Subversion Repositories wimsdev

!set methtit=Direct change of variable

!set methenv=ZZ QQ RR

!set methparmtype=parm function integrate, function

!set methhelp=This method applies the change of variable on an indefinite\

integral.

!if $wims_read_parm iswordof form check

 !goto $wims_read_parm

!endif

!exit

:form

 !set N=!linecnt $mtobj1

 !if $N>1 and $methsubstep=1

  :first

  !set methsubstep=2

  Apply a change of variable for: <p>

  !read deduc/methparm.phtml 1

 !else

  !bound methparm1 between integer 0 and $N default 1

  !if $methparm1=0 or $error!=$empty

   !goto first

  !endif

  <input type=hidden name=methparm1 value=$methparm1/>

  !set methsubstep=1

  !set l=!line $methparm1 of $mtobj1

  !set l=!item 2 to -1 of $l

  !set k=!mathsubst integrate= in $l

  !set k=!declosing $k

  !set v=!item 2 of $k

  !set nvar=!item 1 of $newvariables

  Change of variable:

   <div class="wimscenter">

 	\($l = integrate(f($v),$v) = integrate(f(h($nvar))h'($nvar),$nvar)) ,

  </div>

  with

  \($v = h($nvar) = )

  !read deduc/methparm.phtml 2,36

.

 !endif

!exit

:check

 ker=!item 2 of $methparmobj1

 ker=!mathsubst integrate= in $ker

 ker=!trim $ker

 ker=!declosing $ker

 !distribute items $ker into iker,ivar

 vartest=!varlist $ivar

 !if $ivar != $vartest

  error=Fail

  !exit

 !endif

 newvar=!item 1 of $newvariables

 vv=!varlist nofn $methparm2

 vtest=!listcomplement $newvar,e,pi,euler in $vv

 !if $vtest!=$empty

  error=\($methparm2) must be a function of \($newvar) only.

  !exit

 !endif

 diff=!exec maxima diff($methparm2,$newvar);

 !if $diff=$empty

  :bad_data

  error=bad_data

  !exit

 !endif

 inv=!exec maxima solve($ivar=$methparm2,$newvar);

 inv=!declosing $inv

 n=!itemcnt $inv

 inv2=!nospace $inv

 eq==

 !if $n!=1 or +++**$newvar$eq notin +++**$inv2

  error=Impossible to find the inverse function of $methparm2, which is\

 	necessary for future substitution:\

	use the reverse change of variable.

  !exit

 !endif

 substed=!mathsubst $ivar=($methparm2) in $iker

 !read deduc/sub/checkzero diff(($substed)*($diff),$newvar)

 difftest=$out

 !read deduc/sub/simplify ($substed)*($diff)\

	($substed)*($diff)*$newvar

 !distribute lines $out into newker,ktest

 !if $newker=$empty or $ktest=$empty or $difftest=$empty

  !goto bad_data

 !endif

 !if strictintegrate iswordof $m_options and $difftest=yes

  error=This change of variable is not allowed for this environment.\

	Please change the method.

  !exit

 !endif

 !if $difftest=yes

  newobject1=$ktest

 !else

  newobject1=integrate($newker,$newvar)

 !endif

 newobject0=$inv

 oldobject=0,1

 methexp=\($ivar=$methparm2)

 variables=$variables,$newvar 

!exit