d_{x}[ sin-e[n](x) ] = d_{x}[ e^{nx}·sin(x) ] = ...
... n·sin-e[n](x)+( e^{2nx}+(-1)·( sin-e[n](x) )^{2} )^{(1/2)}
d_{y}[ e[n]-sin(y) ] = ...
... ( 1/( ny+( e^{2n·e[n]-sin(y)}+(-1)·y^{2} )^{(1/2)} ) )
f(x) = ( n·sin-e[n](y)+cos-e[n](y) )·d_{x}[y]
int[ f(x) ] d[x] = e^{ny}·sin(y)
int[ f(x) ] d[x] = sin-e[n](y)
e[n]-sin( int[ f(x) ] d[x] ) = y(x)
d_{x}[ sin-arc[n](x) ] = d_{x}[ x^{n}·sin(x) ] = ...
... (1/x)·( n·sin-arc[n](x)+x·( x^{2n}+(-1)·( sin-arc[n](x) )^{2} )^{(1/2)} )
d_{y}[ arc[n]-sin(y) ] = ...
... arc[n]-sin(y)·( 1/( n·y+arc[n]-sin(y)·( ( arc[n]-sin(y) )^{2n}+(-1)·y^{2} )^{(1/2)} ) )
f(x) = (1/y)·( n·sin-arc[n](y)+y·cos-arc[n](y) )·d_{x}[y]
int[ f(x) ] d[x] = y^{n}·sin(y)
int[ f(x) ] d[x] = sin-arc[n](y)
arc[n]-sin( int[ f(x) ] d[x] ) = y(x)
mucho [o] muchos
mucha [o] muchas
poco [o] pocos
poca [o] pocas
mult [o] mults
multa [o] multes
poc [o] pocs
poca [o] poques
multotzok [o] multotzoks
multotzak [o] multotzaks
pocotzok [o] pocotzoks
pocotzak [o] pocotzaks
mult-bicup-çí [o] mult-bicup-çís
mult-bicup-çuá [o] mult-bicup-çuás
poc-bicup-çí [o] poc-bicup-çís
poc-bicup-çuá [o] poc-bicup-cuás
és-de-puá mult-bicup-çí catalán.
és-de-puá poc-bicup-çí catalán.
ha muerto [o] está muerta
ha molido [o] está molida
ha mort [o] està morta
ha molit [o] està molida
ha-de-tek mortu-dut [o] està-de-tek morta-dat
ha-de-tek molitu-dut [o] està-de-tek molita-dat
ha-de-puá mortu-dom [ mort ] [o] està-de-puá morta-dam [ morta ]
ha-de-puá molitu-dom [ molit ] [o] està-de-puá molita-dam [ molita ]
d_{t}[z(t)] = a·h^{m+1}+b·( n^{n+1}+(-1)·y^{n+1} )^{( (m+1)/(n+1) )}
z(t) = ( (-1)·( cos[h^{m+1},y^{n+1}](at) )^{[o(t)o](m+1)}+( sin[h^{m+1},y^{n+1}](bt) )^{[o(t)o](m+1)} )
h(t) = sin[h^{m+1},y^{n+1}](at)
y(t) = sin[h^{m+1},y^{n+1}](bt)
d_{tt}^{2}[y(t)] = (-1)·qg+2F·( y/( x^{2}+y^{2} )^{(1/2)} )
d_{t}[y(t)]^{2} = (-1)·qgy+2F·( x^{2}+y^{2} )^{(1/2)}
d_{t}[z(t)]^{2} = (-1)·qgh+2F·( x^{2}+y^{2} )^{(1/2)}
y(t) = norm[(z(t),h(t))-->y(t)][ ( (-1)·( cosh[h,y^{2}]( qg·t ) )+( sinh[h,y^{2}]( 2F·x^{3}·t ) ) )^{[o(t)o](1/2)} ]
( x^{2}+y^{2} )^{(1/2)} = x^{4}·( 1+(y/x)^{2} )^{(1/2)}
d_{tt}^{2}[x(t)] = (-1)·kx+2F·( x/( y^{2}+x^{2} )^{(1/2)} )
d_{t}[x(t)]^{2} = (-1)·(1/2)·kx^{2}+2F·( y^{2}+x^{2} )^{(1/2)}
d_{t}[z(t)]^{2} = (-1)·(1/2)·kh^{2}+2F·( y^{2}+x^{2} )^{(1/2)}
x(t) = norm[(z(t),h(t))-->x(t)][ ...
