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<center><h3>Random parameters in an interactive exercise</h3></center> <p>

The use of random parameters makes your exercise much more interesting,

because it will be a different exercise each time it is requested.

<p>

For example, the following line defines a parameter under the name of

<font color=blue><b>x1</b></font>, whose value will be a random integer

between -10 and 10 (inclusive):

<pre>

\integer{x1=random(-10..10)}

</pre>

This random parameter may then be called by the word

<b><tt>\x1</tt></b>, in the statement, the replis, the hint and the solution.

That is, each word <tt>\x1</tt> in these texts will be replaced

by the random value of the parameter. This substitution will also take

place in the definitions of other parameters which follow that of x1.

<p>

Suppose now that you have entered

<pre>

\integer{x1=random(-10..10)}

\integer{y1=\x1+3}

</pre>

in the field of the definition of parameters, and the question

<pre>

Compute the multiplication of \x1 by \y1.

</pre>

in the statement of the exercise. Suppose that for a certain request of

the exercise, a random value <font color=red>-7</font>

is attributed to \x1. Then the following parameter \y1 will take the value

-4, and the statement of the exercise will be presented under the form<p>

<center>Compute the multiplication of -7 by -4.

</center> <p>

You may then define a numerical reply in the name of <tt>The product</tt>,

having for the good solution <tt>(\x1)*(\y1)</tt>. (Remark that here

the parentheses are necessary, because the substitution is done literarily.)

<a name=list></a>

!endif

<p>$table_header

<caption>Some other examples of parameters

!href cmd=help&special_parm=$special_parm,oefparm#list [complete list]

</caption>

$table_hdtr<th>Definition<th>Effect

$table_tr<td><tt>\real{x=random(-5..5)}</tt>

    <td>\x will be a random real number<br>between -5 and 5

$table_tr<td><tt>\real{a=random(-5,-3,0.3,4)}</tt>

    <td>\a will be a real number taken randomly<br>among -5,-3,0.3 and 4

$table_tr<td><tt>\complex{z=(1+2*i)^3}</tt>

    <td>\z will be the complex number (1+2*i)^3

$table_tr<td><tt>\text{sign=random(+,-)}</tt>

    <td>\sign will be a random sign: + ou -

$table_tr<td><tt>\integer{n=3*exp(\a)}</tt>

    <td>\n will be the closest integer to 3*e<sup>\a</sup> <br>(it depends on

    the value of \a)

$table_tr<td><tt>\function{f=random<br> (x^2+1,sin(x),log(x))}</tt>

    <td>\f will be a random function: either x^2+1,<br>or sin(x), or

    log(x)

$table_tr<td><tt>\real{a=evalue(x^2+sin(y),x=3,y=4)}</tt>

    <td>Evaluation of the function x^2+sin(y),<br>

    for x=3, y=4

$table_tr<td><tt>\real{r=solve(x^3-3*x+1,x=0..1)}</tt>

    <td>\r will the the simple root of x^3-3x+1 between 0 and 1

$table_tr<td><tt>\function{h=simplify(x^5*y^3*x^2/y)}</tt>

    <td>Simplified expression: x<sup>7</sup>y<sup>2</sup>

$table_tr<td><tt>\function{g=diff(sin(x)+cos(y),x)}</tt>

    <td>\g will the the derivative of sin(x)+cos(y) with respect to x

$table_tr<td><tt>\function{F=int(x^2+3*x+1,x)}</tt>

    <td>\F will an antiderivative of x^2+3*x+1,<br>

     the constant term being not garanteed to be always the same

!!$table_tr<td><tt>\function{F=int(t^2+3*t+1,t=1..x)}</tt>

!!    <td>\F will the antiderivative of x^2+3*x+1 with g(1)=0

$table_tr<td><tt>\real{a=int(t^2+3*t+1,t=0..1)}</tt>

    <td>\a will the numerical integral of x^2+3*x+1 from 0 to 1

$table_tr<td><tt>\text{f=htmlmath(2*x^2+3*x)}</tt>

    <td>\f will be rendered in html as: 2x<sup>2</sup>+3x

$table_tr<td><tt>\text{f=texmath(2*x^2+3*x)}</tt>

    <td>\f will be the TeX source for the expression.

$table_tr<td><tt>\integer{n=items(a,b,c,d,e,f)}</tt>

    <td>\n will be the number of items (here it is 6) in the list

     {a,b,c,d,e,f}

$table_tr<td><tt>\text{i=item(3,a,b,c,d,e,f)}</tt>

    <td>\i will be the item number 3 of the list

     {a,b,c,d,e,f} (hence c).

$table_tr<td><tt>\text{s=shuffle(6)}</tt>

    <td>\s will be a list of 6 integers 1,2,...,6, in random order.

$table_tr<td><tt>\text{s=shuffle(a,b,c,d,e)}</tt>

    <td>\s will be the letters {a,b,c,d,e} in random order.

$table_tr<td><tt>\matrix{m=1,2,3<br>4,5,6<br>7,8,9}</tt>

    <td>\m will be the matrix of 3 rows and 3 columns.

$table_end <p>

Conditional parameters: You may write<p>

<tt>\text{ttt=_condition?_def1}</tt> or <br>

<tt>\text{ttt=_condition?_def1:_def2}</tt>

<p>

In this case, <tt>ttt</tt> will be set to <tt>_def1</tt> if

<tt>_condition</tt> is true, or to <tt>_def2</tt> otherwise (in the second

syntax).

!href target=wims_mhelp cmd=help&special_parm=if List of conditions

<p>

The relative positionning of the definition and the statement is important:

if a variable is defined AFTER the statement, the evaluation of the variable

will take place only AFTER the user has replied to the question. In this

case, the definition may involve user replies, via <tt>\reply1</tt>,

<tt>\reply2</tt>, etc. And the variable can be used in solutions, testing

conditions or feedbacks.