0

2) Stoke's theorem

\int \int_{\sum} \vec{\nabla} \times \vec{F} \dot d\sum = \oint_{\partial \sum} \vec{F}\dot d\vec{r}

3) Tensor analysis

Y^i(X_j) = \Delta^i_{\ j}

Einstein notation: contravariant = superscript, covariant = subscript

4) creation operator

\hat{a}^+ |n\rangle = \sqrt{n+1} |n+1\rangle

\sigma_x \sigma_p \geq \frac{\hbar}{2}

uncertainty principle

To evaluate:

* character count

* rendering

Content MathML for 1:

<math xmlns="http://www.w3.org/1998/Math/MathML">

<apply>

<eq/>

<apply>

<plus/>

<apply><ci>a</ci> <power/><ci> x </ci><ci> 2 </ci></apply>

<apply><ci>b</ci> <ci> x </ci> </apply>

<apply><ci>c</ci> </apply>

</apply>

<apply>

<cn>0</cn>

</apply>

</apply>

</math>

Presentation MathML for 1:

<mrow>

<mrow>

<msup>

<mrow><mi> x </mi></mrow>

<mrow><mi> n </mi></mrow>

</msup>

<mo>+</mo>

<msup>

<mrow><mi> y </mi></mrow>

<mrow><mi> n </mi></mrow>

</msup>

</mrow>

<mo>=</mo>

<msup>

<mrow><mi> z </mi></mrow>

<mrow><mi> n </mi></mrow>

</msup>

</mrow>

* what are we comparing?

** presentation mathml, content mathml, mathematica, latex, abstract syntax tree

* what is the evaluation?

** can it describe all the notation necessary for physics

** how easy is the input method? (character count)

** can it be transformed to other representations

20141206

Statement stored as abstract syntax tree could generate MathML, Latex, CAS input

Mathematica has "tree form"

What I refer to as "statement", Mathematica calls "expressions"

Mathematica has "atomq" which indicates whether the expression

atom = {symbols, numbers, ...}

20141027

Mike found the basis for my inference rules

http://hotmath.com/hotmath_help/topics/properties-of-equality.html

"add X to both sides" = Addition Property

"multiply both sides by" = Multiplication Property

"substitute X for Y" = Substitution Property

"replace left side of equation 1 with left side of equation 2" =

Transitive Property

Knowing the right jargon makes all the difference!

http://www.mathwords.com/m/member_of_an_equation.htm

20141027

Famous physics equations

https://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation

https://en.wikipedia.org/wiki/Maxwell%27s_equations

https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion

https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

https://en.wikipedia.org/wiki/Carnot%27s_theorem_(thermodynamics)

https://en.wikipedia.org/wiki/Ideal_gas_law

https://en.wikipedia.org/wiki/Bridgman%27s_thermodynamic_equations

https://en.wikipedia.org/wiki/Dirac_equation

https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

Physics areas covered: Quantum, Classical, Astro, ElectroMagnetism, Thermodynamics, Relativity

These draw on algebra, calculus, differential equ, PDE, and linear algebra

It's not clear to me how

https://en.wikipedia.org/wiki/Einstein_notation

https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation

fit mathematically as syntax rules

20140930

I kept the iterative drafts associated with getting a "simple" derivation into the proper level of detail needed to put into the graph database. The initial problem fits on one page, but to get the steps explicit took 7 iterations and about 8 pages of repeated expansion. This measurement is biased by the fact I had to guess some of the inference rules, and ended up missing some (I needed to go back and further expand).

The result of this experiment is that the scope of the project is currently too grand. I have multiple distinct goals, each of which is non-trivial. Instead of trying to tackle all the problems at once, I'm going to prioritize tasks.

Motivating goals (full scope)

* write down all math-physics knowledge

* perform derivations in atomic steps using common inference rules

* be able to check derivations using a CAS

* display graph of derivations

** interactive graph feature: add new content

** interactive graph feature: zoom in/out

The objective of being explicit about derivations allows for checking by a CAS.

Being explicit causes most of the work currently.

My objective about having a pretty interface is useless without content.

Therefore, to both minimize workload and create content, I need to focus on just writing down the derivation relations.