... ( ( cosh[h^{2},x^{2}]( (1/2)·k·t ) )+( sinh[h^{2},x^{2}]( 2F·y^{3}·t ) )^{[o(t)o](1/2)} )^{[o(t)o](1/2)} ...
... ]
funciones elípticas:
( cos[n](t) )^{n+1}+( sin[n](t) )^{n+1} = n^{(n+1)}
( cos[p](t) )^{p+1}+( sin[q](t) )^{q+1} = ( (p+q)/2 )^{((p+1)/2)+((q+1)/2)}
( sin[p](t) )^{p+1}+( cos[q](t) )^{q+1} = ( (p+q)/2 )^{((p+1)/2)+((q+1)/2)}
d_{t}[sin[p](t)] = cos[p](t)
d_{t}[sin[q](t)] = cos[q](t)
d_{t}[cos[p](t)] = (-1)·sin[p](t)
d_{t}[cos[q](t)] = (-1)·sin[q](t)
{
a = 1;
b = 1;
for( k = 1 ; k [< n ; k++ )
{
c = a+b
b = a
a = c
escriure(a);
escriure(b);
}
}
{
a = not(1);
b = not(1);
for( k = not(1) ; k >] not(n) ; k-- )
{
not(c) = not(a)+not(b)
not(b) = not(a)
not(a) = not(c)
escriure(not(a));
escriure(not(b));
}
}
not(b) = a:
{
mov bx,a
mov ax,[bx]
mov bx,b
mov dx,ax
not dx
mov [bx],dx
}
not(b) = not(a):
{
mov bx,a
mov ax,[bx]
not ax
mov bx,b
mov dx,ax
not dx
mov [bx],dx
}
b = a:
{
mov bx,a
mov ax,[bx]
mov bx,b
mov dx,ax
mov [bx],dx
}
b = not(a):
{
mov bx,a
mov ax,[bx]
not ax
mov bx,b
mov dx,ax
mov [bx],dx
}
a_{n} = a_{n+(-1)}+a_{n+(-2)}
a_{1} = a ==> ...
... a_{6k+1} = (4k·11^{k+(-1)}+1)·a+(4k·(k+1))·6^{k+(-1)}·b
a_{2} = b ==> ...
... a_{6k+2} = (4k·(k+1))·6^{k+(-1)}·a+(4k·(3^{3(k+(-1))}+2)+1)·b
a_{3} = a+b ==>
a_{4} = a+2b ==>
a_{5} = 2a+3b ==>
a_{6} = 3a+5b ==>
a_{7} = 5a+8b
a_{8} = 8a+13b
a_{9} = 13a+21b
a_{10} = 21a+34b
a_{11} = 34a+55b
a_{12} = 55a+89b
a_{13} = 89a+144b
a_{14} = 144a+233b
a_{n} = a_{n+(-1)}+(-1)·a_{n+(-2)}
a_{6k+1} = a
a_{6k+2} = b
a_{6k+3} = b+(-a)
a_{6k+4} = (-a)
a_{6k+5} = (-b)
a_{6k+6} = (-b)+a
a_{n} = ( a_{n+(-1)}/a_{n+(-2)} )
a_{6k+1} = a
a_{6k+2} = b
a_{6k+3} = (b/a)
a_{6k+4} = (1/a)
a_{6k+5} = (1/b)
a_{6k+6} = (a/b)
