Elements Distinctions

There are several math environment software products including Elements. Each has evolved to meet the requirements of its users. Some characteristics reflect the nature of the problems solved. Other characteristics are special performance options.

This is technical discussion about Elements software technologies and special characteristics. It may help the experienced user decide the suitability of Elements to his problem. For the typical problem, usually only a few characteristics are relevant. You may prefer a more general description.

Elements' distinct characteristics are:

  • Typed math objects: Scalar, Vector, Matrix, Polynomial, Hypermatrix, etc. Operations, conversions, and promotions between type combinations is handled by nested C++ virtual functions.
  • Polynomials are full-fledged data types that can be directly added, multiplied, convoluted, etc.
  • Polynomial representation has coefficients in ascending degree.
  • Hypermatrix whose elements are other objects.
  • Matrix subscripts are 0-based by default. Optionally subscripts can be 1-based.
  • Complex valued objects are column oriented to be consistent with their 2D vector character.
  • Complex valued literals can be abbreviated with easy-to-type syntax a&b, as well as traditional a+bi.
  • Array literals represented by syntax 1 2,3 4 with rows separated by a comma. Columns are separated by the Noop, or missing, operator.
  • Built-in function names are case insensitive.
  • User-defined function names are case sensitive.
  • User-defined function can be entered interactively or loaded from a script with any filename.
  • Most functions are templates. Each returns whatever data type naturally results from its input arguments.
  • Built-in units conversion with function Convert().
  • Built-in equation-of-state functions for common gases.
  • Re-designed as a Microsoft Windows application.
  • Each plot is embedded within text output. It is an OLE object that is in-place editable. It is re-sizeable.
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  • The plotting component assumes a GUI where plot attributes are changed using dialog boxes rather than hard-to-remember commands.
  • Geodesic computation.
  • Salient assemblage representation of bumpy geometry.
  • A computational option allows cumulative flops-estimate count instead of normal expression evaluation.
  • Optional prompt mode that allows user substituted values during evaluation.
  • Elements' document is fully-editable. Commands are entered on the bottom line. All other lines respond to conventional MS Windows editing methods.
  • A command is terminated with an explicit semicolon. This is consistent with most C-like languages. It allows multiple commands per line and any one command can span multiple lines.
  • Syntax is similar to standard JavaScript, e.g. M[2][1]=sin(0.5).
  • No syntactical difference between continuous functions and discrete (table of values) functions.
  • Evaluation results are not displayed after an assignment statement.
  • Multiple document types in one Elements workspace, i.e. a Windows MDI application. Within an Elements' document, the NewProblem statement clears all variables and starts a new problem.
  • Runs inside MS Internet Explorer 4.0 as an ActiveX document server.
  • Automatic download and installation over the Internet.
  • Since Elements' document is an OLE container, you can insert any OLE object such as a spreadsheet or typeset equation from Equation Editor.
  • On first encounter, each user statement is compiled into intermediate representation for faster subsequent execution.

These characteristics evolved during Elements' history since 1982.