# ch.9 problem.P5

## 1664 days ago by g1.kjiwon

a,b,c,d=var('a,b,c,d') A=matrix([[a,b], [c,d]]) AT=A.transpose() print A+AT
 Traceback (click to the left of this block for traceback) ... ValueError: variable names must be alphanumeric, but one is '[a, b]' which is not. Traceback (most recent call last): File "", line 1, in File "_sage_input_70.py", line 10, in exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("YSxiLGMsZD12YXIoJ2EsYixjLGQnKSAgICAKQT1tYXRyaXgoUVFbW2EsYl0sIFtjLGRdXSkKQVQ9QS50cmFuc3Bvc2UoKQpwcmludCBBK0FU"),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in File "/tmp/tmp_qGeZR/___code___.py", line 3, in A=matrix(QQ[[a,b], [c,d]]) File "ring.pyx", line 301, in sage.rings.ring.Ring.__getitem__ (sage/rings/ring.c:3386) File "/root/sage-5.8/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py", line 480, in PolynomialRing R = _multi_variate(base_ring, names, n, sparse, order, implementation) File "/root/sage-5.8/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py", line 577, in _multi_variate names = normalize_names(n, names) File "parent_gens.pyx", line 207, in sage.structure.parent_gens.normalize_names (sage/structure/parent_gens.c:2477) File "parent_gens.pyx", line 146, in sage.structure.parent_gens._certify_names (sage/structure/parent_gens.c:2006) ValueError: variable names must be alphanumeric, but one is '[a, b]' which is not.
M = MatrixSpace(ZZ,2,2) h(A)=[A+AT] T=linear_transformation(M,M,h,side='right') print T print T.kernel() print T.image()
 Traceback (click to the left of this block for traceback) ... TypeError: first argument must be a matrix or a vector space, not Full MatrixSpace of 2 by 2 dense matrices over Integer Ring Traceback (most recent call last): File "", line 1, in File "_sage_input_73.py", line 10, in exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("TSA9IE1hdHJpeFNwYWNlKFpaLDIsMikKaChBKT1bQStBVF0KVD1saW5lYXJfdHJhbnNmb3JtYXRpb24oTSxNLGgsc2lkZT0ncmlnaHQnKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in File "/tmp/tmpBUVDQf/___code___.py", line 5, in exec compile(u"T=linear_transformation(M,M,h,side='right')" + '\n', '', 'single') File "", line 1, in File "/root/sage-5.8/local/lib/python2.7/site-packages/sage/modules/vector_space_morphism.py", line 701, in linear_transformation raise TypeError('first argument must be a matrix or a vector space, not {0}'.format(arg0)) TypeError: first argument must be a matrix or a vector space, not Full MatrixSpace of 2 by 2 dense matrices over Integer Ring

 A |--> [A + a c] [ b A + d] Traceback (click to the left of this block for traceback) ... AttributeError: 'sage.symbolic.expression.Expression' object has no attribute 'kernel' A |--> [A + a c] [ b A + d] Traceback (most recent call last): File "", line 1, in File "_sage_input_74.py", line 10, in exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cHJpbnQgVApwcmludCBULmtlcm5lbCgpCnByaW50IFQuaW1hZ2UoKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in File "/tmp/tmpap9Fww/___code___.py", line 3, in print T.kernel() File "element.pyx", line 344, in sage.structure.element.Element.__getattr__ (sage/structure/element.c:3637) File "misc.pyx", line 257, in sage.structure.misc.getattr_from_other_class (sage/structure/misc.c:1507) AttributeError: 'sage.symbolic.expression.Expression' object has no attribute 'kernel'