--> don't bother about being explicit

--> don't bother with dynamic interface [static png is sufficient]

This resolves the difficulty of using Content MathML since I'm not going to use a CAS! Using Latex is sufficient at this time.

New task: gather derivations, determine how they are related (how to hop from one domain to another).

--> how is Maxwell's equations related to E=mc^2?

--> how is E=mc^2 related to F=ma?

* http://www.mrelativity.net/relationshipef/the_relationship_between_e_and_f_p1.htm

* http://www.spaceandmotion.com/wave-equations-elastic-medium-space.htm

This one gives the best explanation:

* http://www.laserpablo.com/teacherresources/files/E-mc2_Derivation2.ppt

The summary is: "On the first pass, don't bother being rigerous; just collect information."

In retrospect, this conclusion is obvious.

20140915

alternative to MathJax is released

https://news.ycombinator.com/item?id=8320439

http://khan.github.io/KaTeX/

I don't think this has significance for this project, because I don't expect to use in-browser rendering

20140907

Rendering graphs in browsers:

directly edit a directed graph with spring layout.

http://jsfiddle.net/vfu78/16/

directed graph editor with zoom; no spring layout

http://bl.ocks.org/cjrd/6863459

directed graph editor with spring layout; no zoom:

http://bl.ocks.org/rkirsling/5001347

20140907

Was able to convert presentation MathML to Latex using

http://sourceforge.net/projects/xsltml/

Instructions:

Extract the .zip

place your .xml with PMathML in the same directory

place the following tags in your .xml file at the top:

<?xml version="1.0" encoding="UTF-8"?>

<?xml-stylesheet type="text/xsl" href="mmltex.xsl"?>

Open in Firefox to view the generated Latex

20140907

I found some examples of PMathML at the Digital Library of Mathematical Functions

http://dlmf.nist.gov/1.7

Example:

http://dlmf.nist.gov/1.7.E1.pmml

I downloaded this file and saved it as

nist.xml

Opening in Firefox, this works as desired

rename the file nist.html

and Firefox doesn't render correctly.

Neither nist.xml nor nist.html render correctly in Chrome.

I added in the tags

<html><body> MathML here </body></html>

and also tried

<html><?xml version="1.0" encoding="UTF-8"?><body> MathML here </body></html>

<html><body><?xml version="1.0" encoding="UTF-8"?> MathML here </body></html>

but none of these three variations helped with rendering "nist.html" in Firefox.

Conclusions:

-file extension must be .xml

-does not render in Chrome

-works in Firefox

Firefox is happy with the file extension .xml and this tag ordering:

<?xml version="1.0" encoding="UTF-8"?><html><body> Presentation MathML here </body></html>

20140905

I've been researching the steps to take

Content MathML <--> Presentation MathML <--> Latex

Content MathML help:

http://cnx.org/contents/2bae0fb8-e5ea-48bd-b893-503033db6cfd@16

However, I realized the conversions I care about are

Content MathML --> CAS (i.e., sympy)

Content MathML --> graph rendering

Content MathML --> Latex for PDF

I suspect I will need

Content MathML --> Presentation MathML --> graph

--> or mathjax --> graph

MathJax

http://docs.mathjax.org/en/latest/mathml.html

I don't see any capability in Sympy to read in Content MathML. I would need to create a converter.

20140831

After talking with Mike G about this project, I realized having the Latex/SymPy representation separate was a cause for me being stuck. Whether I attacked the GUI, the CAS, or adding content to the database, there was a lack of unification between presentation (Latex) and symbolic manipulation (XML+SymPy).

MathML seems a likely candidate for unifying presentation and symbolic manipulation. I need to learn more about it.

OpenMath is a more flexible version of MathML

http://www.openmath.org/overview/om-mml.html

I will need to find where MathML doesn't work prior to using OpenMath

http://tex.stackexchange.com/questions/57717/relationship-between-mathml-and-tex

http://www.access2science.com/latex/StaceyLatexNote.html

Latex is an input format (meant to be written by humans)

MathML is an output format (not meant to be written by humans)

Suppose I have the statements_database.xml in MathML. I would need to be more specific -- presentation or

