Use the Simplify > Display Step command, click on the icon on the command toolbar, or press Ctrl+D to show the steps in the simplification of mathematical expressions and the transformation rules justifying the steps.


This command performs the next step in the simplification of the currently highlighted expression or subexpression, and then displays the resulting expression in the algebra window.  The expression is highlighted and has its own #n label number, where n is a positive integer.  Its annotation is displayed on the status bar and is of the form Step(#n).  If only a subexpression was highlighted, the annotation is of the form Step(#n’).


Also, if Display Rules mode is on, immediately before the result, a new text object is created showing the transformation rule that was applied.  Use the Display Rules check boxDisplay_Rules_mode of the Options > Mode Settings > Simplification command19_L5FP to turn Display Rules mode on or off.


Repeatedly issue the Simplify > Display Step command to display successive steps in the simplification of an expression.  At any time you can issue a Simplify > Basic commandBQ.NIL to skip the remaining steps and obtain a completely simplified result.  For example, try step-simplifying

DIF(SIN(a·x)^2/x, x)


Derive simplifies expressions in two phases:  A reduction phase and a restoration phase.  These phases become apparent to the user when expressions are step-simplified.  For example, 

LN(2*x)

step-simplifies to

LN(x) + LN(2)

which in turn step-simplifies to

LN(2*x)

Although futile in this case, the first step above is a reduction phase transformation that allows for cancellations and collections to occur with other expressions.  The second step is a restoration phase transformation that produces a more compact result.  Note that when LN(2*x) is just simplified, it looks like nothing happens since the two transformations cancel each other out.


Since it has no meaning in the context of iterative programming, step-simplification is disabled within the scope of PROG and LOOP constructs in user-defined functions.  Instead the new DISPLAY and WRITE function can be used within user-defined functions to display intermediate values during the execution of Derive programs (for details, see Programming FunctionsProgramming_Functions).


You can try stepping through the simplification of any expression, however some or all of the intermediate steps may not be displayed.  Also, some algorithms (for example integer, polynomial, and matrix factoring) are not amenable to step-simplifying, since there are no equivalent intermediate steps to display.


An alternative to the Simplify > Display Step command is to turn on Display Steps mode using the Display Steps check boxDisplay_Steps_mode of the Options > Mode Settings > Simplification command19_L5FP.  In this mode the steps resulting from all simplify commands are displayed.  


Other Simplify commandsSimplify_commands 

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