sábado, 5 de septiembre de 2020

italiano-castellán-portuguésh & occità-català-bascotzok-françé

[ italiano ]-[ castellán ]-[ portuguésh ]:

yo canto

tú cantas

élui canta <==> ello canta <==> ellu canta

élai canta <==> ella canta <==> ella canta


nosotri cantamo <==> nosotros cantamos <==> nusotrush cantamush 

vosotri cantái <==> vosotros cantáis <==> vusotrush cantáish

éluis cantan <==> ellos cantan <==> ellush cantan

élais cantan <==> ellas cantan <==> ellash cantan


aquélui canta <==> aquello canta <==> aquellu canta

aquélai canta <==> aquella canta <==> aquella canta

aquéluis cantan <==> aquellos cantan <==> aquellush cantan

aquélais cantan <==> aquellas cantan  <==> aquellash cantan


aquéstui canta <==> aquesto canta <==> aquestu canta

aquéstai canta <==> aquesta canta <==> aquesta canta

aquéstuis cantan <==> aquestos cantan <==> aquestush cantan

aquéstais cantan <==> aquestas cantan <==> aquestash cantan


uno [o] lo

una [o] la

unos [o] los

unas [o] las


unu [o] lu

una [o] la

unus [o] lus

unas [o] las


[ occità-de-le-patuá ]-[ català ]-[ bascotzok ]-[ françé-de-le-patuá ]:

ye cantû <==> yo cantû

tú cantes

él canta <==> ell canta <==> ell-lek canta-tek <==> il canta-puá

ela canta <==> ella canta <==> ella-lek canta-tek <==> ila canta-puá


nusuá cantems <==> nûsaltres cantem <==> noekotrek cantemek <==> nusuá cantems-de-puá

vusuá cantéus <==> vûsaltres cantéu <==> voekotrek cantéuek <==> vusuá cantéus-de-puá

éls canten <==> ells canten <==> ells-lek canten-tek <==> ils canten-puá 

eles canten <==> elles canten <==> elles-lek canten-tek <==> iles canten-puá



aquel canta <==> aquell canta <==> aquell-lek canta-tek <==> aquil canta-puá

aquela canta <==> aquella canta <==> aquella-lek canta-tek <==> aquila canta-puá

aquels canten <==> aquells canten <==> aquells-lek canten-tek <==> aquils canten-puá

aqueles canten <==> aquelles canten <==> aquelles-lek canten-tek <==> aquiles canten-puá


aquet-ço canta <==> aquet canta <==> aquet-lek canta-tek <==> aquit-ço canta-puá

aquet-ça canta <==> aquesta canta <==> aquesta-lek canta-tek <==> aquit-ça canta-puá

aquet-ços canten <==> aquets canten <==> aquets-lek canten-tek <==> aquit-ços canten-puá

aquet-ças canten <==> aquestes canten <==> aquestes-lek canten-tek <==> aquit-ças canten-puá


[ occità-de-le-patuá ]-[ françé-de-le-patuá ]

{

celui-lí canta <==> celui-lí canta-puá

celui-luá canta <==> celui-luá canta-puá

celui-lís canten <==> celui-lís canten-puá

celui-luás canten <==> celui-luás canten-puá

}

{

celui-çí canta <==> celui-çí canta-puá

celui-çuá canta <==> celui-çuá canta-puá

celui-çís canten <==> celui-çís canten-puá

celui-çuás canten <==> celui-çuás canten-puá

}


cantar <==> cantar <==> cantare-dut <==> cantare-dom

cantant <==> cantant <==> cantantu-dut <==> cantantu-dom


cantat <==> cantat <==> cantatu-dut <==> cantatu-dom

cantada <==> cantada <==> cantata-dat <==> cantata-dam


vull-de-puá cantar <==> vull cantar <==> vull-de-tek cantare-dut <==> vull-de-puá cantare-dom

vols-de-puá cantar <==> vols cantar <==> vols-de-tek cantare-dut <==> vols-de-puá cantare-dom

vol-de-puá cantar <==> vol cantar <==> vol-de-tek cantare-dut <==> vol-de-puá cantare-dom


un [o] el 

una [o] la

uns [o] els

unes [o] les


un [o] le

una [o] la

uns [o] les-des

unes [o] las-das

viernes, 4 de septiembre de 2020

determinant tensorial de penta-curvatura de ordre 2

det( a^{k}_{ijuv} ) = ...

