## 3299 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```