HP Solve Equation Library application card

Hewlett-Packard Journal, June, 1991 by Eric L. Vogel

As the equation selection proceeded, we found that related equations were usually needed as a group, rather than independently (Fig. 3). While there are certainly instances where only one of the equations is needed, more often the entire set is used to find the value for a particular variable. To provide simplified access to related equations, we group them together under a single title, such as Linear Motion or Ohm's Law and Power, rather than forcing the user to return to the Equation Library to select each equation individually.

When we examined how a user typically interacts with a group of equations, we realized that the solution procedure is straightforward, but gets tedious as the number of equations and variables gets large. Here is the manual process for finding all the variables for a set of equations given that some of them are known:

Use the known variables to select an equation containing only one unknown.

Solve for the unknown.

Add the variable just calculated to the set of known variables.

Use the combined set of known and calculated variables to select another equation containing only one unknown.

Solve for the unknown.

Repeat this process until either all the unknowns have been found or as many unknowns as possible have been found from the given set of knowns.

To make using the equations more straightforward, we have automated this manual select-and-solve process by developing an extension to HP Solve called the Multiple Equation Solver (MES). The MES selects the appropriate equation to solve based on whether it has one remaining unknown, and then solves for that unknown using the same numerical root finder used by the HP Solve application. It tracks the variables that have been solved for, and uses different equations to calculate other unknowns as soon as there is enough information available.

The barrier to proper functioning of the MES was identifying whether a variable is known or unknown. The existence of the variable alone is not sufficient - after a solution has been determined, all the variables exist. The key underlying principle is that the state of a variable (known or unknown) is independent of the value of the variable. The MES uses this state information to select the equations to be solved and the order in which to solve them.

Displaying Variable States

The MES user interface is similar to that of HP Solve. A menu of variable names is displayed in the menu key area at the bottom of the display. The appearance of the menu keys is used to distinguish the MES state information. An extra key, ALL, appears at the end of the menu.

Initially all the menu keys are white with black letters (like HP Solve), indicating that all of the variables are unknown (Fig. 4a). Typing a value and pressing a menu key stores the value in that variable and changes the key to black with white letters, indicating that the variable is known (Fig. 4b).

Pressing the ALL key solves for all remaining variables, or as many as can be found from the given set of knowns.