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1 | !set |
1 | !set methtit=Cambio inverso de variable |
2 | !set methenv=ZZ QQ RR |
2 | !set methenv=ZZ QQ RR |
3 | !set methparmtype=parm function integrate, function, function |
3 | !set methparmtype=parm function integrate, function, function |
4 | !set |
4 | !set methhelp=Este método aplica el cambio inverso de variable \ |
5 |
|
5 | en una integración indefinida. |
6 | 6 | ||
7 | !if $wims_read_parm iswordof form check |
7 | !if $wims_read_parm iswordof form check |
8 | !goto $wims_read_parm |
8 | !goto $wims_read_parm |
9 | !endif |
9 | !endif |
10 | 10 | ||
11 | !exit |
11 | !exit |
12 | :form |
12 | :form |
13 |
|
13 | !set N=!linecnt $mtobj1 |
14 |
|
14 | !if $N>1 and $methsubstep=1 |
15 | :first |
15 | :first |
16 | !set methsubstep=2 |
16 | !set methsubstep=2 |
17 |
|
17 | Aplicar un cambio inverso de variable para: |
- | 18 | <p> |
|
18 | !read deduc/methparm.phtml 1 |
19 | !read deduc/methparm.phtml 1 |
- | 20 | </p> |
|
19 |
|
21 | !else |
20 | !bound methparm1 between integer 0 and $N default 1 |
22 | !bound methparm1 between integer 0 and $N default 1 |
21 | !if $methparm1=0 or $error!=$empty |
23 | !if $methparm1=0 or $error!=$empty |
22 | !goto first |
24 | !goto first |
23 | !endif |
25 | !endif |
24 | <input type="hidden" name="methparm1" value="$methparm1" /> |
26 | <input type="hidden" name="methparm1" value="$methparm1" /> |
25 | !set methsubstep=1 |
27 | !set methsubstep=1 |
26 | !set l=!line $methparm1 of $mtobj1 |
28 | !set l=!line $methparm1 of $mtobj1 |
27 | !set l=!item 2 to -1 of $l |
29 | !set l=!item 2 to -1 of $l |
28 | !set k=!mathsubst integrate= in $l |
30 | !set k=!mathsubst integrate= in $l |
29 | !set k=!declosing $k |
31 | !set k=!declosing $k |
30 | !set v=!item 2 of $k |
32 | !set v=!item 2 of $k |
31 | !set nvar=!item 1 of $newvariables |
33 | !set nvar=!item 1 of $newvariables |
32 |
|
34 | Cambio inverso de variable para \($l): poniendo<br/> |
33 | \($nvar = h($v) = ) |
35 | \($nvar = h($v) = ) |
34 | !read deduc/methparm.phtml 2,18 |
36 | !read deduc/methparm.phtml 2,18 |
35 | , on a |
37 | , on a |
36 | <div class="wimscenter"> |
38 | <div class="wimscenter"> |
37 | \($l = integrate(f(h($v))h'($v)d$v) = integrate(f($nvar)d$nvar)) , |
39 | \($l = integrate(f(h($v))h'($v)d$v) = integrate(f($nvar)d$nvar)) , |
38 | </div> |
40 | </div> |
39 | où |
41 | où |
40 | \(f($nvar) = ) |
42 | \(f($nvar) = ) |
41 | !read deduc/methparm.phtml 3,36 |
43 | !read deduc/methparm.phtml 3,36 |
42 | . |
44 | . |
43 |
|
45 | !endif |
44 | !exit |
46 | !exit |
45 | :check |
47 | :check |
46 |
|
48 | ker=!item 2 of $methparmobj1 |
47 |
|
49 | ker=!mathsubst integrate= in $ker |
48 |
|
50 | ker=!trim $ker |
49 |
|
51 | ker=!declosing $ker |
50 |
|
52 | !distribute items $ker into iker,ivar |
51 |
|
53 | vartest=!varlist $ivar |
52 |
|
54 | !if $ivar != $vartest |
53 | error=Fail |
55 | error=Fail |
54 | !exit |
56 | !exit |
55 |
|
57 | !endif |
56 | 58 | ||
57 |
|
59 | newvar=!item 1 of $newvariables |
58 |
|
60 | vv=!varlist nofn $methparm2 |
59 |
|
61 | vtest=!listcomplement $ivar,e,pi,euler in $vv |
60 |
|
62 | !if $vtest!=$empty |
61 | error=\(h($ivar)) |
63 | error=\(h($ivar)) debe ser una función de \($ivar) solamente. |
62 | !exit |
64 | !exit |
63 |
|
65 | !endif |
64 |
|
66 | hprime=!exec maxima diff($methparm2,$ivar); |
65 |
|
67 | !if $hprime=$empty |
66 | :bad_data |
68 | :bad_data |
67 | error=bad_data |
69 | error=bad_data |
68 | !exit |
70 | !exit |
69 |
|
71 | !endif |
70 |
|
72 | vv=!varlist nofn $methparm3 |
71 |
|
73 | vtest=!listcomplement $newvar,e,pi,euler in $vv |
72 |
|
74 | !if $vtest!=$empty |
73 | error=\(f($newvar)) |
75 | error=\(f($newvar)) debe ser una función de \($newvar) únicamente. |
74 | !exit |
76 | !exit |
75 |
|
77 | !endif |
76 |
|
78 | substed=!mathsubst $newvar=($methparm2) in $methparm3 |
77 |
|
79 | !read deduc/sub/checkzero ($substed)*($hprime)-($iker)\ |
78 | diff($methparm3,$newvar) |
80 | diff($methparm3,$newvar) |
79 |
|
81 | !distribute lines $out into ztest,difftest |
80 |
|
82 | !if $ztest=$empty or $difftest=$empty |
81 | !goto bad_data |
83 | !goto bad_data |
82 |
|
84 | !endif |
83 |
|
85 | !if $ztest!=yes |
84 |
|
86 | error=¡Fórmula incorrecta para el cambio de variable! |
85 | !advance penalty |
87 | !advance penalty |
86 | !exit |
88 | !exit |
87 |
|
89 | !endif |
88 | 90 | ||
89 |
|
91 | !read deduc/sub/simplify $methparm3\ |
90 | ($methparm3)*($newvar) |
92 | ($methparm3)*($newvar) |
91 |
|
93 | !distribute lines $out into newker,res |
92 |
|
94 | !if $newker=$empty or $res=$empty |
93 | !goto bad_data |
95 | !goto bad_data |
94 |
|
96 | !endif |
95 |
|
97 | !if strictintegrate iswordof $m_options and $difftest=yes |
96 |
|
98 | error=No está permitido poner una constante para \(f($newvar)). \ |
97 |
|
99 | Por favor, cambie el método. |
98 | !exit |
100 | !exit |
99 |
|
101 | !endif |
100 | 102 | ||
101 |
|
103 | !if $difftest=yes |
102 | newobject1=($res) |
104 | newobject1=($res) |
103 |
|
105 | !else |
104 | newobject1=integrate($newker,$newvar) |
106 | newobject1=integrate($newker,$newvar) |
105 |
|
107 | !endif |
106 |
|
108 | oldobject=0,1 |
107 |
|
109 | newobject0=$newvar=$methparm2 |
108 |
|
110 | methexp=\($newvar=$methparm2) |
109 |
|
111 | variables=$variables,$newvar |
110 | !exit |
112 | !exit |
111 | - |