Complemento directo:
Que + verbo ?
Complemento de régimen verbal directo:
Preposición + Que + verbo ?
Sujeto:
Quien + verbo ?
Complemento de régimen verbal indirecto:
Preposición + Quien + verbo ?
Complemento circunstancial de manera:
Como + verbo ?
Complemento circunstancial de lugar:
Donde + verbo ?
Complemento predicativo de participio:
Participio en:
( verbo + Participio )
Complemento predicativo de gerundio:
Gerundio en:
( verbo + Gerundio )
A_{ij} = ( < (-a), b >,< (-b),a > )
(-1)·(a+x)·(a+(-x))+b^{2} = ( x^{2}+(-1)·a^{2})+b^{2} = 0
x = ( a^{2}+(-1)·b^{2} )^{(1/2)}
Forma de canónica:
( a^{2}+(-1)·b^{2} )^{(1/2)}·Id_{22} = ...
... ( < ( a^{2}+(-1)·b^{2} )^{(1/2)},0 >,< 0,( a^{2}+(-1)·b^{2} )^{(1/2)} > )
(-1)·( a+( a^{2}+(-1)·b^{2} )^{(1/2)} )·( a+(-1)·( a^{2}+(-1)·b^{2} )^{(1/2)} )+b^{2} = 0
Base canónica:
X_{ij} = ...
... ( < a+(-1)·( a^{2}+(-1)·b^{2} )^{(1/2)} , (-b) >,< (-b) , a+( a^{2}+(-1)·b^{2} )^{(1/2)} > )
det[A] = 2b^{2}
Inversa de la base canónica:
( X_{ij} )^{o(-1)} = ( 1/(2b^{2}) )·...
... ( < a+( a^{2}+(-1)·b^{2} )^{(1/2)} , b >,< b , a+(-1)·( a^{2}+(-1)·b^{2} )^{(1/2)} > )
Cálculo provisional:
( X_{ij} )^{o(-1)} o A_{ij} = ...
( < (-a)·( a+( a^{2}+(-1)·b^{2} )^{(1/2)} )+(-1)·b^{2},...
... b·( a^{2}+(-1)·b^{2} )^{(1/2)} >,
< b·( a^{2}+(-1)·b^{2} )^{(1/2)} , ...
... b^{2}+a·( a+(-1)·( a^{2}+(-1)·b^{2} )^{(1/2)} ) > )
( X_{ij} )^{o(-1)} o A_{ij} o X_{ij} = ( a^{2}+(-1)·b^{2} )^{(1/2)}·Id_{22}
A_{ij} = ( < (-a),b >,< (-b),a > )
Composición Nil-potente:
( < (-a)+(-x) , b >,< (-b), a+(-y) > ) o ( < (-a)+(-x) , b >,< (-b), a+(-y) > ) = ...
... ( < ( (-a)+(-x) )^{2}+(-1)·b^{2} , b·((-a)+(-x))+b·(a+(-y) ) >,...
... < (-b)·((-a)+(-x))+(-b)·(a+(-y)), ( a+(-y) )^{2}+(-1)·b^{2} > ) = 0_{ij}
x = (-a)+b & y = a+(-b)
Base nil-potente:
( < (-b),b >,< (-b),b > )^{o1} ==> <x,x>
( < (-b),b >,< (-b),b > )^{o2} ==> <x,y> & x != y
Y_{ij} = ( < x,x>,<x,y> )
Z_{ij} = ( < y,x >,< x,x > )
det[Y_{ij}] = det[Z_{ij}]
A_{ij} o Y_{ij} = ...
... ( < (-a)·x+b·x , (-a)·x+by >,< (-b)·x+ax , (-b)·x+ay > )
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < ( (-a)+b )·det[Y_{ij}] , b·(y^{2}+(-1)·x^{2}) >,< 0,(a+b)·det[Y_{ij}] > )
Base de Jordan:
y = ( x^{2}+(1/b) )^{(1/2)}
( < x,x >,< x,( x^{2}+(1/b) )^{(1/2)} > )
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < (-a)·det[Y_{ij}],0 >,< 0,a·det[Y_{ij}] > )+( < b·det[Y_{ij}],1 >,< 0,b·det[Y_{ij}] > )
A_{ij} = ( <a,b>,<b,a> )
Composición Nil-potente:
( < a+(-x) , b >,< b, a+(-y) > ) o ( < a+(-x) , b >,< b, a+(-y) > ) = ...
