\n"}︡{"done":true}︡
︠cbad0a89-e8b4-426e-a203-4f39776c6366s︠
isinstance(a, Integer)
isinstance(a, str)
︡19931635-c393-4526-b61b-3475303ebf9d︡{"stdout":"True\n"}︡{"stdout":"False\n"}︡{"done":true}︡
︠05d01a38-4b29-426d-8482-f83cf0c32086i︠
%html
Booleans
bool has one of two values: True and False.
There are three boolean operators: and, or, & not.
You can convert something into a boolean by the bool function.
︡b2ee09b5-d479-4b67-8b32-bdc98629ceae︡{"done":true,"html":"Booleans
\n\n bool has one of two values: True and False.\n
\n\n There are three boolean operators: and, or, & not.\n
\n\n You can convert something into a boolean by the bool function.\n
"}
︠460f0aeb-f9d7-482a-9aed-448de63196fds︠
type(True)
︡1d0cbfff-15fb-4483-8a86-7037fbd86cf6︡{"stdout":"\n"}︡{"done":true}︡
︠71d848b0-77eb-4e24-afb3-0cb7cd417198s︠
bool(1)
bool(0)
bool(-1)
︡7962e245-cb2f-4fdd-b002-92159895afcb︡{"stdout":"True\n"}︡{"stdout":"False\n"}︡{"stdout":"True\n"}︡{"done":true}︡
︠76192771-ab83-4d4e-acec-fd1838756ea1s︠
True and False
︡011b427d-2fdb-460b-84fa-c2bf6e90b45f︡{"stdout":"False\n"}︡{"done":true}︡
︠446127bb-a1be-4152-a086-9bde53b52aa6s︠
not True
︡5ecbe17c-87b4-4ff5-964c-13f952b3e63f︡{"stdout":"False\n"}︡{"done":true}︡
︠0bf73127-11b6-442a-b1af-b4152ee6232as︠
False or True
︡e2cf0745-c366-4179-8102-d738b6b09c57︡{"stdout":"True\n"}︡{"done":true}︡
︠4a44f9d5-f570-457c-8e34-beffaede2486i︠
%html
Integers/Floats
int is the python built-in integer type. The problem with the python version is the integer conversion problem.
Due to this restriction, Sage uses its own type called Integer.
float is the python built-in rational number type. Due to similar restrictions, Sage uses the RealLiteral type.
︡1ab9e3c6-550f-4526-a314-126413479d9d︡{"done":true,"html":"Integers/Floats
\n\n int is the python built-in integer type. The problem with the python version is the integer conversion problem.\n Due to this restriction, Sage uses its own type called Integer.\n
\n\n float is the python built-in rational number type. Due to similar restrictions, Sage uses the RealLiteral type.\n
"}
︠e9924e42-1084-431e-8106-51e86a137c59s︠
int(5)/int(2)
︡109005e7-c603-4828-9e3c-b98ca5948448︡{"stdout":"2\n"}︡{"done":true}︡
︠6d173746-37b5-43b9-8910-612afa6bc68es︠
type(1)
type(1.2)
︡9e899121-e3b2-4855-b2dd-89f7d54be4bf︡{"stdout":"\n"}︡{"stdout":"\n"}︡{"done":true}︡
︠09dda59f-9900-49b5-854f-3060baafcc72i︠
%html
Strings
The str type is fairly common. You can use single or double quotes. Additionally you can use triple quotes if you want a multi-line string. You can also fill a string using dictionary substitutions as can be seen in the following example.
︡8d819b53-0adf-4616-b584-8d094604366c︡{"done":true,"html":"\n Strings\n
\n\n The str type is fairly common. You can use single or double quotes. Additionally you can use triple quotes if you want a multi-line string. You can also fill a string using dictionary substitutions as can be seen in the following example.\n
"}
︠e82313cb-0563-4632-bb17-d857ce81a6bbs︠
aram = 'Aram'
print """Hello %s,
You're a pretty cool person.
