ZadaniaZRozkladuPrymarnego

2799 days ago by jakub.witaszek

# prosty przyklad rozkladu prymarnego idealu z wykladu R.<x,y> = PolynomialRing(QQ, 2, order='lex') I = (x^2, x*y)*R; print "Rozpatrzmy ideal \n", I radI=I.radical(); print "\n Radykal I to \n", radI cpdI = I.complete_primary_decomposition(); print "\n Rozklad prymarny idealu I zawiera dwa idealy\n podane tutaj z odpowiadajacym im radykalami" print "\n >> ideal prostej \n", cpdI[0] print "\n >> ideal podwojnego punktu\n", cpdI[1] 
       
Rozpatrzmy ideal 
Ideal (x^2, x*y) of Multivariate Polynomial Ring in x, y over
Rational Field

 Radykal I to 
Ideal (x) of Multivariate Polynomial Ring in x, y over Rational
Field

 Rozklad prymarny idealu I zawiera dwa idealy
 podane tutaj z odpowiadajacym im radykalami

 >> ideal prostej 
(Ideal (x) of Multivariate Polynomial Ring in x, y over Rational
Field, Ideal (x) of Multivariate Polynomial Ring in x, y over
Rational Field)

 >> ideal podwojnego punktu
(Ideal (y, x^2) of Multivariate Polynomial Ring in x, y over
Rational Field, Ideal (y, x) of Multivariate Polynomial Ring in x, y
over Rational Field)
# prosty przyklad rozkladu prymarnego idealu z wykladu R.<x,y,z> = PolynomialRing(QQ, 3, order='lex') I = (x*y, x-y*z)*R; print "Rozpatrzmy ideal \n", I radI=I.radical(); print "\n Radykal I to \n", radI cpdI = I.complete_primary_decomposition(); print "\n Rozklad prymarny idealu I zawiera idealy\n podane tutaj z odpowiadajacym im radykalami" print "\n", cpdI[0] print "\n", cpdI[1] print "\n", cpdI[2] 
       
Rozpatrzmy ideal 
Ideal (x*y, x - y*z) of Multivariate Polynomial Ring in x, y, z over
Rational Field

 Radykal I to 
Ideal (x, y*z) of Multivariate Polynomial Ring in x, y, z over
Rational Field

 Rozklad prymarny idealu I zawiera idealy
 podane tutaj z odpowiadajacym im radykalami

(Ideal (y^2, x - y*z) of Multivariate Polynomial Ring in x, y, z
over Rational Field, Ideal (y, x) of Multivariate Polynomial Ring in
x, y, z over Rational Field)

(Ideal (z, x) of Multivariate Polynomial Ring in x, y, z over
Rational Field, Ideal (z, x) of Multivariate Polynomial Ring in x,
y, z over Rational Field)

Traceback (click to the left of this block for traceback)
...
IndexError: list index out of range
# prosty przyklad rozkladu prymarnego idealu z wykladu R.<x,y,z> = PolynomialRing(QQ, 3, order='lex') I1 = (x, y)*R; I2 = (x, z)*R; I = I1 * I2; print "Rozpatrzmy ideal \n", I radI=I.radical(); print "\n Radykal I to \n", radI cpdI = I.complete_primary_decomposition(); print "\n Rozklad prymarny idealu I zawiera idealy\n podane tutaj z odpowiadajacym im radykalami" print "\n", cpdI[0] print "\n", cpdI[1] print "\n", cpdI[2] print "\n", cpdI[3] 
       
Rozpatrzmy ideal 
Ideal (x^2, x*z, x*y, y*z) of Multivariate Polynomial Ring in x, y,
z over Rational Field

 Radykal I to 
Ideal (x, y*z) of Multivariate Polynomial Ring in x, y, z over
Rational Field

 Rozklad prymarny idealu I zawiera idealy
 podane tutaj z odpowiadajacym im radykalami

(Ideal (z, x) of Multivariate Polynomial Ring in x, y, z over
Rational Field, Ideal (z, x) of Multivariate Polynomial Ring in x,
y, z over Rational Field)

(Ideal (y, x) of Multivariate Polynomial Ring in x, y, z over
Rational Field, Ideal (y, x) of Multivariate Polynomial Ring in x,
y, z over Rational Field)

(Ideal (z, y, x^2) of Multivariate Polynomial Ring in x, y, z over
Rational Field, Ideal (z, y, x) of Multivariate Polynomial Ring in
x, y, z over Rational Field)

Traceback (click to the left of this block for traceback)
...
IndexError: list index out of range
# prosty przyklad rozkladu prymarnego idealu z wykladu R.<x,y,z> = PolynomialRing(QQ, 3, order='lex') I1 = (x^2, x*y, y^2)*R; I2 = (x*z-y^2)*R; I = I1 * I2; print "Rozpatrzmy ideal \n", I radI=I.radical(); print "\n Radykal I to \n", radI cpdI = I.complete_primary_decomposition(); print "\n Rozklad prymarny idealu I zawiera idealy\n podane tutaj z odpowiadajacym im radykalami" print "\n", cpdI[0] print "\n", cpdI[1] print "\n", cpdI[2] print "\n", cpdI[3] 
       
Rozpatrzmy ideal 
Ideal (x^3*z - x^2*y^2, x^2*y*z - x*y^3, x*y^2*z - y^4) of
Multivariate Polynomial Ring in x, y, z over Rational Field

 Radykal I to 
Ideal (-x*z + y^2) of Multivariate Polynomial Ring in x, y, z over
Rational Field

 Rozklad prymarny idealu I zawiera idealy
 podane tutaj z odpowiadajacym im radykalami

(Ideal (x*z - y^2) of Multivariate Polynomial Ring in x, y, z over
Rational Field, Ideal (x*z - y^2) of Multivariate Polynomial Ring in
x, y, z over Rational Field)

(Ideal (y^2, x^2*y, x^3) of Multivariate Polynomial Ring in x, y, z
over Rational Field, Ideal (y, x) of Multivariate Polynomial Ring in
x, y, z over Rational Field)

Traceback (click to the left of this block for traceback)
...
IndexError: list index out of range