... ( < ( a+(-x) )^{2}+b^{2} , b·(a+(-x))+b·(a+(-y) ) >,...
... < b·(a+(-x))+b·(a+(-y)), ( a+(-y) )^{2}+b^{2} > ) = 0_{ij}
x = a+ib & y = a+(-1)·ib
Base nil-potente:
( < (-1)·ib , b >,< b, ib > )^{o1} ==> < x , ix >
( < (-1)·ib , b >,< b, ib > )^{o2} ==> < ix , y > & y != (-x)
Y_{ij} = ( < x,ix>,<ix,y> )
Z_{ij} = ( < y,(-i)x >,< (-i)x,x > )
det[Y_{ij}] = det[Z_{ij}]
A_{ij} o Y_{ij} = ...
... ( < ax+bix , aix+by >,< bx+aix , bix+ay > )
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < ( a+bi )·det[Y_{ij}] , b·(y^{2}+x^{2}) >,< 0,(a+bi)·det[Y_{ij}] > )
Base de Jordan:
y = ( (-1)·x^{2}+(1/b) )^{(1/2)}
( < x,ix>,<ix,( (-1)·x^{2}+(1/b) )^{(1/2)}> )
( (-1)·x^{2}+(1/b) )^{(1/2)} = (-x)
x != (1/2b)^{(1/2)} & x != (-1)·(1/2b)^{(1/2)}
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < a·det[Y_{ij}],0 >,< 0,a·det[Y_{ij}] > )+( < bi·det[Y_{ij}],1 >,< 0,bi·det[Y_{ij}] > )
A_{ij} = ( <a,b>,<a,a> )
Composición Nil-potente:
( < a+(-x) , b >,< a, a+(-y) > ) o ( < a+(-x) , b >,< a, a+(-y) > ) = ...
... ( < ( a+(-x) )^{2}+ba , b·(a+(-x))+b·(a+(-y) ) >,...
... < a·(a+(-x))+a·(a+(-y)), ( a+(-y) )^{2}+ab > ) = 0_{ij}
x = a+i·(ab)^{(1/2)} & y = a+(-i)·(ab)^{(1/2)}
Base nil-potente:
( < (-1)·i·(ab)^{(1/2)} , b >,< a , i·(ab)^{(1/2)} > )^{o1} ==> < b·x , (ab)^{1/2})·ix >
( < (-1)·i·(ab)^{(1/2)} , b >,< a , i·(ab)^{(1/2)} > )^{o2} ==> ...
... < (ab)^{(1/2)}·x , y > & y != a·ix
Y_{ij} = ( < bx,(ab)^{(1/2)}·ix >,< (ab)^{(1/2)}·x,y > )
Z_{ij} = ( < y,(-1)·(ab)^{(1/2)}·ix >,< (-1)·(ab)^{(1/2)}·x,bx > )
det[Y_{ij}] = det[Z_{ij}]
A_{ij} o Y_{ij} = ...
... ( < a·bx+b·(ab)^{(1/2)}·x, a·(ab)^{(1/2)}·ix+by >,...
... < a·bx+a·(ab)^{(1/2)}·x, a·(ab)^{(1/2)}·ix+ay > )
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < ( a+(ab)^{(1/2)} )·det[Y_{ij}], b(y^{2}+(-1)·a^{2}·x^{2}) >,...
... < 0, ( a+(-1)·(ab)^{(1/2)} )·det[Y_{ij}] > )
Base de Jordan:
y = ( a^{2}x^{2}+(1/b) )^{(1/2)}
( < bx,(ab)^{(1/2)}·ix >,< (ab)^{(1/2)}·x,( a^{2}x^{2}+(1/b) )^{(1/2)} > )
a^{2}x^{2}+(1/b) = (-1)·a^{2}·x^{2}
x != (i/a)·(1/2b)^{(1/2)} & x != (-1)·(i/a)·(1/2b)^{(1/2)}
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < (ab)^{(1/2)}·det[Y_{ij}], 0 >,< 0,(-1)·(ab)^{(1/2)}·det[Y_{ij}] > )+...
... ( < a·det[Y_{ij}], 1 >,< 0,a·det[Y_{ij}] > )
A_{ij} = ( <a,0,b>,<0,a,0>,<b,0,a> )
Composición Nil-potente:
( < a+(-x),0,b >,< 0,a+(-y),0 >,< b,0,a+(-z) > ) o ...