- %s
""" % ('human', aram)
︡e9349a30-abca-47aa-86e3-dcaeb70d9b1b︡{"stdout":"Hello human,\nYou're a pretty cool person.\n- Aram\n\n"}︡{"done":true}︡
︠8b21002f-379c-44da-8ab1-64e23160718ass︠
print a, "factors into", a.factor()
︡4bc64b8f-b219-4674-9611-b07d61cc53d6︡{"stdout":"123 factors into 3 * 41\n"}︡{"done":true}︡
︠e2716743-5900-40c0-a3d3-ce96462466eds︠
print str(a) + " factors into " + str(a.factor())
︡ad88ce6c-d3f2-4aa9-8c28-9cb05d5ae7dc︡{"stdout":"123 factors into 3 * 41\n"}︡{"done":true}︡
︠80d785a3-5597-49fe-8588-f4ba4554ce76i︠
%html
Sets, lists, tuples, and dictionaries
Because, why not.
set - is a set of items with no multiplicites or order.list - is an ordered list of itemstuple - is the same as a list, but it is immutable (it cannot be changed).dict - Is an associative array which associates values with keys.
︡c6639e79-77b1-44db-a7a9-30e680228a50︡{"done":true,"html":"Sets, lists, tuples, and dictionaries
\nBecause, why not.
\n\n set - is a set of items with no multiplicites or order.list - is an ordered list of itemstuple - is the same as a list, but it is immutable (it cannot be changed).dict - Is an associative array which associates values with keys.
"}
︠d448cdd4-fe85-48d0-b81f-f342154ae919i︠
%html
Some basic commands
Constructing stuff
︡367def72-c5bc-41c2-857e-0d409a792ce7︡{"done":true,"html":"Some basic commands
\n\n Constructing stuff\n
"}
︠6cf7c75d-2b96-4bab-8239-42185026ff48s︠
S = set([1,2,3])
L = [1,2,3]
T = (1,2,3)
D = {2:1, 3:2, 4:3}
S
L
T
D
︡e7df4c1a-367b-40ae-a6f0-d1db3311c702︡{"stdout":"set([1, 2, 3])\n"}︡{"stdout":"[1, 2, 3]\n"}︡{"stdout":"(1, 2, 3)\n"}︡{"stdout":"{2: 1, 3: 2, 4: 3}\n"}︡{"done":true}︡
︠9cd1c57b-b990-4d4e-b85d-1a0b02279b52s︠
set([1])
[1]
{1:2}
︡df625e2e-f993-4ae7-97d7-32087a99e563︡{"stdout":"set([1])\n"}︡{"stdout":"[1]\n"}︡{"stdout":"{1: 2}\n"}︡{"done":true}︡
︠a651cdd6-0bc8-4ea7-b300-f38b2441c395s︠
(1)
(1,2)
︡35a6e52f-7327-44c7-9606-5cacf9cc4c37︡{"stdout":"1\n"}︡{"stdout":"(1, 2)\n"}︡{"done":true}︡
︠e4950c90-5090-4b04-87af-fc63f729330es︠
(1,)
︡dbadfe79-394d-4567-bd08-1564db9e108e︡{"stdout":"(1,)\n"}︡{"done":true}︡
︠94e93079-9f43-4e22-946e-688847728fbdi︠
%html
How many stuff does it have?
Use the len function.
︡fa3f6add-986c-4a14-8a48-9ac71f59b56d︡{"done":true,"html":"\n How many stuff does it have?\n
\nUse the len function."}
︠967a422e-7b3b-44b3-b898-167f0f877644s︠
len(S)
len(L)
len(T)
len(D)
︡52a8e4df-e4a6-426d-9504-59755152e962︡{"stdout":"3\n"}︡{"stdout":"3\n"}︡{"stdout":"3\n"}︡{"stdout":"3\n"}︡{"done":true}︡
︠5cb5e9f1-3b84-40e5-98c5-57b3eea083d0i︠
%html
Is this object present?
Use the in operator.
Note: The in operator for dictionaries looks at the keys!
︡8989c085-16e2-48f2-b33c-a47bd2f9af2e︡{"done":true,"html":"\n Is this object present?\n
\n\nUse the in operator.
\nNote: The in operator for dictionaries looks at the keys!"}
︠a3ab964b-badf-4530-9a45-959097c5410ds︠
S = set([1,2,3])
L = [1,2,3]
T = (1,2,3)
D = {2:1, 3:2, 4:3}
1 in S
1 in L
1 in T
1 in D
︡667ede1a-87b1-405b-a053-83ca39438e9d︡{"stdout":"True\n"}︡{"stdout":"True\n"}︡{"stdout":"True\n"}︡{"stdout":"False\n"}︡{"done":true}︡
︠e4809fe6-c0fd-491e-8f26-cae056a6b1d9s︠
4 not in S
4 not in L
4 not in T
4 not in D
︡2a6b3737-16b8-437b-963e-9f64dc1dea68︡{"stdout":"True\n"}︡{"stdout":"True\n"}︡{"stdout":"True\n"}︡{"stdout":"False\n"}︡{"done":true}︡
︠1651c02a-7aac-473f-94b6-19853be8a3e9i︠
%html
How do I access elements?
