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