... ( < a+(-x),0,b >,< 0,a+(-y),0 >,< b,0,a+(-z) > o ...
... ( < a+(-x),0,b >,< 0,a+(-y),0 >,< b,0,a+(-z) > ) = ...
... ( < ( a+(-x) )^{2}+b^{2} , 0 , b·(a+(-x))+b·(a+(-z) ) >,...
... < 0 , (a+(-y))^{2} , 0 >,...
... < b·(a+(-x))+b·(a+(-z)) , 0 , ( a+(-z) )^{2}+b^{2} > ) o ...
... ( < a+(-x),0,b >,< 0,a+(-y),0 >,< b,0,a+(-z) > ) = 0_{ij}
x = a+ib & y = a & z = a+(-i)·b
Base nil-potente:
( < ix,0,x >,< 0,y.0 >,< ix,0,z > ) & ( y != x || z != x )
Y_{ij} = ( < ix,0,x >,< 0,y.0 >,< ix,0,z > )
Z_{ij} = ( < z,0,(-x) >,< 0,y.0 >,< (-i)·x,0,ix > )
det[Y_{ij}] = det[Z_{ij}]
A_{ij} o Y_{ij} = ...
... ( < a·ix+bix,0,ax+bz >,< 0,ay.0 >,< b·ix+aix,0,bx+az > )
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < (a+b)·(1/y)·det[Y_{ij}],0,b·(z^{2}+(-1)·x^{2}) >,...
... < 0,ay^{2},0 >,...
... < 0,0,(a+(-b))·(1/y)·det[Y_{ij}] > )
Base de Jordan:
y = 1
z = ( x^{2}+(1/b) )^{(1/2)}
( < ix,0,x >,< 0,1,0 >,< ix,0,( x^{2}+(1/b) )^{(1/2)} > )
Z_{ij} o A_{ij} o Y_{ij} = ...
... ( < b·det[Y_{ij}],0,0 >,< 0,a,0 >,< 0,0,(-b)·det[Y_{ij}] > )+ ...
... ( < a·det[Y_{ij}],0,1 >,< 0,0,0 >,< 0,0,a·det[Y_{ij}] > )
Sintagma nominal de infinitivo:
Complemento del nombre directo:
[ [w] es infinitivo [h(a)] ]-[ [h(a)] es sintagma nominal ]
[ [w] es infinitivo [h(b)] ]-[ [h(b)] es no sintagma nominal ]
Complemento del nombre circunstancial:
[ [w] es infinitivo preposición [h(a)] ]-[ [h(a)] es sintagma nominal ]
[ [w] es infinitivo preposición [h(b)] ]-[ [h(b)] es no sintagma nominal ]
pronombre-personal-A + verbo + sintagma-nominal + preposición + pronombre-transitivo-B
[ [x(i)] verbo [i] [w(z)] preposición [j] ]
pronombre-personal-B + verbo + sintagma-nominal + preposición + pronombre-transitivo-A
[ [y(j)] verbo [j] [w(z)] preposición [i] ]
ye vule ye-de-muá fatzoire-dom un café avec tú-de-tuá.
tú vule tú-de-tuá fatzoire-dom un café avec ye-de-muá.
pronombre-personal-A + verbo + sintagma-nominal + preposición + pronombre-transitivo-B
[ [x(i)] verbo [k] [w(z)] preposición [j] ]
pronombre-personal-B + verbo + sintagma-nominal + preposición + pronombre-transitivo-A
[ [y(j)] verbo [k] [w(z)] preposición [i] ]
il vule pont-de-suá fatzoire-dom un café avec ila-de-suá.
ila vule pont-de-suá fatzoire-dom un café avec il-de-suá.
pronombre-personal-A + verbo + sintagma-nominal + preposición + pronombre-transitivo-B
[ [x(i)] verbo [h(z)] preposición [j] ]
pronombre-personal-B + verbo + sintagma-nominal + preposición + pronombre-transitivo-A
[ [y(j)] verbo [h(z)] preposición [i] ]
nus parloms le Françé avec tú-de-tuá.
vus parloz le Françé avec ye-de-muá.
pronombre-personal-A + verbo + ...
... preposición + subordinada + preposición + pronombre-transitivo-B
[ [x(i)] verbo preposición P([z]) preposición [j] ]
pronombre-personal-B + verbo + ...