Use square brackets to access individual items. For dictionaries you use the key. For lists and tuples the counting begins at $0$. Sets have no order so you can't "access" things.
︡40c35db4-5250-45a6-81fa-c8f0599355c2︡{"done":true,"html":"\n How do I access elements?\n
\nUse square brackets to access individual items. For dictionaries you use the key. For lists and tuples the counting begins at $0$. Sets have no order so you can't \"access\" things."}
︠473696a5-16c8-4e6d-a887-1c60815f377cs︠
L = [1,2,3]
T = (1,2,3)
D = {2:1, 3:2, 4:3}
L[0]
T[0]
D[2]
︡102295dd-1269-430a-9243-e6dc1730176f︡{"stdout":"1\n"}︡{"stdout":"1\n"}︡{"stdout":"1\n"}︡{"done":true}︡
︠2698ab54-ae0b-4c46-9bbe-38aa656f0caci︠
%html
Can I modify things?
Only lists and dictionaries! Tuples are immutable, so they can't be altered.
︡f46e1e38-3d26-4a87-89a9-36e587650792︡{"done":true,"html":"\n Can I modify things?\n
\nOnly lists and dictionaries! Tuples are immutable, so they can't be altered."}
︠7508ae96-18db-499a-837d-75448d5724aes︠
L[0] = 5
D[2] = 5
L
D
︡b4a0a975-45a9-4f7c-a1c2-e33e48cf3c0f︡{"stdout":"[5, 2, 3]\n"}︡{"stdout":"{2: 5, 3: 2, 4: 3}\n"}︡{"done":true}︡
︠7f484d77-9f33-4108-b7e7-77ebc157c497i︠
%html
How do I add new things?
There are many ways my young padawan.
Sets - Use the add function
Lists - You can append a list at the end, extend a list with another list, or just plain add two lists together.
Tuples - They are immutable, so we can't alter them! We can add two of them together and create a new tuple though.
Dictionaries - Just add a new key and put in a value.
︡988f7a35-a7fd-4307-bde3-f7d523330954︡{"done":true,"html":"\n How do I add new things?\n
\nThere are many ways my young padawan.\n\n Sets - Use the add function\n
\n\n Lists - You can append a list at the end, extend a list with another list, or just plain add two lists together.\n
\n\n Tuples - They are immutable, so we can't alter them! We can add two of them together and create a new tuple though.\n
\n\n Dictionaries - Just add a new key and put in a value.\n
"}
︠dd5247ac-9185-4b43-9c84-78538bd77c7cs︠
S = set([1,2,3])
S.add(2)
S.add(4)
S
︡c24d1559-ecb4-4a8f-908d-2495cbd8b3d2︡{"stdout":"set([1, 2, 3, 4])\n"}︡{"done":true}︡
︠1f53ee06-0007-464c-8230-8a5cc3bdd320s︠
L = [1,2,3]
L2 = ["a", "b"]
L3 = [(1,2), (4,5)]
L.append(4)
L.extend(L2)
L
L4 = L2 + L3
L4
︡6b14f080-82a3-454e-a37c-ed63e786132b︡{"stdout":"[1, 2, 3, 4, 'a', 'b']\n"}︡{"stdout":"['a', 'b', (1, 2), (4, 5)]\n"}︡{"done":true}︡
︠e46d39f8-8224-4573-a364-0f4fba956ccas︠
T = (1,2,3)
T2 = (0,0)
T3 = T + T2
T3
︡1fac299a-4b66-421e-aec9-76fbf6d3e164︡{"stdout":"(1, 2, 3, 0, 0)\n"}︡{"done":true}︡
︠7e9f037b-6ec2-4b91-aeb7-1728b73cf074s︠
D = {2:1, 3:2, 4:3}
D[10] = fibonacci(10)
D[(3,2,1)] = Permutation([3,2,1])
D
︡89850356-be1c-4e81-80ea-260cfeaf7810︡{"stdout":"{2: 1, 3: 2, 4: 3, 10: 55, (3, 2, 1): [3, 2, 1]}\n"}︡{"done":true}︡
︠ed531dcd-1923-43fe-9e58-c8e009d76400i︠
%html
Note: For lists we can't add additional items like we do in dictionaries.
