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17 17 |
14 14 |
12/7 12/7 |
0 0 |
1/2 1/2 |
I + 1 I + 1 |
2*I 2*I |
-1/2*I + 1/2 -1/2*I + 1/2 |
Traceback (click to the left of this block for traceback) ... TypeError: unsupported operand parent(s) for //: 'Symbolic Ring' and 'Symbolic Ring' Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_15.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("MS8vYQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpeuVjxc/___code___.py", line 3, in <module> exec compile(u'_sage_const_1 //a File "", line 1, in <module> File "sage/structure/element.pyx", line 1818, in sage.structure.element.Element.__floordiv__ (build/cythonized/sage/structure/element.c:13353) File "sage/structure/coerce.pyx", line 1091, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9657) File "sage/structure/coerce.pyx", line 1087, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:9596) File "sage/structure/element.pyx", line 1816, in sage.structure.element.Element.__floordiv__ (build/cythonized/sage/structure/element.c:13318) File "sage/structure/element.pyx", line 1851, in sage.structure.element.Element._floordiv_ (build/cythonized/sage/structure/element.c:13639) TypeError: unsupported operand parent(s) for //: 'Symbolic Ring' and 'Symbolic Ring' |
0.745705212176720 0.745705212176720 |
0 0 |
e e |
File: /home/sage/build/sage-8.1/local/lib/python2.7/site-packages/sage/functions/trig.py Type: <class ‘sage.functions.trig.Function_sin’> Definition: sin(coerce=True, hold=False, dont_call_method_on_arg=False, *args) Docstring:
File: /home/sage/build/sage-8.1/local/lib/python2.7/site-packages/sage/functions/trig.py Type: <class ‘sage.functions.trig.Function_sin’> Definition: sin(coerce=True, hold=False, dont_call_method_on_arg=False, *args) Docstring:
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[1 2] [3 4] [1 2] [3 4] |
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[ 8 -1] [ 3 9] [ 8 -1] [ 3 9] |
[ 7 7] [21 11] [ 7 7] [21 11] |
[ 49 -36] [ 0 25] [ 49 -36] [ 0 25] |
[ -2 1] [ 3/2 -1/2] [ -2 1] [ 3/2 -1/2] |
[ -2 1] [ 3/2 -1/2] [ -2 1] [ 3/2 -1/2] |
1 1 |
1 1 |
[1 2] [3 4] [1 2] [3 4] |
2 2 |
2 2 |
(-3, 5) (-3, 5) |
[ 7 -3] [ 0 5] [ 7 -3] [ 0 5] |
[7 0] [0 0] [7 0] [0 0] |
[ 7 0] [-1 0] [ 7 0] [-1 0] |
[1 0 0] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [0 0 1] |
2 2 |
[1 2] [3 4] [1 2] [3 4] |
[1 3] [2 4] [1 3] [2 4] |
-2 -2 |
x^2 - 5*x - 2 x^2 - 5*x - 2 |
[1 2] [3 4] [1 2] [3 4] |
[1 2] [3 4] [1 2] [3 4] |
[0 2] [3 4] [0 2] [3 4] |
[0 2] [3 4] [0 2] [3 4] |
[1 2] [3 4] [1 2] [3 4] |
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[1 2] [3 4] [1 2] [3 4] |
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(2, 1, -2) (2, 1, -2) |
(2, 1, -2) (2, 1, -2) |