... preposición + subordinada + preposición + pronombre-transitivo-A
[ [y(j)] verbo preposición P([z]) preposición [i] ]
ye ne sé-pont de-le-com vack sere-dom bacboire-dom de la Font sansvec tú-de-tuá.
tú ne saps-pont de-le-com vack sere-dom bacboire-dom de la Font sansvec ye-de-muá.
P([z]) <==> [ vack sere-dom [w] ]-[ [w] es bacboire-dom de [k] ]-[A$1$ [k] ][ [k] es Font ]
Sonido racional:
R·d_{t}[q(t)]+i·C·q(t) = 0
q(t) = potencial[Q(x,y,z)]·(1/A)·e^{(-i)·(C/R)·t}
R·d_{t}[q(t)]+(-i)·C·q(t) = 0
q(t) = div[Q(x,y,z)]·A·e^{i·(C/R)·t}
Q(x,y,z) = aq_{0}·< x,y,z >
q(t) = aq_{0}·(1/2)·( x^{2}+y^{2}+z^{2} )·(1/A)·e^{(-i)·(C/R)·t}
q(t) = 3aq_{0}·A·e^{i·(C/R)·t}
Q(x,y,z) = (-1)·aq_{0}·< x,y,z >
q(t) = (-1)·aq_{0}·(1/2)·( x^{2}+y^{2}+z^{2} )·(1/A)·e^{(-i)·(C/R)·t}
q(t) = (-3)·aq_{0}·A·e^{i·(C/R)·t}
Q(x,y,z) = a^{2n+1}q_{0}·< x^{2n+1},y^{2n+1},z^{2n+1} >
q(t) = ...
... a^{2n+1}q_{0}·( 1/(2·(n+1)) )·( x^{2·(n+1)}+y^{2·(n+1)}+z^{2·(n+1)} )·...
... (1/A)·e^{(-i)·(C/R)·t}
q(t) = a^{2n+1}q_{0}·(2n+1)·( x^{2n}+y^{2n}+z^{2n} )·A·e^{i·(C/R)·t}
Q(x,y,z) = (-1)·a^{2n+1}q_{0}·< x^{2n+1},y^{2n+1},z^{2n+1} >
q(t) = ...
... (-1)·a^{2n+1}q_{0}·( 1/(2·(n+1)) )·( x^{2·(n+1)}+y^{2·(n+1)}+z^{2·(n+1)} )·...
... (1/A)·e^{(-i)·(C/R)·t}
q(t) = (-1)·a^{2n+1}q_{0}·(2n+1)·( x^{2n}+y^{2n}+z^{2n} )·A·e^{i·(C/R)·t}
Sonido irracional:
L·d_{tt}^{2}[q(t)]+C·q(t) = 0
q(t) = potencial[Q(x,y,z)]·(1/A)·e^{(-i)·(C/L)^{(1/2)}·t}
L·d_{tt}^{2}[q(t)]+C·q(t) = 0
q(t) = div[Q(x,y,z)]·A·e^{i·(C/L)^{(1/2)}·t}
Q(x,y,z) = aq_{0}·< x,y,z >
q(t) = aq_{0}·(1/2)·( x^{2}+y^{2}+z^{2} )·(1/A)·e^{(-i)·(C/L)^{(1/2)}·t}
q(t) = 3aq_{0}·A·e^{i·(C/L)^{(1/2)}·t}
Q(x,y,z) = (-1)·aq_{0}·< x,y,z >
q(t) = (-1)·aq_{0}·(1/2)·( x^{2}+y^{2}+z^{2} )·(1/A)·e^{(-i)·(C/L)^{(1/2)}·t}
q(t) = (-3)·aq_{0}·A·e^{i·(C/L)^{(1/2)}·t}
Sonido racional cuadrático:
R·d_{t}[q(t)]+i·C·q(t) = 0
q(t) = anti-potencial[Q(x,y,z)]·(1/A^{2})·e^{(-i)·(C/R)·t}
R·d_{t}[q(t)]+(-i)·C·q(t) = 0
q(t) = anti-div[Q(x,y,z)]·A^{2}·e^{i·(C/R)·t}
Q(x,y,z) = bq_{0}·< yz,zx,xy >