︡f738358f-cb1a-42c7-89c9-db17a2c3f7f1︡{"done":true,"html":"Note: For lists we can't add additional items like we do in dictionaries."}
︠be6ff520-d74c-4a76-a44b-3d934e474161s︠
L[10] = fibonacci(10)
︡4fd4fdc2-863f-47b3-bcde-e7454a80947e︡{"stderr":"Error in lines 1-1\nTraceback (most recent call last):\n File \"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 905, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \nIndexError: list assignment index out of range\n"}︡{"done":true}︡
︠6dcf9053-19d4-4e1c-9007-566aab867b2fi︠
%html
Note: We also can't add mutable items as keys for dictionaries.
︡f6d20c88-7e55-4b58-b401-e3fecdbe3618︡{"done":true,"html":"Note: We also can't add mutable items as keys for dictionaries."}
︠b96760af-be25-4d89-b94f-72939b1f5928s︠
D[[1]] = 'fail'
︡5c36bf37-dd28-4c67-b11a-356b78d6b870︡{"stderr":"Error in lines 1-1\nTraceback (most recent call last):\n File \"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 905, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \nTypeError: unhashable type: 'list'\n"}︡{"done":true}︡
︠a79655be-763f-4133-a272-5c5fcd1cc321i︠
%html
Russell's paradox
Sets of sets can't happen
︡420a4d1f-7403-465c-8585-4ead901ae009︡{"done":true,"html":"\n Russell's paradox\n
\n\n Sets of sets can't happen\n
"}
︠96b76308-b3a2-469e-ad0f-9d81a3deeb46s︠
S1 = set([1,2,3])
S2 = set([S1])
S2
︡65964482-5d53-4a9f-8c25-122221d4bb3a︡{"stderr":"Error in lines 2-2\nTraceback (most recent call last):\n File \"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 905, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \nTypeError: unhashable type: 'set'\n"}︡{"done":true}︡
︠963da764-c237-46f9-bb92-0f5367eda3a2s︠
S1 = frozenset([1,2,3])
S2 = set([S1])
S2
︡2a22db94-adc9-462a-9cf4-91709cfc8955︡{"stdout":"set([frozenset([1, 2, 3])])\n"}︡{"done":true}︡
︠c6a2a22c-ac22-4573-a65c-d11db45047fbi︠
%html
Exercise: Look at the following code and make a guess as to what will be displayed.
︡d6fe3fab-8097-4469-bc0f-fc7fa52cfb92︡{"done":true,"html":"Exercise: Look at the following code and make a guess as to what will be displayed."}
︠4f07d38e-8a73-4a05-a716-3da6db0fa7a0s︠
L = [1,"z",3,4,5]
L.append("c")
L = L + [9,10]
L[6]
︡ab233445-da70-4967-823a-f0d973850495︡{"stdout":"9\n"}︡{"done":true}︡
︠27a1e87f-1b3e-48bb-8d94-ff8c3805980ei︠
%html
But I added too much! How do I delete things I don't want?