... ( a^{1}_{1111}a^{2}_{2222}+(-1)·a^{2}_{1111}a^{1}_{2222} )+...


A^{k}_{ijuv}·a_{i}a_{j}a_{u}a_{v} = a^{k}

a_{1} = a & a_{2} = b

A^{1}_{1111} = (1/a^{3}) & A^{2}_{2222} = (1/b^{3})

A^{2}_{1111} = (b/a^{4}) & A^{1}_{2222} = (a/b^{4})

A^{1}_{2111} = (1/(ba^{2})) & A^{2}_{1222} = (1/(b^{2}a))

A^{1}_{1211} = (1/(ba^{2})) & A^{2}_{2122} = (1/(b^{2}a))

A^{1}_{1121} = (1/(ba^{2})) & A^{2}_{2212} = (1/(b^{2}a))

A^{1}_{1112} = (1/(ba^{2})) & A^{2}_{2221} = (1/(b^{2}a))

A^{2}_{2111} = (1/a^{3}) & A^{1}_{1222} = (1/b^{3})

A^{2}_{1211} = (1/a^{3}) & A^{1}_{2122} = (1/b^{3})

A^{2}_{1121} = (1/a^{3}) & A^{1}_{2212} = (1/b^{3})

A^{2}_{1112} = (1/a^{3}) & A^{1}_{2221} = (1/b^{3})

A^{1}_{2211} = (1/(b^{2}a)) & A^{2}_{1122} = (1/(a^{2}b))

A^{1}_{1221} = (1/(b^{2}a)) & A^{2}_{2112} = (1/(a^{2}b))

A^{1}_{1122} = (1/(b^{2}a)) & A^{2}_{2211} = (1/(a^{2}b))

A^{2}_{1221} = (1/(a^{2}b)) & A^{1}_{2112} = (1/(b^{2}a))

A^{1}_{1212} = (1/(b^{2}a)) & A^{2}_{2121} = (1/(a^{2}b))

A^{2}_{1212} = (1/(a^{2}b)) & A^{1}_{2121} = (1/(b^{2}a))

det( A^{k}_{ijuv} ) = 0

geodesiques

R^{k}_{i_{1}...i_{n}}·d_{t}[x_{i_{1}}(t)]·...·d_{t}[x_{i_{n}}(t)] = d_{t...t}^{n}[x_{k}(t)]


x_{k}(t) = t^{k}

R^{k}_{i_{1}...i_{n}} = ( 1/(i_{1}...i_{n}) )·( k!/(k+(-n))! )·t^{k+(-1)·(i_{1}+...+i_{n})}


x_{k}(t) = e^{k·t}

R^{k}_{i_{1}...i_{n}} = ( 1/(i_{1}...i_{n}) )·( k^{n} )·e^{(k+(-1)·(i_{1}+...+i_{n}))·t}


x_{k}(t) = ln(t^{k})

R^{k}_{i_{1}...i_{n}} = ( 1/(i_{1}...i_{n}) )·( (-1)^{n+1}·k·n! )

determinant tensorial de curvatura de ordre 2

det( a^{k}_{ijs} ) = ...

... ( a^{1}_{111}a^{2}_{222}+(-1)·a^{2}_{111}a^{1}_{222} )+...

... ( a^{1}_{122}a^{2}_{211}+(-1)·a^{2}_{122}a^{1}_{211} )+...

... ( a^{1}_{212}a^{2}_{121}+(-1)·a^{2}_{212}a^{1}_{121} )+...