Render MathML online

http://www.compileonline.com/try_mathml_online.php

Latex to presentation MathML translator:

http://www.mathtowebonline.com/

http://www.mathmlcentral.com/Tools/ToMathML.jsp

http://www.mathtoweb.com/cgi-bin/mathtoweb_home.pl

http://math.etsu.edu/LaTeXMathML/

https://www.maths.nottingham.ac.uk/personal/drw/lm.html

http://dlmf.nist.gov/LaTeXML/

http://www.csun.edu/~hcmth008/mathml/acc_tutorial.html

http://www.orcca.on.ca/MathML/texmml/textomml.html

MathML to Tex translator:

http://www.orcca.on.ca/MathML/texmml/mmltotex.html

20140829

I have 3 potential tasks:

-graph visualization. Takes a lot of work

-implement CAS checker. Somewhat useless since {Latex, symbol definitions, SymPy} are not actually related

-add content to graph database. However, I want confidence that it is correct (CAS checker) and I want to visualize it.

Based on this analysis, I need a better desing of the database to relate Latex, symbol definitions, and SymPy statements.

I don't want to generate Latex from SymPy

--> MathML?

Latex is pretty, but too flexible to be reliably interpreted by a CAS

20140817

From talking with other projects which share overlap (Formula Database, Symbolab, EquationMap), the back-end databases might be similar. I think it would be worth having a common syntax. However, what motivation would private, commercial projects have for supporting shared syntax?

No one wants to supply me with their backend info, but I don't want to replicate previous work.

Equation map doesn't have a backend database. FD and Symbolab do.

20140617

Asked an astrophysicist what the most important equations are in his field. Ended up talking about how the various fields are differentiated

-astronomy = observing the sky. Depends on atomic physics and optics

-astrophysics = how the stuff in the sky works. Depends on thermal physics + gravity

-cosmology = study of the whole universe

-space physics = travel in space

-planetary science = how does the planet work

-astrobiology = how do living creatures in extreme environments exist?

Astrophysics then depends on classical mechanics and radiative transfer. Find equilibrium for pressure, radiation, gravity.

Famous equation: GR tensor (General Relativity tensor)

Good reference textbook: Icko Iben, Stellar Evolution Physics

20140527

Called and spoke with Jon Seaton of Formula Database

His team has been working on formula-database for 2-3 years. He describes it as a "math search engine" which has a built-in equation editor. The search feature isn't just matching the Latex input. It understands dot product, cross product.

The objective is to allow students to search through literature. If you are a researcher, you might want to find whether the model already exists in literature.

The backend database of equations and symbols was hand-entered. The data is stored as a high-dimensional graph.

Jon says the team plans on launching the product commercially, but everyone is busy.

The status is that the project is "mostly done" as they have the proof of concept working.

They have created a browser-based equation editor, similar to the equation editor in Microsoft Word

The grand view is that formula-database will serve as a universal reference for equations.

Jon says his team has studied the market and students aren't interested in purchasing a subscription. More likely is an advertising-based revenue.

The service is oriented towards homework help, rather than the professional researcher. [Professional researchers already know which equations matter to their work.]

Jon has three Master's degrees -- engineering, math, and physics.

Jon says a common question he gets is "how does your search product compare to wolfram alpha?"

Jon sees Symbolab as their competitor

Jon is familiar with mathdox

Jon brought up Wojciech's project, though he couldn't recall the name EquationMap.

Jon describe's Wojciech's project as graph visualization with hand-entered equations.

Jon says Wojciech's project is more an online tool for concept maps, based entirely on user input.

draw links between equations

product

Reason for not collaborating is Wojciech is in Poland

20140527

Although HTML5 Canvas is fun to move graphs around with, I need an example showing that it can be used to visualize graphs larger than fits on a single page. Can I think of the canvas as a window for viewing a graph larger than the screen? The ability to zoom in/out would be useful.

Graph Dracula

http://www.graphdracula.net/

Upsides:

-simple and intuitive for development.

-it can render graphs with SVG and PNG nodes

Downsides:

-not clear how to render graphs larger than the screen

-no zoom in/out

-I didn't find support for spring force graph layout

20140524

I was contacted by Wojciech on May 15 via email. We talked via phone about our projects.

I emailed 3 of the project developers for Formula-database and Jon Seaton replied. I will call him Tuesday to talk about status and plans.