︡0091226d-93b2-4bd8-bccb-9d5ff3d9452b︡{"done":true,"html":"\n But I added too much! How do I delete things I don't want?\n
"}
︠7f69192e-e0f3-4627-a72d-f7f47ff24b63ss︠
S = set([1,2,3])
S.discard(2)
S
︡81d9d178-ba33-41e9-88a9-5971089b674d︡{"stdout":"set([1, 3])\n"}︡{"done":true}︡
︠0eb67729-3cf0-446a-a004-346ff39e0f65s︠
L = [1,2,3,4,5]
del L[1]
poppedItem = L.pop(0)
L.remove(3)
L
poppedItem
L.remove(3)
︡5214d175-3055-4db1-9dc0-c03109e64f10︡{"stdout":"[4, 5]\n"}︡{"stdout":"1\n"}︡{"stderr":"Error in lines 7-7\nTraceback (most recent call last):\n File \"/projects/sage/sage-6.10/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 905, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \nValueError: list.remove(x): x not in list\n"}︡{"done":true}︡
︠c31c8a9e-f50e-46d1-8ae1-03ba899af0d6s︠
L = [1, 2, 3, 2]
L.remove(2)
L
︡bf510e82-25d0-4462-ad00-8185f7ca0bdb︡{"stdout":"[1, 3, 2]\n"}︡{"done":true}︡
︠4c461870-370e-459d-bec2-155618483a66s︠
L2 = [1,2,3,4,5]
L2 = L2[1:3]
L2
︡a4dbbac0-02a9-4eb0-9c71-9865efea6539︡{"stdout":"[2, 3]\n"}︡{"done":true}︡
︠f6bad326-8944-4ab8-a2f7-6dbf8f670290s︠
T = (1,2,3,4,5)
T = T[1:3]
T
︡f4f04eb4-8d6c-4dfb-852c-4b1a398fe0ea︡
︠9860df18-8068-4963-8318-3ac578201c06s︠
D = {2:1, 3:2, 4:3}
del D[3]
poppedItem = D.pop(4)
D
︡b22d306f-029c-4a96-bffe-7226dc7d0f77︡{"stdout":"{2: 1}\n"}︡{"done":true}︡
︠0d3f073e-f27f-4870-b3f9-c8dc9d5adc28i︠
%html
Some other useful commands (Lists only!):
︡31dc7b81-9476-4ba1-bd8f-3bd7b74f2b6b︡{"done":true,"html":"\n Some other useful commands (Lists only!):\n
\n"}
︠2d68ef01-9dbe-41c0-85e3-648503d8fc03s︠
L = [5,4,1,2,3]
L.sort()
L
︡a62d24f0-579a-4fd1-b42c-f0781003ef01︡{"stdout":"[1, 2, 3, 4, 5]\n"}︡{"done":true}︡
︠41a7a3b2-05b8-4878-aa9a-fb54a6e3e773︠
︡5f6b15ea-3703-4b0d-bf90-c1cb3d43f5f4︡
︠48eb6f1b-29cd-42c2-8005-fe8392ce43f1s︠
L = [5,4,1,2,3]
L.reverse()
L
︡6a01449a-5caf-4b44-a65d-14d32fade2c7︡{"stdout":"[3, 2, 1, 4, 5]\n"}︡{"done":true}︡
︠d6a9c3c6-33ca-4b35-9259-9c9d90bbcd48i︠
%html
Some basic commands
| Operation |
set |
list |
tuple |
dict |
| Construction |
set([]) |
[] |
() |
{} |
| One element construction |
set([1]) |
[1] |
(1,) |
{1:1} |
| Size |
len(set) |
len(list) |
len(tuple) |
len(dict) |
| Contains |
x in set |
x in list |
x in tuple |
key in dict |
| Accessing entries |
- |
list[0] |
tuple[0] |
dict[key] |
| Adding stuff |
set.add(x) |
list.append(x)
list.extend(list2)
list3 = list1 + list2 |
tuple3 = tuple1 + tuple2 |
dict[key] = x
key must be immutable |
| Deleting stuff |
set.discard(item) |
list.pop(i)
del list[i]
list = list[start:end]
list.remove(value) |
tuple = tuple[start:end] |
dict.pop(key)
del dict[key] |
︡9f99c451-cdf7-4471-a9cc-86ac2e80b872︡{"done":true,"html":"Some basic commands
\n\n \n \n | Operation | \n set | \n list | \n tuple | \n dict | \n
\n \n \n \n | Construction | \n set([]) | \n [] | \n () | \n {} | \n
\n \n | One element construction | \n set([1]) | \n [1] | \n (1,) | \n {1:1} | \n
\n \n | Size | \n len(set) | \n len(list) | \n len(tuple) | \n len(dict) | \n
\n \n | Contains | \n x in set | \n x in list | \n x in tuple | \n key in dict | \n
\n \n | Accessing entries | \n - | \n list[0] | \n tuple[0] | \n dict[key] | \n
\n \n | Adding stuff | \n set.add(x) | \n list.append(x)
list.extend(list2)
list3 = list1 + list2 | \n tuple3 = tuple1 + tuple2 | \n dict[key] = x
key must be immutable | \n
\n \n | Deleting stuff | \n set.discard(item) | \n list.pop(i)
del list[i]
list = list[start:end]
list.remove(value) | \n tuple = tuple[start:end] | \n dict.pop(key)
del dict[key] | \n
\n \n
"}
︠412b180b-e828-49c9-8018-eabb7ebeb1c6i︠
%html
Exercise:
- Create the list
[5,1,3,6,7,2,12].