... ( a^{1}_{221}a^{2}_{112}+(-1)·a^{2}_{221}a^{1}_{112} )


A^{k}_{ijs}·a_{i}a_{j}a_{s} = a^{k}

a_{1} = a & a_{2} = b

A^{1}_{111} = (1/a^{2}) & A^{2}_{222} = (1/b^{2})

A^{2}_{111} = (b/a^{3}) & A^{1}_{222} = (a/b^{3})

A^{1}_{211} = (1/(ab)) & A^{2}_{122} = (1/(ba))

A^{1}_{112} = (1/(ab)) & A^{2}_{221} = (1/(ba))

A^{1}_{121} = (1/(ab)) & A^{2}_{212} = (1/(ba))

A^{2}_{211} = (1/a^{2}) & A^{1}_{122} = (1/b^{2})

A^{2}_{121} = (1/a^{2}) & A^{1}_{212} = (1/b^{2}) 

A^{2}_{112} = (1/a^{2}) & A^{1}_{211} = (1/b^{2})

det( A^{k}_{ijs} ) = 0


Primera contracció tensorial:

A^{k}_{ijj}·a_{i}a_{j}a_{j} = a^{k}

a_{1} = a & a_{2} = b

A^{1}_{111} = (1/a^{2}) & A^{2}_{222} = (1/b^{2})

A^{2}_{111} = (b/a^{3}) & A^{1}_{222} = (a/b^{3})

A^{1}_{211} = (1/(ab)) & A^{2}_{122} = (1/(ba)) 

A^{2}_{211} = (1/a^{2}) & A^{1}_{122} = (1/b^{2}) 

det( A^{k}_{ijj} ) = 0


A^{k}_{jij}·a_{j}a_{i}a_{j} = a^{k}

a_{1} = a & a_{2} = b

A^{1}_{111} = (1/a^{2}) & A^{2}_{222} = (1/b^{2})

A^{2}_{111} = (b/a^{3}) & A^{1}_{222} = (a/b^{3})

A^{1}_{121} = (1/(ab)) & A^{2}_{212} = (1/(ba)) 

A^{2}_{121} = (1/a^{2}) & A^{1}_{212} = (1/b^{2})

det( A^{k}_{jij} ) = 0


A^{k}_{jji}·a_{j}a_{j}a_{i} = a^{k}

a_{1} = a & a_{2} = b

A^{1}_{111} = (1/a^{2}) & A^{2}_{222} = (1/b^{2})

A^{2}_{111} = (b/a^{3}) & A^{1}_{222} = (a/b^{3})

A^{1}_{112} = (1/(ab)) & A^{2}_{221} = (1/(ba)) 

A^{2}_{112} = (1/a^{2}) & A^{1}_{221} = (1/b^{2})

det( A^{k}_{jji} ) = 0


Teorema de contraccions tensorials:

Sum[ A^{k}_{ijs} ] = Sum[ ( A^{k}_{ijj}+A^{k}_{jij}+A^{k}_{jji} ) ]+(-2)·Sum[ A^{k}_{iii} ]

Prod[ A^{k}_{ijs} ] = ( Prod[ ( A^{k}_{ijj}·A^{k}_{jij}·A^{k}_{jji} ) ]/( Prod[ A^{k}_{iii} ] )^{2} )


Segona contraccció tensorial:

A^{j}_{jii}·a_{j}a_{i}a_{i} = a^{j}

a_{1} = a & a_{2} = b

A^{1}_{111} = (1/a^{2}) & A^{2}_{222} = (1/b^{2})

A^{2}_{211} = (1/a^{2}) & A^{1}_{122} = (1/b^{2})

det( A^{j}_{jii} ) = 0


A^{j}_{iji}·a_{i}a_{j}a_{i} = a^{j}

a_{1} = a & a_{2} = b

A^{1}_{111} = (1/a^{2}) & A^{2}_{222} = (1/b^{2})

A^{2}_{121} = (1/a^{2}) & A^{1}_{212} = (1/b^{2})

det( A^{j}_{iji} ) = 0


A^{j}_{iij}·a_{i}a_{i}a_{j} = a^{j}

a_{1} = a & a_{2} = b

A^{1}_{111} = (1/a^{2}) & A^{2}_{222} = (1/b^{2})

A^{2}_{112} = (1/a^{2}) & A^{1}_{221} = (1/b^{2})

det( A^{j}_{iij} ) = 0

jueves, 3 de septiembre de 2020

determinant tensorial de ordre 3

det( a^{k}_{ij} ) = ...

