'combine' 

The combine command is the true inverse of the expand command. combine attempts to apply trigonometric, exponential, logarithmic, and algebraic rules of arithmetic to combine terms in sums and products into a single term. The syntax is combine(expr). 

Examples follow. 

>	combine(ln(2)+ln(x));

 

(1.1)

 

>	combine(exp(2*x)*exp(-x));

 

(1.2)

 

>	combine(sin(x)*cos(y)+sin(y)*cos(x));

 

(1.3)

 

>

 

'assume' and 'assuming' 

These commands allow you to specify properties about variables or constants which Maple can then use in calculations. The assume command specifies properties which last until remove, while assuming only makes a specification for the current calculation.  

assume is entered on its own line. The syntax is assume(expr). When assuming is used, it is entered on the line of the calculation in question. The syntax is assuming(expr). 

Examples 

>	assume(a>0);

 

>	sqrt(a^2);

 

(2.1)

 

>	sqrt(b^2) assuming(b>0);

 

(2.2)

 

Notice that a has a tilde after it. This indicates that a has assumptions attached to it. The second assumption is essentially the same as the first, but b does not have permanent assumptions attached. 

>	sqrt(a^2);

 

(2.3)

 

>	sqrt(b^2);

 

(2.4)

 

These commands are both very useful. We will explore their use in some of the exercises. 

>

 

Exercises
 

1. Consider the following rational expression.
                                                                            
Transform this expression with Maple into
(a)   

(b)    

2. Consider the following rational expression.
                                                                           
Transform it into:
(a)   

(b)   

(c)   

(d)   
 

3. Consider the polynomial .
Transform it into:
(a)   

(b)   

(c)   
 

4. Consider the polynomial .
Transform it into:
(a)   

(b)   

(c)   

(d)    

5. Compute cos() and sin() under the assumptions that is
- an integer.
- an odd integer.
- an odd and positive integer less than 3. 

(Refer to the Maple help for further information on the assume command.)