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DELIB       Requirements

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DELIB: Requirements

These are the DELIB requirements.

  1. Overall
  2. DELIB web site
  3. Inputs to the DELIB system
  4. Outputs from the DELIB system
  5. DELIB Database
  6. DELIB Code
  7. Use of LaTeX in DELIB
  8. Definitions
    1. Overall
      1. Use of the DELIB site shall be free to users.
      2. The site may grow to incorporate other aspects of differential equations.
    2. DELIB web site
      1. There shall be a FAQ.
      2. There shall be a requirements document.
      3. There shall be an advisory board and a description of them.
      4. There shall be a press release page.
      5. There shall be a user guide.
      6. There shall be a contact information page.
      7. There shall be a facility to review user input that will get incorporated into the DELIB database.
      8. There shall be a "chat" facility to discuss all equations
      9. There will be a facility for correcting errors on any output.
      10. External links shall regularly be verified for availability
      11. Color, and other special effects, shall be used only when appropriate.
      12. The CSS and XTML will be validated.
        13. !! PUT IN URL !!
      13. The python code shall be written to the python standards in !! REPHRASE AND PUT IN URL !!
      14. The site will meet accessibility criteria (i.e., Bobby).
      15. To make this facility accessible to people with disabilities, DELIB will conforms to W3C's "Web Content Accessibility Guidelines 1.0", available at http://www.w3.org/TR/1999/WAI-WEBCONTENT-19990505, level A.
      16. DELIB will embed Dublin Core metadata. in the relevant web pages (see dublincore.org)
      17. The languages used in the web site shall be freely available: MySQL (database), xHTML, css, php, python (for cgi), png (for graphics)
    3. Inputs to the DELIB system
      1. Inputs shall be by both ascii files and via the web interface.
      2. No user input shall be visible to DELIB system users without DELIB review and approval.
    4. Outputs from the DELIB system
      1. There shall be several types of outputs presented to users by the system
      2. A single output may contain more than one output type
      3. Types of output include:
        1. Static text; such as the FAQ, advisory board information, how to use instructions, etc
        2. A form with which a differential equation systems DELIB number may be entered
        3. A form with which a differential equation systems name may be entered
        4. A form with which differential equation systems features may be entered
        5. Common information including:
          1. A graphic for DELIB
          2. Links to pages in the DELIB site: home page, properties form, FAQ, advisory board, how to use, etc
        6. A list of references
        7. An expandable table of contents
        8. A form for contacting DELIB.
        9. A list of differential equation systems
        10. A single differential equation system in detail containing its features
          1. allow input/modification of BC/IC and re-submittal
          2. allow input/modification of features and re-submittal
    5. DELIB Database
      1. Information in the database shall be maintained with a time stamp
      2. Information in the database shall be maintained so that previous versions may be identified
      3. The database shall be implemented in MySQL
      4. The database shall be backed up regularly
      5. The database shall be normalized
      6. The database shall contain standardized information for each equation.
      7. The database shall contain special information about some equations (for example, hand edited information about very popular equations such as Airy's equation may be included.)
    6. DELIB code
      1. All code shall be documented.
      2. The system shall have a program for converting from common expressions (in representations such as LaTeX or maybe Mma) into a unambiguous LaTeX-based representation. This facility shall:
        1. Handle sub-scripted functions and variables such as "x_a" and "x_{alpha_2}"
        2. Handle greek letters such as "\alpha"
        3. There shall be error checking to identify problems such as \frac{d^2 y}{d x^4}
        The results of this program shall NOT be guaranteed to be correct.
      3. There shall be a program, usable stand-alone and also through a web interface, that determines equation features for an input equation. Input equations may be in some subset of: ascii, LaTeX, LaTeX with the special DELIB macro package, Mathematica, and MathML. The results of this program shall NOT be guaranteed to be correct.
    7. Use of LaTeX in DELIBs
      1. The underlying storage of expressions shall be in LaTeX modified to contain semantic information.
      2. There shall be a DELIB macro package that facilitates writing differential equations in LaTeX. This package shall include:
        1. Names for operations such as divergence, curl, Laplacian, etc
        2. Options for printing differential equations in two-dimensional or one-dimensional form.
        3. Options for printing differential equations with properties indicated "graphically".
        4. Specific macros with names:
          1. \InvisibleMultiplicationSign
          2. \Derivative[optional order]{indep var}{dep var}
          3. \PartialDerivative[optional order]{indep var}{dep var}
    8. Definitions
      1. A differential equation system shall be a collection of one or more differential equations and/or algebraic equations.
        1. Note that constraints shall be treated as algebraic equations.
        2. Note that a differential equation system may consist of a single equation.
      2. A differential equation system shall include the following features (if known for this system and to DELIB):
        1. name of the differential equation system
        2. a short word summary of the differential equation system type (i.e., "quasilinear equation in 3 independent variables")
        3. time stamp information (date of creation and modifications)
        4. a history of the content (with the version at each date)
        5. solution
        6. references to print and electronic publications (including the information source)
        7. references to print publications shall be in BibTeX format (like www.citeseer.com)
        8. initial and/or boundary conditions
        9. meta data
        10. characterization (linear, quasi-linear, sclae invariant, Riccati equation, Bernoulli equation, ODE, PDE, etc)
        11. other relevant details (existence of a Lie group, genreators for a Lie group, known asymptotics, etc)
        12. links to other differential equation systems
        13. links to appropriate numerical/graphical solvers
        14. key words
        15. links to the differential equations and algebraic equations making up the differential equation system
        16. features of all the differential equations and algebraic equations making up the differential equation system; and statistics of those features (such maximal degree or maximal order)
        17. the number of differential equations and algebraic equations making up the differential equation system
        18. the number of dependent and independent variables and their name(s)
        19. a representation of the system in LaTeX, Mma, MathML, etc
      3. Features of a differential equation or algebraic equation shall include:
        1. name of the equation
        2. a short word summary of the differential equation system type (i.e., "quasilinear equation in 3 independent variables")
        3. number of terms in the equation
        4. order
        5. degree
        6. lists of constants in the equations (such as "2" or "e",)
        7. lists of special properties of the equation (delay equation, etc)
        8. lists of special functions appearing in the equation (sine, cosine, etc)
        9. list of function composition pairs (powers of sines, cosines of linear functions, etc)
        10. lists of operators appearing in the equation (powers, square roots, divergence, curl, Laplacian, etc)
        11. lists of mathematical types appearing in the equation (scalars, vectors, matrices, tensors, etc)
        12. links to related or transformed equations
        13. an image of the equation
        14. an image of the equation showing the features (perhaps functions in different colors, perhaps show implicit multiplication signs, etc)
        15. a representation of the equation in LaTeX, Mma, MathML, etc
      4. Two equations (and their related IC/BC) shall be related if
        1. the equations are identical (i.e., disregarding the BC/IC)
        2. the BC/IC are identical (i.e., disregarding the equations)
        3. no BC/IC are given for either equation and the equations differ in one term
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