... ( a^{1}_{11}a^{2}_{22}a^{3}_{33}+(-1)·a^{1}_{33}a^{2}_{22}a^{3}_{11} )+...

... ( a^{2}_{11}a^{3}_{22}a^{1}_{33}+(-1)·a^{2}_{33}a^{3}_{22}a^{1}_{11} )+...

... ( a^{3}_{11}a^{1}_{22}a^{2}_{33}+(-1)·a^{3}_{33}a^{1}_{22}a^{2}_{11} )+...


... ( a^{1}_{23}a^{2}_{31}a^{3}_{12}+(-1)·a^{3}_{13}a^{2}_{22}a^{1}_{31} )+...

... ( a^{1}_{21}a^{2}_{32}a^{3}_{13}+(-1)·a^{3}_{23}a^{2}_{32}a^{1}_{11} )+...

... ( a^{1}_{31}a^{2}_{12}a^{3}_{23}+(-1)·a^{3}_{33}a^{2}_{12}a^{1}_{21} )+...


... ( a^{1}_{32}a^{2}_{13}a^{3}_{21}+(-1)·a^{3}_{31}a^{2}_{22}a^{1}_{13} )+...

... ( a^{1}_{12}a^{2}_{23}a^{3}_{31}+(-1)·a^{3}_{32}a^{2}_{23}a^{1}_{11} )+...

... ( a^{1}_{13}a^{2}_{21}a^{3}_{32}+(-1)·a^{3}_{33}a^{2}_{21}a^{1}_{12} )


A^{k}_{ij}·a_{i}a_{j} = a^{k}

a_{1} = a & a_{2} = b & a_{3} = c

A^{1}_{11} = (1/a) & A^{2}_{22} = (1/b) & A^{3}_{33} = (1/c)

A^{2}_{11} = (b/a^{2}) & A^{3}_{22} = (c/b^{2}) & A^{1}_{33} = (a/c^{2})

A^{3}_{11} = (c/a^{2}) & A^{1}_{22} = (a/b^{2}) & A^{2}_{33} = (b/c^{2})

A^{1}_{21} = (1/b) & A^{2}_{32} = (1/c) & A^{3}_{13} = (1/a)

A^{1}_{31} = (1/c) & A^{2}_{12} = (1/a) & A^{3}_{23} = (1/b)

A^{1}_{12} = (1/b) & A^{2}_{23} = (1/c) & A^{3}_{31} = (1/a)

A^{1}_{13} = (1/c) & A^{2}_{21} = (1/a) & A^{3}_{32} = (1/b)

A^{1}_{23} = (a/(bc)) & A^{2}_{31} = (b/(ca)) & A^{3}_{12} = (c/(ab))

A^{1}_{32} = (a/(cb)) & A^{2}_{13} = (b/(ac)) & A^{3}_{21} = (c/(ba))

det( A^{k}_{ij} ) = 0

miércoles, 2 de septiembre de 2020

determinant tensorial de ordre 2

det( a^{k}_{ij} ) = ...

... ( a^{1}_{11}a^{2}_{22}+(-1)·a^{2}_{11}a^{1}_{22} )+...

... ( a^{1}_{12}a^{2}_{21}+(-1)·a^{2}_{12}a^{1}_{21} )


A^{k}_{ij}·a_{i}a_{j} = a^{k}

a_{1} = a & a_{2} = b

A^{1}_{11} = (1/a) & A^{2}_{22} = (1/b)

A^{2}_{11} = (b/a^{2}) & A^{1}_{22} = (a/b^{2})

A^{1}_{21} = (1/b) & A^{2}_{12} = (1/a)

A^{2}_{21} = (1/a) & A^{1}_{12} = (1/b)

det( A^{k}_{ij} ) = 0


A^{k}_{ij}·a_{i}a_{j} = ( a^{k} )^{n}

a_{1} = a & a_{2} = b

A^{1}_{11} = a^{(n+(-2))} & A^{2}_{22} = b^{(n+(-2))}

A^{2}_{11} = (b^{n}/a^{2}) & A^{1}_{22} = (a^{n}/b^{2})

