Use the Simplify > Basic command, click on the icon on the command toolbar, or press Ctrl+B to numerically and algebraically simplify mathematical expressions.


This command simplifies the currently highlighted expression or subexpression, and then displays the resulting expression in the algebra window.  The new 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 Simp(#n).  If only a subexpression was highlighted, the annotation is of the form Simp(#n’).  Also the computation time required to simplify the expression is displayed on the status line of the algebra window next to the clock icon.


If you have no interest in seeing the unsimplified version of an expression, you can enter and simplify an expression in a single step using the Author > Expression commandFJQ5GW.  After entering an expression on the expression entry line, click on the Simplify button or press Alt+S instead of clicking on the OK button.  Then the new expression will be simplified and only the result displayed.


If you want to see both the input and the simplified result displayed on a single line, enter the expression on the expression entry line followed by an equal sign (=) and click on the OK button.  Derive will then display an equation whose left side is the unsimplified form of the expression and whose right side is its simplified form.


The Simplify > Basic command algebraically simplifies mathematical expressions.  The following are some of the simplifications this command performs:

•        It combines numeric subexpressions.  For example, 2·y·3 simplifies to 6·y.

•        It collects similar factors of a product.  For example, x²·y·x simplifies to x³·y.

•        It collects similar terms of a sum.  For example, 3·x+7+x simplifies to 4·x+7.

•        It employs identities involving 0.  For example, x+0 simplifies to x.

•        It employs identities involving 1.  For example, 1·x simplifies to x.

•        It distributes integer exponents over a product.  For example,

(3·x·y^3)^2

simplifies to

   2  6 
9·x ·y  

•        It cancels polynomial greatest common divisors.  For example,

(x^2 + 2·x·y + y^2)/(x^2 - y^2)

simplifies to

 x + y  
——————— 
 x - y  

•        It expands products and integer powers of polynomials to the extent that it may eliminate a variable or reduce the degree in a variable.  For example,

(x + 1)^2 - x^2

simplifies to 2·x+1.

•        It puts sums of expressions over a common denominator to the extent that it may eliminate a variable or reduce the degree in a variable.  For example,

2·x/(x^2 - 1) - 1/(x - 1)

simplifies to 1/(x+1).


Some of the classes of mathematical expressions that Derive can simplify are:


•        Univariate  polynomials composed of one variable, rational numbers, addition, subtraction, multiplication, and integer powers;

•        Multivariate polynomials similarly composed but having more than one variable;

•        Rational expressions composed of polynomials and ratios of polynomials;

•        Extended rational expressions composed of rational expressions and fractional powers of variables;

•        Algebraic expressions composed of rational expressions and fractional powers of rational and algebraic expressions; and

•        Elementary transcendental expressions composed of algebraic expressions and elementary functions (exponential, logarithmic, trigonometric, hyperbolic, and their inverses).


An expression in sufficiently simple form has no superfluous variables, roots, or functions, and no reducible polynomial degrees.  An expression not in sufficiently simple form may mislead you about the dependence and qualitative behavior of the expression.  For example, a result would be highly misleading if it appeared to be quadratic in a variable when it was actually linear.


The primary goal of the Simplify > Basic command is to transform expressions into a sufficiently simple form.  To accomplish this, it converts expressions to a normal form that automatically reduces most expressions to a sufficiently simple form.


Beyond the class of extended rational expressions, it is impractical and often impossible to guarantee a sufficiently simple form.  The Simplify > Basic command tries hard nonetheless, and often succeeds even for these more complicated expressions.


The secondary goal of the Simplify > Basic command is to transform expressions as little as necessary to achieve the primary goal.  In support of this, the normal form is as flexible as practical while still ensuring a sufficiently simple form for most expressions.  Thus the normal form often permits expressions to remain unexpanded, unfactored, or not put over a common denominator.  


Despite its flexibility, the normal form can force transformations that do not yield a class simplification.  Therefore, Derive makes it easy to simplify just part of an expression.  Before issuing the Simplify > Basic command, highlight just the subexpression that you want simplified.  The result is a copy of the whole expression in which only the highlighted portion is simplified.


Often simplifying an entire expression results in an expression that does not annihilate a variable or reduce the degree.  Whereas, simplifying just the subexpression results in a simpler, more compact form of the expression.


The single quote mark in the annotation of an expression indicates that the expression was the result of simplifying a subexpression.


Depending on the expression, it can take a long time to do the expansions and canceling of common divisors, etc. necessary to simplify an expression.  After a few seconds, a Calculation Progress dialog box will appear indicating the following:

•        the expression being simplified;

•        the time spent thus far simplifying the expression; and

•        the percentage of memory being used to simplify the expression.  Note that this percentage is only updated periodically when Derive has to recycle memory for reuse.


Click on the dialog box's Abort button or press the Esc key to abort a Simplify > Basic command that is taking too long.  You can then try simplifying only portions of the expression.  For example, you can separately simplify complicated numerators and denominators.  The resulting expression may be incompletely simplified, but it is better than no simplification at all.


Simplification can also require a large amount of computer memory to store intermediate results.  If space is exhausted while simplifying an expression, the warning message Memory Full is displayed on the message line, an error beep is sounded, and no result is returned.


If the Simplify > Basic command generates a large expression that is not of interest, use the Edit > Delete commandBAGNGA to save computer memory and screen space.


Other Simplify commandsSimplify_commands 

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