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International Futures Help System

Understanding the Equations

As a general rule, the equations closely follow the computer code. Insofar as possible without confusion, variable and parameter names here are the same as those in the computer program, but in a few cases equation names differ to enhance readability. Computer code shows a single computed variable on the left and one or more input variables and parameters on the right. In fact, computer code frequently shows the computed variable on both the left and the right hand side, which is NOT standard mathematical equation form and a few traditional purists have difficulty understanding this (as well as preferring non-mnemonic single letter variable names and Greek symbols to much more intelligible computer-based variable names). As an appropriate accommodation, this documentation sometimes uses asterisks to distinguish different values of the same variable name on left and right-hand sides of equations.

IFs has multiple modules: population, economic, agriculture, energy, and socio-political. An environmental "module" is scattered across other modules, especially agriculture and energy. Equations are presented by module and cross references in the documentation of each module indicate linkages.

IFs is a recursive dynamic system and equation sequence is therefore important. This text presents equations in largely the same sequence as in the computer program. Program flow exits from and returns to each module up to three times each time step (year), however, and it would break up discussions of module too much if we were to follow computational flow slavishly. Moreover, to facilitate understanding this documentation sometimes presents the key equations of a module or a section of one first, with subsequent explanation of the compu"tational procedures for variables used therein (thereby deviating further from actual computation sequence). Equation form here is the same as in the computer program, including the presentation of a single "computed" variable on the left side of the equal sign.

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