I updated the content on

https://sites.google.com/site/physicsderivationgraph/

20140216

more cleanup tasks:

-move "lib/images_op_*" to "lib/images_infrule_*"

-move "lib/images_eq_*" to "lib/images_statement_*"

consequences:

-single change in each of "create_pictures_of_*"

-change "build_connections_graph.py"

20140216

Successfully completed run on existing connections with CAS check (sympy). Report:

number_of_rules_not_checkable=58

number_of_checkable_rules_not_checked=93

number_of_tested_true_connections=19

number_of_tested_false_connections=15

number_of_connection_setups_with_error=0

20140215

Problem: sympy doesn't recognize the validity of simple statements:

import sympy

x = sympy.Symbol('x') # from outputs

a = sympy.Symbol('a') # from outputs

b = sympy.Symbol('b') # from outputs

c = sympy.Symbol('c') # from outputs

out_lhs0=(x**2) + ((b/a)*x) + (c/a)

in_lhs0=(a*(x**2)) + (b*x) + c

feed0=a

>>> in_lhs0/feed0

(a*x**2 + b*x + c)/a

>>> out_lhs0

x**2 + b*x/a + c/a

>>> out_lhs0 == in_lhs0/feed0

False

20140215

How do I define success for this project?

When someone else learns something new as a result of using this tool.

The first user will either be a developer (someone accessing the xml database) or, more likely, a user accessing the content through a GUI.

Thus, although the content and framework are necessary, they are not sufficient -- a GUI is needed to make the tool user friendly.

The GUI should be introduced through a walkthrough. A video would be a good tutorial.

20140215

I repeatedly use the following functions, so these should be made Python functions:

convert statement_punid to array of symbol_punid

convert statement_punid to statement_latex

convert statement_punid to cas_sympy_LHS,cas_sympy_RHS

convert feed_tunid to feed_latex

convert feed_tunid to feed_sympy

convert feed_tunid to array of symbol_punid

convert symbol_punid to cas_sympy

20140214

XML tags currently in use:

****************************

inference rules xml:

"inference_rule_name" (string)

symbols xml

"name" (string)

"label" (integer)

statements xml

"statement_index" (integer)

feeds xml

"feed_label" (integer)

connections xml

"op_name" (string)

"op_label" (integer)

"statement_index" (integer)

"statement_label" (integer)

"feed_label" (integer)

comments xml

"applies_to_statement" (integer)

****************************

"inference_rule_name" and "op_name" are supposed to be the same for linking purposes

"statement_index" in statements xml is same as "statement_index" in connections

in connections xml, "op_label" and "statement_label" are temporary integers local to the connection_set.

op_label allows for duplicate use of the same inference rule on the graph.

statement_label allows for duplicate use of a statement_index in a tex document.

To be more clear, I'm eliminating "index" and "label" as descriptors. Instead, I'll use "tunid" and "punid" for temporary/permanent unique numeric identifier.

****************************

inference rules xml:

"inference_rule_name" (string) --> infrule_name

symbols xml

"name" (string) --> symbol_name

"label" (integer) --> symbol_punid

statements xml

"statement_index" (integer) --> statement_punid

feeds xml

"feed_label" (integer) --> feed_tunid

connections xml

"op_name" (string) --> infrule_name

"op_label" (integer) --> infrule_tunid

"statement_index" (integer) --> statement_punid

"statement_label" (integer) --> statement_tunid

"feed_label" (integer) --> feed_tunid

comments xml

"applies_to_statement" (integer)

****************************

20140213

Major tasks in priority order:

-implement CAS [completed 20140216]

-focus on getting a single inference rule to work in all cases [completed 20140215]

-make jargon consistent (remove "op_label" with "inference_rule", label versus index) [completed 20140214]

-command-line prompt

-web GUI

-add content

-better graph rendering

-SVG support

20140213

view existing graph

full graph or single connection_set

generate full graph

which connection_set?

generate connection_set graph

view existing connection_set PDF

which connection_set?

list existing inference rules

edit existing inference rule

create new inference rule

list existing connection_sets

edit existing connection_sets

which connection_set

which connection

which field to edit?

create new connection_set

set name

add new connection

use existing inference rule

which inference rule?

create new inference rule

20140213

fixed bugs:

-png graph now shows feeds

-no more static date in lib_physics_graph

-PDF generation works

extras:

-created bash script to test all Python scripts in bin

-modified tgz generator to detect date and svn automatically

20140213

algorithm for doing a derivation.