- Remove the element 12.
- Add the element 4.
- Sort the list and reverse it.
︡4f3d6a9b-db3c-4f30-9f72-e5103b321ad1︡{"done":true,"html":"Exercise:\n\n - Create the list
[5,1,3,6,7,2,12]. \n - Remove the element 12.
\n - Add the element 4.
\n - Sort the list and reverse it.
\n
"}
︠9a6ba292-6865-479b-98bc-ec85f93e899c︠
# Try it out!
︡b220a64b-e07e-4c53-abc6-72c36944f3f2︡
︠e0e4f341-f592-46e6-9b75-8a48af2a15d6i︠
%html
The modification problem.
Or things that should be illegal.
Changing lists and dictionaries can have unintended consequences.
︡2498f3d2-e771-4bc4-aa2d-914faa8b6e93︡{"done":true,"html":"\n The modification problem.\n
\n\n Or things that should be illegal.\n
\nChanging lists and dictionaries can have unintended consequences."}
︠e0b35070-7fb6-49f3-b9b6-e4fa2830bb82s︠
L = ["a", "b", "c"]
L2 = [L, L]
L2
︡8374c55e-6605-4112-9b8a-a8b37af88ffa︡{"stdout":"[['a', 'b', 'c'], ['a', 'b', 'c']]\n"}︡{"done":true}︡
︠d07ecc4d-add7-4135-ac50-60b25930b0e2s︠
L.append("d")
L2
︡7ac7111c-49c0-42d1-9556-0d992f017bd7︡{"stdout":"[['a', 'b', 'c', 'd'], ['a', 'b', 'c', 'd']]\n"}︡{"done":true}︡
︠2cd873ab-4efc-4ce9-bfd3-6b7adf4fa21ds︠
L = ["a", "b", "c"]
L2
︡2160aa79-e5eb-4c3f-9a58-df84b40a4e28︡{"stdout":"[['a', 'b', 'c', 'd'], ['a', 'b', 'c', 'd']]\n"}︡{"done":true}︡
︠686e3d1e-e58f-418a-88fa-6e5be9da8e11s︠
L2[0].remove("c")
L2
︡fe394fa9-99db-4c5d-8c9b-d90797d30488︡{"stdout":"[['a', 'b', 'd'], ['a', 'b', 'd']]\n"}︡{"done":true}︡
︠948d2a61-98f0-44ba-b7f5-7d569ef09f08i︠
%html
Stop this nonsense! How do we fix this?
deepcopy to the rescue!
︡fc1a3029-b45a-4090-87c5-9b9356771653︡{"done":true,"html":"\n Stop this nonsense! How do we fix this?\n
\n\n deepcopy to the rescue!\n
"}
︠82815d43-cb4c-44a6-b164-cc89b9d335ebs︠
L = ["a", "b", "c"]
L2 = [deepcopy(L), deepcopy(L)]
L2
︡4355817a-54f0-40e3-be1d-ec7690ccdc22︡{"stdout":"[['a', 'b', 'c'], ['a', 'b', 'c']]\n"}︡{"done":true}︡
︠051549da-8968-4efb-a7f3-08e35100d57fs︠
L.append("d")
L2
︡e3051b7e-0fd4-4d33-8223-751e3f773ef5︡{"stdout":"[['a', 'b', 'c'], ['a', 'b', 'c']]\n"}︡{"done":true}︡
︠81395411-69a0-4657-b545-786fc37007a7i︠
%html
The None type
If you want to set a variable but don't want to set it as any particular type, you can use None
︡537fc1f9-6a81-44bd-8a73-15a90d3f3026︡{"done":true,"html":"\n The None type\n
\n\n If you want to set a variable but don't want to set it as any particular type, you can use None\n
"}
︠80faa48a-5d6b-47ba-97f9-3cd108774b12s︠
v = None
v
︡6b1777a3-54af-4ee3-bd4a-699b8e3ed043︡{"done":true}︡
︠c873a2bd-3f88-4721-ba15-ceab71d9428bi︠
%html
Ranges
Lists made easy
Ranges allow us to make numerical lists easily. We use the range function to construct a range.
︡97c92072-e8b7-4004-be8c-e0efcd02dd26︡{"done":true,"html":"Ranges
\nLists made easy
\n\n Ranges allow us to make numerical lists easily. We use the range function to construct a range.\n
"}
︠e0c4cb2b-910e-4816-a2f8-0882b5294261s︠
range?