q(t) = bq_{0}·(1/4)·( (yz)^{2}+(zx)^{2}+(xy)^{2} )·(1/A^{2})·e^{(-i)·(C/L)^{(1/2)}·t}
q(t) = 3bq_{0}·A^{2}·e^{i·(C/R)·t}
Q(x,y,z) = (-1)·bq_{0}·< yz,zx,xy >
q(t) = (-1)·bq_{0}·(1/4)·( (yz)^{2}+(zx)^{2}+(xy)^{2} )·(1/A^{2})·e^{(-i)·(C/L)^{(1/2)}·t}
q(t) = (-3)·bq_{0}·A^{2}·e^{i·(C/R)·t}
Serie dos-geométrica:
( 1/(1+(-a)) )·( 1/(1+(-b)) )+(-1)·( 1/(1+(-a)) )+(-1)·( 1/(1+(-b)) )+1
sum[ i+j = k ][ a^{i}b^{j} ] = ( a/(1+(-a)) )·( b/(1+(-b)) )
x+y(x) = f(x)+nx = 0
f(x)-[+]-sum[n](x) = 0
x = anti-f(x)-[+]-sum[n](0)
y(x) = (-1)·anti-f(x)-[+]-sum[n](0)
x·y(x) = x^{k}·f(x) = 1
f(x)-pow[k](x) = 1
x = anti-f(x)-pow[k](1)
y(x) = ( 1/anti-f(x)-pow[k](1) )
x+y(x) = f(x)+nx^{k+1} = 0
x^{k}·( f(x)-pow[(-k)]-[+] sum[n](x) ) = 0
f(x)-[+]-sum[n]-pow[k](x) = 0
x = anti-f(x)-[+]-sum[n]-pow[k](0)
y(x) = (-1)·anti-f(x)-[+]-sum[n]-pow[k](0)
x+y(x) = f(x)+n_{1}x^{k_{1}+1}+...(m)...+n_{m}x^{k_{m}+1} = 0
f(x)-[+]-sum[n_{1}]-pow[k_{1}]-[+]-...(m)...-[+]-sum[n_{m}]-pow[k_{m}](x) = 0
x = anti-f(x)-[+]-sum[n_{1}]-pow[k_{1}]-[+]-...(m)...-[+]-sum[n_{m}]-pow[k_{m}](0)
y(x) = ...
... (-1)·anti-f(x)-[+]-sum[n_{1}]-pow[k_{1}]-[+]-...(m)...-[+]-sum[n_{m}]-pow[k_{m}](0)
sum[n](x) = nx
f(x)-[+]-(sum[n]-[+]-sum[m])(x) = f(x)-[+]-sum[n+m](x)
f(x)+(nx+mx) = f(x)+(n+m)x
f(x)-[+]-(sum[n]-[+]-sum[0])(x) = f(x)-[+]-sum[n](x)
f(x)-[+]-(sum[n]-[+]-sum[(-n)])(x) = f(x)-[+]-sum[0](x) = f(x)
f(x)-[+]-((sum[a]-[+]-sum[b])-[+]-sum[c])(x) = f(x)-[+]-(sum[a]-[+]-(sum[b]-[+]-sum[c]))(x)
f(x)-[+]-(sum[a]-[+]-sum[b])(x) = f(x)-[+]-(sum[b]-[+]-sum[a])(x)
pow[n] = x^{n}
f(x)-(pow[n]-pow[m])(x) = f(x)-pow[n+m](x)
x^{n}·x^{m}·f(x) = x^{n+m}·f(x)
f(x)-(pow[n]-pow[0])(x) = f(x)-pow[n](x)
f(x)-(pow[n]-pow[(-n)])(x) = f(x)-pow[0](x) = f(x)
f(x)-((pow[a]-pow[b])-pow[c])(x) = f(x)-(pow[a]-(pow[b]-pow[c]))(x)
f(x)-(pow[a]-pow[b])(x) = f(x)-(pow[b]-pow[a])(x)
d_{xy}^{2}[ ( f(x)+g(y) )^{n+2} ] = ...
... (n+2)·(n+1)·( f(x)+g(y) )^{n}·d_{x}[f(x)]·d_{y}[g(y)]
d_{yx}^{2}[ ( f(x)+g(y) )^{n+2} ] = ...
... (n+2)·(n+1)·( f(x)+g(y) )^{n}·d_{y}[g(y)]·d_{x}[f(x)]
d_{xy}^{2}[ ( f(x)·g(y) )^{n+2} ] = ...