1) start by declaring initial equation

-declaration has no input statement

-declaration has no feeds

-declaration has one output statement

[repeat as needed]

2) apply an inference rule

-inference rule has at least one input statements

-inference rule has zero or more "feeds"

-inference rule has at least one output statement

[repeat as needed]

3) declare derivation finished

-declaration has at least one input statement

-declaration has no feeds

-declaration has no output statements

20131222

bugs:

in "def make_picture_from_latex" in "lib_physics_graph.py"

the date should not be statically set. It should be passed to the function as an argument

in "bin/build" the feeds probably aren't being done correctly.

For example, "multbothsidesby" is not getting the correct number of arguments in the .tex file

"op_name" should be "inference_rule_name"

20131222

previously re-factored "feeds" into separate database.

This broke "build_connections" and "create_pictures" scripts

Added a "build deployable tgz" shell script which works

A "test scripts" script would be useful to check that changes don't break functionality.

Currently not sure how to test correctness of scripts

20131124

wrote "generate_new_random_index" for each database

wrote "list_inference_rules" and "list_connection_sets"

created website

https://sites.google.com/site/physicsderivationgraph/

20131117

Removed from bin/build:

No longer requires "dvisvgm"

"dvisvgm" is from http://dvisvgm.sourceforge.net/

Removed from main README: links

SVG, Latex, GraphViz on WordPress:

http://e.metaclarity.org/wordpress-plugins/wprender/

http://e.metaclarity.org/142/rendering-tex-graphs-to-svg-in-wordpress/

Creating animations with graphviz

http://gromgull.net/blog/2011/02/creating-animations-with-graphviz/

20131110

reorganized structure closer to

https://en.wikipedia.org/wiki/Filesystem_Hierarchy_Standard

20131110

I realized I have two diverging objectives, and I was stuck at the fork since taking both seems insurmountable. The two projects are (1) enlarge the database of relations and (2) build a pleasant web interface which reads and can be used to add to the graph database.

My vision and strength is in building the database, not the GUI. How can I best spend my effort on this part?

There are two subtasks:

-developing/choosing a syntax to express the equations. Latex, Mathematica, ML, XML,

-determining what the audience is interested in getting from this work. What would motivate interest in this project by users and developers?

I think non-physicists and beginners are aware of a one or a few mathematical elements of physics. The most common is "E=mc^2". Although practically everyone is aware of it, few know how it's related to anything else. Undergrads in physics are aware of "F=ma" and "distance=rate*time" but there's not clear connection.

Thus, this project can demonstrate value by showing the relation between things people already have familiarity with.

A list of "common" equations in physics, in order of priority:

E=mc^2

F=ma

x=vt

Heisenberg uncertainty

diffusion

simple harmonic oscillator [done for particle in a box]

Maxwell's equations [done]

Schrodinger eq [done]

A second tier, but of interest:

creation/annihilation operators

superconductivity

Lorentz contraction/dialation

Boson/Fermion distributions

If I can show the relation between these in my database, that would cover much of the scope.

What I currently have in connections_database.xml by subdiscipline:

math basics:

quadratic_equation_derivation: for 2nd order polynomial, solve for roots

euler_equation_proof: \exp(i x) = \cos(x)+i \sin(x)

euler_equation_trig_sqrt: (\sin(x))^2 = \frac{1-\cos(2x)}{2}

euler_equation_trig_relations:

integration_by_parts: generic u,v

curl_curl_identity: used in E&M

example_of_Godel_problem: using a,b,c, make a false relation

variance_relation

physics basics:

frequency_relations: k=omega/v, lambda=v/f, T=1/f

quantum:

derivation_of_Schrodinger_Eq: ends up at {\cal H} \psi\left(\vec{r},t)\right) = i \hbar \frac{\partial}{\partial t}\psi(\vec{r},t)

particle_in_a_1D_box: starting from \frac{d^2}{dx^2} \psi(x) = -k^2 \psi(x), solve for \psi

quantum_basics_orthogonality:

quantum_basics_Hermitian_operators_have_realvalued_observables:

E&M:

maxwell_to_electric_field_wave_equation

electric_field_wave_equation_time_dependent_to_time_independent