︡6a161932-f8f7-4304-af26-90ccc646b59e︡{"code":{"filename":null,"lineno":-1,"mode":"text/x-rst","source":"File: \nDocstring :\nrange(stop) -> list of integers range(start, stop[, step]) -> list of\nintegers\n\nReturn a list containing an arithmetic progression of integers.\nrange(i, j) returns [i, i+1, i+2, ..., j-1]; start (!) defaults to 0.\nWhen step is given, it specifies the increment (or decrement). For\nexample, range(4) returns [0, 1, 2, 3]. The end point is omitted!\nThese are exactly the valid indices for a list of 4 elements."}}︡{"done":true}︡
︠96e00d78-cce4-4b9f-ba4c-f4253674a70cs︠
range(1,10)
︡c96a05f7-0fa5-43d2-8a20-c567a12a6492︡{"stdout":"[1, 2, 3, 4, 5, 6, 7, 8, 9]\n"}︡{"done":true}︡
︠8096e392-b458-4be7-b041-e637f7a3a27es︠
range(1,10,2)
︡36e75bce-1a7d-404f-acba-58cef72f41d8︡{"stdout":"[1, 3, 5, 7, 9]\n"}︡{"done":true}︡
︠8b298316-ccc1-4cc8-8d98-6569b40ddeads︠
range(20,1,-1)
︡bbd29314-d481-473f-a374-9eb3b5637f4b︡{"stdout":"[20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n"}︡{"done":true}︡
︠318ea4f2-a764-485a-a0bc-cebb3986919ei︠
%html
Exercise: Use range to construct the list of even numbers between $1$ and $40$ (including $40$).
Bonus: Put it in reverse order.
︡f5639df7-1801-4aed-a449-71b3b0fdd419︡{"done":true,"html":"Exercise: Use range to construct the list of even numbers between $1$ and $40$ (including $40$).
\nBonus: Put it in reverse order."}
︠cd841134-6dc8-40e9-bf31-697ee615a63bs︠
# Try it out!
range(2,41,2)
range(40,1,-2)
︡6265881e-c029-4c19-af0f-d3bf5b1fe81e︡{"stdout":"[2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]\n"}︡{"stdout":"[40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]\n"}︡{"done":true}︡
︠0ff37a08-bf4b-48bf-b187-16acdc7e2019i︠
%html
Third parts the charm:
Control Flows
if - Does something if the condition is true.for - Loops through a range of objects.while - Keeps looping until condition is false.
For more details you can visit the control flow page on the Python docs.
︡4292fa19-a443-47b8-a7a8-41b7f3f8c0ff︡{"done":true,"html":"Third parts the charm:
\nControl Flows
\n\n if - Does something if the condition is true.for - Loops through a range of objects.while - Keeps looping until condition is false.
\n\nFor more details you can visit the control flow page on the Python docs."}
︠158cf406-9c1c-4211-9dbc-7d2ff6f508b7i︠
%html
Quick aside: Comparisons
or and not - Boolean operators== - Equal!= - Not equal< > <= >= - Inequalitiesis - Object identityis not - Negated object identity
︡f4cd5983-338a-4593-a864-8f0ef85e7f8d︡{"done":true,"html":"\n Quick aside: Comparisons\n
\n\n or and not - Boolean operators== - Equal!= - Not equal< > <= >= - Inequalitiesis - Object identityis not - Negated object identity
"}
︠2d57448c-6c4c-4979-b506-75c1fb747b71i︠
%html
if
with its siblings elif and else.
︡bd203f29-b592-44b0-b5a0-e9fff2b4cc7a︡{"done":true,"html":"\n if\n
\n\n with its siblings elif and else.\n
"}
︠b339d952-01bb-4d39-8e28-bb6075d65e8es︠
if 2 in (1,2,3,4):
print "2 is in our tuple!"
︡c01af4e5-3460-4a76-8e08-acd961a428cd︡{"stdout":"2 is in our tuple!\n"}︡{"done":true}︡
︠9fdfab85-093f-426a-99b0-e4738e43d4f1s︠
R = range(1,10,2)
if 2 in R:
print "2 is in range."
elif 4 in R:
print "4 is in range."
else:
print "By faulty induction our range is only odd numbers."
