210.sagews

R.<p12,p13,p14,p23,p24,p34>=PolynomialRing(QQ,6); R

Multivariate Polynomial Ring in p12, p13, p14, p23, p24, p34 over Rational Field

S.<x1,x2,x3,x4,y1,y2,y3,y4>=PolynomialRing(QQ,8,order='lex'); S

Multivariate Polynomial Ring in x1, x2, x3, x4, y1, y2, y3, y4 over Rational Field

A=matrix(S,2,S.gens()); A

[x1 x2 x3 x4] [y1 y2 y3 y4]

M=A.minors(2); M

[x1*y2 - x2*y1, x1*y3 - x3*y1, x1*y4 - x4*y1, x2*y3 - x3*y2, x2*y4 - x4*y2, x3*y4 - x4*y3]

phi=R.hom(M,S); phi

Ring morphism: From: Multivariate Polynomial Ring in p12, p13, p14, p23, p24, p34 over Rational Field To: Multivariate Polynomial Ring in x1, x2, x3, x4, y1, y2, y3, y4 over Rational Field Defn: p12 |--> x1*y2 - x2*y1 p13 |--> x1*y3 - x3*y1 p14 |--> x1*y4 - x4*y1 p23 |--> x2*y3 - x3*y2 p24 |--> x2*y4 - x4*y2 p34 |--> x3*y4 - x4*y3

I=phi.kernel(); I # doesn't work

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/fwd13/0/code/7.py", line 6, in <module> exec compile(ur'I=phi.kernel(); I # doesn\u0027t work' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> AttributeError: 'sage.rings.morphism.RingHomomorphism_im_gens' object has no attribute 'kernel'

I=phi.inverse_image(S.zero_ideal()); I #not implemented ;-(

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/fwd13/0/code/9.py", line 6, in <module> exec compile(ur'I=phi.inverse_image(S.zero_ideal()); I #not implemented ;-(' + '\n', '', 'single') File "/home/sage/sage_install/sage/local/lib/python2.5/site-packages/Jinja-1.2-py2.5-linux-x86_64.egg/", line 1, in <module> File "morphism.pyx", line 744, in sage.rings.morphism.RingHomomorphism.inverse_image (sage/rings/morphism.c:3828) NotImplementedError

phi(p12*p34 - p13*p24 + p23*p14) #Pluecker relation

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