Traceback (click to the left of this block for traceback) ... AttributeError: 'sage.modules.vector_integer_dense.Vector_integer_dense' object has no attribute 'transpose' Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_62.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dHJhbnNwb3NlKHYp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpV5KD05/___code___.py", line 2, in <module> exec compile(u'transpose(v) File "", line 1, in <module> File "/home/sage/build/sage-8.1/local/lib/python2.7/site-packages/sage/misc/functional.py", line 1645, in transpose return x.transpose() File "sage/structure/element.pyx", line 484, in sage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4377) File "sage/structure/element.pyx", line 497, in sage.structure.element.Element.getattr_from_category (build/cythonized/sage/structure/element.c:4486) File "sage/cpython/getattr.pyx", line 254, in sage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:1901) AttributeError: 'sage.modules.vector_integer_dense.Vector_integer_dense' object has no attribute 'transpose' |
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File: /home/sage/build/sage-8.1/local/lib/python2.7/site-packages/sage/misc/functional.py Type: <type ‘function’> Definition: norm(x) Docstring:
File: /home/sage/build/sage-8.1/local/lib/python2.7/site-packages/sage/misc/functional.py Type: <type ‘function’> Definition: norm(x) Docstring:
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[1 2 3] [4 5 6] [7 8 9] [1 2 3] [0 3 6] [0 0 0] [1 2 3] [4 5 6] [7 8 9] [1 2 3] [0 3 6] [0 0 0] |
[1 2 3] [4 5 6] [7 8 9] [1 2 3] [0 3 6] [0 0 0] [1 2 3] [4 5 6] [7 8 9] [1 2 3] [0 3 6] [0 0 0] |
[1 2] [3 4] [-0.3722813232690144?, 5.372281323269015?] [1 2] [3 4] [-0.3722813232690144?, 5.372281323269015?] |
[1 2] [3 4] [-0.3722813232690144?, 5.372281323269015?] [1 2] [3 4] [-0.3722813232690144?, 5.372281323269015?] |
[ 7 -3] [ 0 5] [7, 5] [ 7 -3] [ 0 5] [7, 5] |
( [7 0] [ 1 1] [0 5], [ 0 2/3] ) ( [7 0] [ 1 1] [0 5], [ 0 2/3] ) |
[(7, [ (1, 0) ], 1), (5, [ (1, 2/3) ], 1)] [(7, [ (1, 0) ], 1), (5, [ (1, 2/3) ], 1)] |
[(7, [ (1, -3/2) ], 1), (5, [ (0, 1) ], 1)] [(7, [ (1, -3/2) ], 1), (5, [ (0, 1) ], 1)] |
-2 -2 |
[0 1 1] [1 0 1] [1 1 0] [0 1 1] [1 0 1] [1 1 0] |
2 2 |
[0 1 1] [1 0 1] [1 1 0] [0 1 1] [1 0 1] [1 1 0] |
3 3 |
[] [-1 2] [ 3 2] [-4 2] [ 3 -1] [-6 2] [ 3 -3] [-8 2] [ 3 -5] [-10 2] [ 3 -7] [-2 2] [ 3 1] [[-1 2] [ 3 2], [-4 2] [ 3 -1], [-6 2] [ 3 -3], [-8 2] [ 3 -5], [-10 2] [ 3 -7], [-2 2] [ 3 1]] [] [-1 2] [ 3 2] [-4 2] [ 3 -1] [-6 2] [ 3 -3] [-8 2] [ 3 -5] [-10 2] [ 3 -7] [-2 2] [ 3 1] [[-1 2] [ 3 2], [-4 2] [ 3 -1], [-6 2] [ 3 -3], [-8 2] [ 3 -5], [-10 2] [ 3 -7], [-2 2] [ 3 1]] |
0 & 1 2 & & & 3 4 & & & & & 0 & 1 2 & & & 3 4 & & & & & |
0 & 1 @ 2 & & & 3 8 4 & & & & & 0 & 1 @ 2 & & & 3 8 4 & & & & & |
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7 7 |
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[ -I + 1 I + 3] [ 2 -2*I + 4] [ -I + 1 I + 3] [ 2 -2*I + 4] |
[ 4 -2] [-3 1] [ 4 -2] [-3 1] |
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0 No 1 No 2 Yes 3 Yes 4 No 5 Yes 6 No 7 Yes 8 No 9 No 10 No 11 Yes 12 No 13 Yes 14 No 15 No 16 No 17 Yes 18 No 19 Yes 0 No 1 No 2 Yes 3 Yes 4 No 5 Yes 6 No 7 Yes 8 No 9 No 10 No 11 Yes 12 No 13 Yes 14 No 15 No 16 No 17 Yes 18 No 19 Yes |