... d_{x}[ (n+2)·( f(x)·g(y) )^{n+1}·d_{y}[g(y)]·f(x) ] = ...
... d_{x}[g(y)]d_{x}[f(x)]·( ...
... (n+2)·(n+1)·( f(x)·g(y) )^{n+1}+(n+2)·( f(x)·g(y) )^{n+1} ) = ...
... d_{x}[g(y)]d_{x}[f(x)]·(n+2)^{2}·( f(x)·g(y) )^{n+1}
Sintagmas Nominales:
( nombre + adjetivo ) || ( adjective + name ).
[ [z] es nombre de tipo de adjetivo [a] ]-[ [a] es adjetivo ].
( nombre + no adjetivo ) || ( not adjective + name ).
[ [z] es nombre de tipo de adjetivo [b] ]-[ [b] es no adjetivo ].
comida rápida.
comida lenta.
( articulo + nombre + adjetivo ) || ( article + adjective + name ).
[ articulo [z] ][ [z] es nombre de tipo de adjetivo [a] ]-[ [a] es adjetivo ].
( articulo + nombre + no adjetivo ) || ( article + not adjective + name ).
[ articulo [z] ][ [z] es nombre de tipo de adjetivo [b] ]-[ [b] es no adjetivo ].
la casa blanca.
la casa negra.
( posesivo + nombre + adjetivo ) || ( posesive + adjective + name ).
[ [z] es nombre de tipo de adjetivo [a] de posesivo [k] ]-...
... [ [a] es adjetivo ]-[ [k] es posesivo ].
( posesivo + nombre + no adjetivo ) || ( posesive + not adjective + name ).
[ [z] es nombre de tipo de adjetivo [b] de posesivo [k] ]-...
... [ [b] es no adjetivo ]-[ [k] es posesivo ].
su coche nuevo.
su coche viejo.
nombre + preposición + sintagma-nominal.
[ [z] es nombre preposición [h(a)] ]-[ [h(a)] es sintagma-nominal ].
nombre + preposición + no sintagma-nominal.
[ [z] es nombre preposición [h(b)] ]-[ [h(b)] es no sintagma-nominal ].
parking para su coche nuevo.
parking para su coche viejo.
articulo + nombre + preposición + sintagma-nominal.
[ articulo [z] ][ [z] es nombre preposición [h(a)] ]-[ [h(a)] es sintagma-nominal ].
articulo + nombre + preposición + no sintagma-nominal.
[ articulo [z] ][ [z] es nombre preposición [h(b)] ]-[ [h(b)] es no sintagma-nominal ].
la vida de mi abuelo.
la vida de mi abuela.
posesivo + nombre + preposición + sintagma-nominal.
[ [z] es nombre de posesivo [k] preposición [h(a)] ]-...
... [ [k] es posesivo ]-[ [h(a)] es sintagma-nominal ].
posesivo + nombre + preposición + no sintagma-nominal.
[ [z] es nombre de posesivo [k] preposición [h(b)] ]-...
... [ [k] es posesivo ]-[ [h(b)] es no sintagma-nominal ].
su casa de la micro-lópolis.
su casa de la mega-lópolis.
sintagma-nominal + preposición + nombre.
[ [h(a)] es sintagma-nominal preposición [z] ]-[ [z] es nombre ].
no sintagma-nominal + preposición + nombre.
[ [h(b)] es no sintagma-nominal preposición [z] ]-[ [z] es nombre ].
la casa blanca de Washington.
la casa negra de Washington.
div[E(x,y,z)] = d_{xyz}^{3}[ anti-potencial[E(x,y,z)] ]
anti-div[E(x,y,z)] = d_{xyz}^{3}[ potencial[E(x,y,z)] ]
anti-potencial[E(x,y,z)] = ...
... int-int[E_{x}(x,y,z)]d[y]d[z]+int-int[E_{y}(x,y,z)]d[z]d[x]+int-int[E_{z}(x,y,z)]d[x]d[y]
potencial[E(x,y,z)] = ...
... int[E_{x}(x,y,z)]d[x]+int[E_{y}(x,y,z)]d[y]+int[E_{z}(x,y,z)]d[z]
div[E(x,y,z)] = ...
... d_{x}[ E_{x}(x,y,z) ]+d_{y}[ E_{y}(x,y,z) ]+d_{z}[ E_{z}(x,y,z) ]
anti-div[E(x,y,z)] = ...
