# HG changeset patch
# User Leif Leonhardy <not.really@online.de>
# Date 1275403412 7200
# Node ID d7686100bc95d57234760f3ce78ed8deb0c07c44
# Parent 21acdff220a43f77712cd51cbd047e2184ae2f51
#9108 Marks timeconsuming examples/doctests in symmetric_ideal.py with "long time".
Actually only two examples/lines time out on older/slower machines, but many other lines
depend on their results.
diff r 21acdff220a4 r d7686100bc95 sage/rings/polynomial/symmetric_ideal.py
a

b


113  113  
114  114  The default ordering is lexicographic. We now compute a Groebner basis:: 
115  115  
116   sage: J=I.groebner_basis() 
117   sage: J 
 116  sage: J=I.groebner_basis() ; J # long time 
118  117  [y_1^5 + y_1^3, y_2*y_1^2  y_1^3, y_2^2  y_1^2, x_1*y_1^2  y_1^4, x_1*y_2  y_1^3, x_1^2 + y_1^2, x_2*y_1  y_1^3] 
119  118  
120  119  Ideal membership in ``I`` can now be tested by commuting symmetric reduction modulo ``J``:: 
121  120  
122   sage: I.reduce(J) 
 121  sage: I.reduce(J) # depends on long time example above 
123  122  Symmetric Ideal (0, 0) of Infinite polynomial ring in x, y over Rational Field 
124  123  
125  124  Note that the Groebner basis is not pointwise invariant under permutation. However, any element 
126  125  of ``J`` has symmetric reduction zero even after applying a permutation:: 
127  126  
128  127  sage: P=Permutation([1, 4, 3, 2]) 
129   sage: J[2] 
 128  sage: J[2] # depends on long time example above 
130  129  y_2^2  y_1^2 
131   sage: J[2]^P 
 130  sage: J[2]^P # depends on long time example above 
132  131  y_4^2  y_1^2 
133   sage: J.__contains__(J[2]^P) 
 132  sage: J.__contains__(J[2]^P) # depends on long time example above 
134  133  False 
135   sage: [[(p^P).reduce(J) for p in J] for P in Permutations(4)] 
 134  sage: [[(p^P).reduce(J) for p in J] for P in Permutations(4)] # long time 
136  135  [[0, 0, 0, 0, 0, 0, 0], 
137  136  [0, 0, 0, 0, 0, 0, 0], 
138  137  [0, 0, 0, 0, 0, 0, 0], 
… 
… 

161  160  Since ``I`` is not a Groebner basis, it is no surprise that it can not detect 
162  161  ideal membership:: 
163  162  
164   sage: [p.reduce(I) for p in J] 
 163  sage: [p.reduce(I) for p in J] # depends on long time example above 
165  164  [y_1^5 + y_1^3, y_2*y_1^2  y_1^3, y_2^2  y_1^2, x_1*y_1^2  y_1^4, x_1*y_2  y_1^3, y_2^2 + y_1^2, x_2*y_1  y_1^3] 
166  165  
167  166  Note that we give no guarantee that the computation of a symmetric Groebner basis will terminate in 