A^{1}_{21} = (a^{(n+(-1))}/b) & A^{2}_{12} = (b^{(n+(-1))}/a)

A^{2}_{21} = (b^{(n+(-1))}/a) & A^{1}_{12} = (a^{(n+(-1))}/b)

det( A^{k}_{ij} ) = 0


A^{k}_{ij}·( a_{i} )^{p}·( a_{j} )^{q} = ( a^{k} )^{n}

a_{1} = a & a_{2} = b

A^{1}_{11} = (a^{n}/a^{(p+q)}) & A^{2}_{22} = (b^{n}/b^{(p+q)})

A^{2}_{11} = (b^{n}/a^{p+q}) & A^{1}_{22} = (a^{n}/b^{p+q})

A^{1}_{21} = (a^{(n+(-q))}/b^{p}) & A^{2}_{12} = (b^{(n+(-q))}/a^{p})

A^{2}_{21} = (b^{(n+(-p))}/a^{q}) & A^{1}_{12} = (a^{(n+(-p))}/b^{q})

det( A^{k}_{ij} ) = 0



det( b^{k}_{i} ) = b^{1}_{1}b^{2}_{2}+(-1)·b^{2}_{1}b^{1}_{2}


B^{k}_{i}·b_{i} = b^{k}

b_{1} = a & b_{2} = b

B^{1}_{1} = 1 & B^{2}_{2} = 1

B^{2}_{1} = (b/a) & B^{1}_{2} = (a/b)

det( B^{k}_{i} ) = 0


B^{k}_{i}·b_{i} = ( b^{k} )^{n}

b_{1} = a & b_{2} = b

B^{1}_{1} = a^{(n+(-1))} & B^{2}_{2} = b^{(n+(-1))}

B^{2}_{1} = (b^{n}/a) & B^{1}_{2} = (a^{n}/b)

det( B^{k}_{i} ) = 0


B^{k}_{i}·( b_{i} )^{m} = ( b^{k} )^{n}

b_{1} = a & b_{2} = b

B^{1}_{1} = a^{(n+(-m))} & B^{2}_{2} = b^{(n+(-m))}

B^{2}_{1} = (b^{n}/a^{m}) & B^{1}_{2} = (a^{n}/b^{m})

det( B^{k}_{i} ) = 0


Contracció Tensorial:

A^{j}_{ij}·a_{i}a_{j} = a^{j}

a_{1} = a & a_{2} = b

A^{1}_{11} = (1/a) & A^{2}_{22} = (1/b)

A^{1}_{21} = (1/b) & A^{2}_{12} = (1/a)

det( A^{j}_{ij} ) = 0


A^{j}_{ji}·a_{j}a_{i} = a^{j}

a_{1} = a & a_{2} = b

A^{1}_{11} = (1/a) & A^{2}_{22} = (1/b)

A^{1}_{12} = (1/b) & A^{2}_{21} = (1/a)

det( A^{j}_{ji} ) = 0


Teorema de contraccions tensorials:

Sum[ A^{k}_{ij} ] = Sum[ ( A^{j}_{ij}+A^{j}_{ii}+A^{j}_{ji} ) ]+(-2)·Sum[ A^{i}_{ii} ]

Prod[ A^{k}_{ij} ] = ( Prod[ ( A^{j}_{ij}·A^{j}_{ii}·A^{j}_{ji} ) ]/( Prod[ A^{i}_{ii} ] )^{2} )

italiano-english

I sader fumator, ney-cuitzey doncader fumators.

yo sere fumadore, no-cuitzo doncare fumadori.

Sóc fumador, no-cuitza aishí doncs fumadors.

Soy fumador, no-cuitza así pues fumadores.


Lus fumadori, no-cuitzo doncare fumadore,

fúmano unus cigarreti, no-cuitzo doncare cigarreto.

Les fumadori, no-cuitzo doncare fumadora,

fúmano unes cigarreti, no-cuitzo doncare cigarreta.