... d_{yz}^{2}[ E_{x}(x,y,z) ]+d_{zx}^{2}[ E_{y}(x,y,z) ]+d_{xy}^{2}[ E_{z}(x,y,z) ]
anti-potencial[ rot[E(x,y,z)] ] = 0
potencial[ anti-rot[E(x,y,z)] ] = 0
rot[E(x,y,z)] = ...
... < ...
... x·( d_{y}[E_{y}(x,y,z)]+(-1)·d_{z}[E_{z}(x,y,z)] ), ...
... y·( d_{z}[E_{z}(x,y,z)]+(-1)·d_{x}[E_{x}(x,y,z)] ), ...
... z·( d_{x}[E_{x}(x,y,z)]+(-1)·d_{y}[E_{y}(x,y,z)] ) ...
... >
anti-rot[E(x,y,z)] = ...
... < ...
... yz·( d_{yy}^{2}[E_{y}(x,y,z)]+(-1)·d_{zz}^{2}[E_{z}(x,y,z)] ), ...
... zx·( d_{zz}^{2}[E_{z}(x,y,z)]+(-1)·d_{xx}^{2}[E_{x}(x,y,z)] ), ...
... xy·( d_{xx}^{2}[E_{x}(x,y,z)]+(-1)·d_{yy}^{2}[E_{y}(x,y,z)] ) ...
... >
rot[E(x,y,z)]+E(x,y,z) = anti-potencial-vector[E(x,y,z)]
anti-rot[E(x,y,z)]+E(x,y,z) = potencial-vector[E(x,y,z)]
anti-potencial[ anti-potencial-vector[E(x,y,z)] ] = anti-potencial[E(x,y,z)]
potencial[ potencial-vector[E(x,y,z)] ] = potencial[E(x,y,z)]
Camp eléctric de un cub rectangular rúbic central:
E_{x}(x,y,z) = ax+byz
E_{y}(x,y,z) = ay+bzx
E_{z}(x,y,z) = az+bxy
div[E(x,y,z)] = 3a
anti-div[E(x,y,z)] = 3b
anti-potencial[E(x,y,z)] = b·( (1/4)·(yz)^{2}+(1/4)·(zx)^{2}+(1/4)·(xy)^{2} )+3a·xyz
potencial[E(x,y,z)] = a·( (1/2)·x^{2}+(1/2)·y^{2}+(1/2)·z^{2} )+3b·xyz
rot[E(x,y,z)] = ...
... a·< x·( 1+(-1) ), y·( 1+(-1) ), z·( 1+(-1) ) > = < 0,0,0 >
anti-rot[E(x,y,z)] = ...
... a·< yz·( 0+(-0) ), zx·( 0+(-0) ), xy·( 0+(-0) ) > = < 0^{2},0^{2},0^{2} >
Camp eléctric de ecuador-meridià rúbic central:
E_{x}(x,y,z) = ae^{isx}+be^{isy+isz}
E_{y}(x,y,z) = ae^{isy}+be^{isz+isx}
E_{z}(x,y,z) = ae^{isz}+be^{isx+isy}
div[E(x,y,z)] = a·(is)·( e^{isx}+e^{isy}+e^{isz} )
anti-div[E(x,y,z)] = b·(is)^{2}·( e^{isy+isz}+e^{isz+isx}+e^{isx+isy} )
anti-potencial[E(x,y,z)] = ...
... a·( e^{isx}yz+e^{isy}zx+e^{isz}xy )+...
... ( b/(is)^{2} )·( e^{isy+isz}+e^{isz+isx}+e^{isx+isy} )
potencial[E(x,y,z)] = ...
... b·( e^{isy+isz}x+e^{isz+isx}y+e^{isx+isy}z )+...
... ( a/(is) )·( e^{isx}+e^{isy}+e^{isz} )
rot[E(x,y,z)] = ...
... a·(is)·< x·( e^{isy}+(-1)·e^{isz} ), y·( e^{isz}+(-1)·e^{isx} ), z·( e^{isx}+(-1)·e^{isy} ) >
anti-rot[E(x,y,z)] = ...
... a·(is)^{2}·< ...
... yz·( e^{isy}+(-1)·e^{isz} ), zx·( e^{isz}+(-1)·e^{isx} ), xy·( e^{isx}+(-1)·e^{isy} ) ...
... >