File: /home/sage/build/sage-8.1/local/lib/python2.7/site-packages/sage/games/sudoku.py Type: <type ‘function’> Definition: sudoku(m) Docstring:
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[0 1 0 0 0 0 0 0 0] [0 0 0 0 0 0 8 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 9 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 1] [8 1 2 3 4 5 9 6 7] [5 3 6 9 2 7 8 1 4] [9 4 7 1 8 6 2 5 3] [6 2 8 4 5 3 1 7 9] [1 5 4 7 9 2 6 3 8] [7 9 3 6 1 8 4 2 5] [3 8 1 5 6 4 7 9 2] [4 7 9 2 3 1 5 8 6] [2 6 5 8 7 9 3 4 1] [8 1 2 3 4 5 9 6 7] [5 3 6 9 2 7 8 1 4] [9 4 7 1 8 6 2 5 3] [6 2 8 4 5 3 1 7 9] [1 5 4 7 9 2 6 3 8] [7 9 3 6 1 8 4 2 5] [3 8 1 5 6 4 7 9 2] [4 7 9 2 3 1 5 8 6] [2 6 5 8 7 9 3 4 1] [0 1 0 0 0 0 0 0 0] [0 0 0 0 0 0 8 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 9 0] [0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 1] [8 1 2 3 4 5 9 6 7] [5 3 6 9 2 7 8 1 4] [9 4 7 1 8 6 2 5 3] [6 2 8 4 5 3 1 7 9] [1 5 4 7 9 2 6 3 8] [7 9 3 6 1 8 4 2 5] [3 8 1 5 6 4 7 9 2] [4 7 9 2 3 1 5 8 6] [2 6 5 8 7 9 3 4 1] [8 1 2 3 4 5 9 6 7] [5 3 6 9 2 7 8 1 4] [9 4 7 1 8 6 2 5 3] [6 2 8 4 5 3 1 7 9] [1 5 4 7 9 2 6 3 8] [7 9 3 6 1 8 4 2 5] [3 8 1 5 6 4 7 9 2] [4 7 9 2 3 1 5 8 6] [2 6 5 8 7 9 3 4 1] |
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[0 0 1 1 1 1 0 0 0 0 0 0] [0 0 0 0 0 0 0 1 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 1 1 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 1 0 0 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] [0 0 1 1 1 1 0 0 0 0 0 0] [0 0 0 0 0 0 0 1 0 1 0 1] [1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 1 1 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 0 0 1 0 0 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 0] [0 1 0 0 0 0 0 0 0 0 0 0] |
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True True |
False False |
False False |
5 5 |
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True True |
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[0] [0, 3] [0, 4] [1] [1, 4] [1, 5] [2] [2, 5] [2, 6] [3] [3, 6] [4] [5] [6] [] [0] [0, 3] [0, 4] [1] [1, 4] [1, 5] [2] [2, 5] [2, 6] [3] [3, 6] [4] [5] [6] [] |
[0, 3] [0, 4] [1, 4] [1, 5] [2, 5] [2, 6] [3, 6] [0, 3] [0, 4] [1, 4] [1, 5] [2, 5] [2, 6] [3, 6] |
7 7 |
0 12 72 0 12 72 |
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0 0 168 0 0 168 |
Standard permutations of 3 [1, 2, 3] [1, 3, 2] [2, 1, 3] [2, 3, 1] [3, 1, 2] [3, 2, 1] Standard permutations of 3 [1, 2, 3] [1, 3, 2] [2, 1, 3] [2, 3, 1] [3, 1, 2] [3, 2, 1] |
Permutations of {1,...,5} of length 3 [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 2], [1, 3, 4], [1, 3, 5], [1, 4, 2], [1, 4, 3], [1, 4, 5], [1, 5, 2], [1, 5, 3], [1, 5, 4], [2, 1, 3], [2, 1, 4], [2, 1, 5], [2, 3, 1], [2, 3, 4], [2, 3, 5], [2, 4, 1], [2, 4, 3], [2, 4, 5], [2, 5, 1], [2, 5, 3], [2, 5, 4], [3, 1, 2], [3, 1, 4], [3, 1, 5], [3, 2, 1], [3, 2, 4], [3, 2, 5], [3, 4, 1], [3, 4, 2], [3, 4, 5], [3, 5, 1], [3, 5, 2], [3, 5, 4], [4, 1, 2], [4, 1, 3], [4, 1, 5], [4, 2, 1], [4, 2, 3], [4, 2, 5], [4, 3, 1], [4, 3, 2], [4, 3, 5], [4, 5, 1], [4, 5, 2], [4, 5, 3], [5, 1, 2], [5, 