[ A$...$ [u] ][ [u] sóno fumadores , no-cuitzo doncare [x] ]

[ A$...$ [v] ][ [v] sóno fumadoras , no-cuitzo doncare [y] ]


El señor del mundo Sauron no habla de hombres ni de mujeres,

 porque no puede dar falso testimonio,

 y solo puede mentir hablando con los infieles.

lunes, 31 de agosto de 2020

morfosintaxis italiano-english

If I huviaser comprated,

I fumaríader.

Si yo huviase comprato,

yo fumaríare.


If I huviaser comprated,

I hauríader fumated.

Si yo huviase comprato,

yo hauríare fumato.


When I comprader,

I fumader.

Quanto yo comprare,

yo fumare.


When I havader comprated,

I havader fumated.

Quanto yo havere comprato,

yo havere fumato.


When I vader comprader,

I vader fumader.

Quanto yo vare comprare,

yo vare fumare.

domingo, 30 de agosto de 2020

morfosintaxis English

I stader, olweys insider the-haws & olweys insider the-hawses.

I ney stader, never insider the-haws & never insider the-hawses.

[ [x] stader , [u] insider [a] & [u] insider [b] ]

[ [x] ney stader , [v] insider [a] & [v] insider [b] ]


I sader, in-cuitzay doncader fumators & yes doncader fumator.

I ney sader, in-cuitzay doncader fumators & ney doncader fumator.

[ [x] sader , in-cuitzay doncader [b] & yes doncader [a] ]

[ [x] ney sader , in-cuitzay doncader [b] & ney doncader [a] ]

morfosintaxis de françé de le patuá

sóc-de-puá avec le tabác, donc-cas fuma-çí.

[ [x] és-de-puá avec [z] , donc-cas [a] ]

[ [a] és-de-puá fuma-çí ]


ne sóc-de-puá avec le tabác, donc-cas fuma-lí.

[ [x] ne és-de-puá avec [z] , donc-cas [b] ]

[ [b] és-de-puá fuma-lí ]


Tant si-com-çí com si-com-çuá.

[ Tant [a] com [c] ]

[ [a] és-de-puá si-com-çí ]

[ [c] és-de-puá si-com-çuá ]


Tant si-com-lí com si-com-luá.

[ Tant [b] com [d] ]

[ [b] és-de-puá si-com-lí ]

[ [d] és-de-puá si-com-luá ]


Tant donc-cas le-com-çí com donc-cas le-com-çuá,

parlen-puá le françé de le patuá.

[ Tant donc-cas [a] com donc-cas [c] , parlen-puá [z] ]

[ [a] és-de-puá le-com-çí ]

[ [c] és-de-puá le-com-çuá ]


Tant donc-cas le-com-lí com donc-cas le-com-luá,

ne parlen-puá le françé de le patuá.

[ Tant donc-cas [b] com donc-cas [d] , ne parlen-puá [z] ]

[ [b] és-de-puá le-com-lí ]

[ [d] és-de-puá le-com-luá ]


Tant long-temps dans le-com-çí com long-temps dans le-com-çuá,

vaitx-de-puá a celui-çí bar.

Tant ne-temps dans le-com-çí com ne-temps dans le-com-çuá,

ne vaitx-de-puá a celui-çí bar.

[ Tant [u] dans [a] com [u] dans [c] , [x] va-de-puá a [p] ]

[ Tant [v] dans [a] com [v] dans [c] , [x] ne va-de-puá a [p] ]

[ [a] és-de-puá le-com-çí ]

[ [c] és-de-puá le-com-çuá ]


Tant long-temps dans le-com-lí com long-temps dans le-com-luá.

vaitx-de-puá a celui-lí bar.

Tant ne-temps dans le-com-lí com ne-temps dans le-com-luá.

ne vaitx-de-puá a celui-lí bar.

[ Tant [u] dans [b] com [u] dans [d] , [x] va-de-puá a [q] ]

[ Tant [v] dans [b] com [v] dans [d] , [x] ne va-de-puá a [q] ]

[ [b] és-de-puá le-com-lí ]

[ [d] és-de-puá le-com-luá ]