GrafEq is an exceptional tool for exploring mathematics. As an introduction, here are some characteristics underlying the design of GrafEq:

• Mathematical
  Algebraic specifications are accepted in a broad variety of intuitive formats. For instance, a linear equation can be entered in the form y = mx + b, (y-k)/(x-l) = m, or ax + by + c = 0.
• Honest
  Any inaccuracy is explicitly revealed. For instance, although a pixel is very small, it is still an area rather than a point; therefore, the ‘coordinates’ of a pixel are reported using a range of values, such as (5.210±0.002, 17.001±0.002).
• Valid
  Graphs plotted are correctly. For instance, the graph of y<=sqrt(16-x²) differs from the graph of y>!sqrt(16-x²), because ‘<=’ is not equivalent to ‘>!’.
• Reliable
  No solutions will be missed: A pixel is off only if it contains no solutions at all; it stays on if it may possibly contain one or more solutions for the graph’s active relations. Extraneous solutions are eliminated when graphing is complete. The program can even use multiple colours to distinguish the pixels that have been proven to contain solutions, the pixels that have been proven to not contain solutions, and the pixels that are currently undecided.

  Hint: A closed and open version of a relation will often have identical graphs on the computer’s monitor. For example: the graph of x<5 will be identical to that of x<=5 unless the edge x=5 falls right between two adjacent pixels.

• Multi-faceted
  Each GrafEq graph can be presented in four forms:
  • Symbolic - an algebraic definition, typseset using mathematics notation, and presented in one or more algebraic relation windows. (Each relation can contain one or more constraints, and each constraint can be an equation, an inequality, a set description, or a conditional definition.)
  • Structural - a flow chart, or tree interpretation, presented in one or more structural relation windows. (Each relation is associated with an algebraic window and a structural window.)
  • Graphical - a cartesian or polar representation, presented in one or more view windows.
  • Printed - physical copies can be printed directly from GrafEq by means of its page editing window, or indirectly from other programs such as wordprocessors or drawing applications by first copying the relations and/or graph views from GrafEq, and then pasting into the other program.