1, 3], [5, 1, 4], [5, 2, 1], [5, 2, 3], [5, 2, 4], [5, 3, 1], [5, 3, 2], [5, 3, 4], [5, 4, 1], [5, 4, 2], [5, 4, 3]] Permutations of {1,...,5} of length 3 [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 2], [1, 3, 4], [1, 3, 5], [1, 4, 2], [1, 4, 3], [1, 4, 5], [1, 5, 2], [1, 5, 3], [1, 5, 4], [2, 1, 3], [2, 1, 4], [2, 1, 5], [2, 3, 1], [2, 3, 4], [2, 3, 5], [2, 4, 1], [2, 4, 3], [2, 4, 5], [2, 5, 1], [2, 5, 3], [2, 5, 4], [3, 1, 2], [3, 1, 4], [3, 1, 5], [3, 2, 1], [3, 2, 4], [3, 2, 5], [3, 4, 1], [3, 4, 2], [3, 4, 5], [3, 5, 1], [3, 5, 2], [3, 5, 4], [4, 1, 2], [4, 1, 3], [4, 1, 5], [4, 2, 1], [4, 2, 3], [4, 2, 5], [4, 3, 1], [4, 3, 2], [4, 3, 5], [4, 5, 1], [4, 5, 2], [4, 5, 3], [5, 1, 2], [5, 1, 3], [5, 1, 4], [5, 2, 1], [5, 2, 3], [5, 2, 4], [5, 3, 1], [5, 3, 2], [5, 3, 4], [5, 4, 1], [5, 4, 2], [5, 4, 3]] |
Permutations of the set ['a', 'b', 'c'] ['a', 'b', 'c'] ['a', 'c', 'b'] Traceback (click to the left of this block for traceback) ... TypeError: unsupported operand parent(s) for *: 'Permutations of the set ['a', 'b', 'c']' and 'Permutations of the set ['a', 'b', 'c']' Permutations of the set ['a', 'b', 'c'] ['a', 'b', 'c'] ['a', 'c', 'b'] Traceback (most recent call last): print p1 File "", line 1, in <module> File "/tmp/tmpftUXT9/___code___.py", line 11, in <module> exec compile(u'print p1*p2 File "", line 1, in <module> File "sage/structure/element.pyx", line 1519, in sage.structure.element.Element.__mul__ (build/cythonized/sage/structure/element.c:12077) File "sage/structure/element.pyx", line 1558, in sage.structure.element.Element._mul_ (build/cythonized/sage/structure/element.c:12466) TypeError: unsupported operand parent(s) for *: 'Permutations of the set ['a', 'b', 'c']' and 'Permutations of the set ['a', 'b', 'c']' |
Permutations of the multi-set [0, 0, 1] [[0, 0, 1], [0, 1, 0], [1, 0, 0]] Permutations of the multi-set [0, 0, 1] [[0, 0, 1], [0, 1, 0], [1, 0, 0]] |
Standard permutations of 4 avoiding [1, 3, 2] [[4, 1, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1], [3, 4, 1, 2], [3, 4, 2, 1], [2, 3, 4, 1], [3, 2, 4, 1], [1, 2, 3, 4], [2, 1, 3, 4], [2, 3, 1, 4], [3, 1, 2, 4], [3, 2, 1, 4]] Standard permutations of 4 avoiding [1, 3, 2] [[4, 1, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1], [3, 4, 1, 2], [3, 4, 2, 1], [2, 3, 4, 1], [3, 2, 4, 1], [1, 2, 3, 4], [2, 1, 3, 4], [2, 3, 1, 4], [3, 1, 2, 4], [3, 2, 1, 4]] |
Standard permutations of 4 avoiding [[1, 3, 2], [1, 2, 3]] [[3, 4, 1, 2], [4, 3, 1, 2], [4, 2, 1, 3], [4, 2, 3, 1], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 2, 1], [4, 3, 2, 1]] Standard permutations of 4 avoiding [[1, 3, 2], [1, 2, 3]] [[3, 4, 1, 2], [4, 3, 1, 2], [4, 2, 1, 3], [4, 2, 3, 1], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 2, 1], [4, 3, 2, 1]] |
Words of length 5 over {'0', '1'} 00000 00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110 11111 Words of length 5 over {'0', '1'} 00000 00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110 11111 |
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