︡6174e741-62a3-4963-8f24-4d0e0b9330c3︡{"stdout":"By faulty induction our range is only odd numbers.\n"}︡{"done":true}︡
︠75e4df11-344b-49ad-bd67-4076b1e2b2bci︠
%html
for
︡4c479fb4-1533-4a7e-a276-907536ed4c31︡{"done":true,"html":"\n for\n
"}
︠6bb509c9-9ac0-421f-ac77-1910a1dd2980s︠
for i in set([3,2,1]):
print i
︡4663e3d6-74e4-4c55-bb35-b26ddf024908︡{"stdout":"1\n2\n3\n"}︡{"done":true}︡
︠c43ac8b7-5d85-456a-a50f-e8d5c50c9e73s︠
for i in range(1,5):
print i
︡6cfb6afe-6dc0-4d4c-9094-bb778cb7dc0b︡{"stdout":"1\n2\n3\n4\n"}︡{"done":true}︡
︠36d87217-6d21-4353-8301-5280d35961a6s︠
for i in range(1,10):
if i % 2 == 0:
print i
︡411fed68-d506-46ee-a3ae-69303b287b68︡{"stdout":"2\n4\n6\n8\n"}︡{"done":true}︡
︠13c31b9b-d81f-470e-af9d-5ee21a533542s︠
for i in range(1,10):
if is_prime(i):
print i
︡1e3df216-e314-4dff-b478-d30ea1264f60︡{"stdout":"2\n3\n5\n7\n"}︡{"done":true}︡
︠81ea5897-8526-491e-8063-ef1642f7f2c2i︠
%html
Exercise: Use a for loop to print out all the non-even primes from $1$ to $100$.
︡8286882b-cdd4-4894-adbf-e0f54fdb9bbd︡{"done":true,"html":"Exercise: Use a for loop to print out all the non-even primes from $1$ to $100$."}
︠3af781b6-0615-4ce0-83d1-a06166262686s︠
# Try it yourself
for i in range(1,100):
if is_prime(i) and i % 2 != 0:
print i
︡d8285ce7-ce8c-4bd0-b22c-ef8a5323ecdc︡{"stdout":"3\n5\n7\n11\n13\n17\n19\n23\n29\n31\n37\n41\n43\n47\n53\n59\n61\n67\n71\n73\n79\n83\n89\n97\n"}︡{"done":true}︡
︠68fe8b8e-8c7d-4daf-b880-729779f94f93i︠
%html
while
︡1d8ddad8-105c-4031-9703-3ea46ebcc844︡{"done":true,"html":"\n while\n
"}
︠95b54ce1-bbbd-4e68-a660-9bd61b10946es︠
C = 3
while C != 1:
print C
if C % 2 == 0:
C /= 2
else:
C = C*3 + 1
︡91547c31-828f-4751-8b18-9a317f146ea9︡{"stdout":"3\n10\n5\n16\n8\n4\n2\n"}︡{"done":true}︡
︠b8befe99-c2c1-4258-a180-284ff1539731i︠
%html
for and list
The super team
We can use for loops in order to create super awesome lists.
︡d3cbee1e-1234-48b0-9c62-61248ddc7e66︡{"done":true,"html":"\n for and list\n
\n\n The super team\n
\nWe can use for loops in order to create super awesome lists."}
︠ef914f90-f2d3-4119-802b-7aa31e4c0a30s︠
[i^2 for i in range(1,10)]
︡5e7a2d9c-4b0b-4843-9447-2afb9a24914f︡{"stdout":"[1, 4, 9, 16, 25, 36, 49, 64, 81]\n"}︡{"done":true}︡
︠fe611baf-a112-4e87-b24f-1d372e99963bi︠
%html
We can even combine if statements!
︡cb8b8b1e-c3c3-489a-a707-2cc17b3ca77c︡{"done":true,"html":"We can even combine if statements!"}
︠cdc0e6bb-7d32-41e6-9d15-063bd25a12des︠
[i for i in range(1,50) if i%7 == 0 or i%5 == 0]
︡0cd03eed-5738-412f-9339-b54df5149ba0︡{"stdout":"[5, 7, 10, 14, 15, 20, 21, 25, 28, 30, 35, 40, 42, 45, 49]\n"}︡{"done":true}︡
︠58322dcb-1137-4138-966f-6f5a56674e62i︠
%html
And take sums!
︡b5538a01-693c-4203-bee5-6f71224c97d0︡{"done":true,"html":"And take sums!"}
︠b18fa781-c811-4c0c-aea4-a92461999248s︠
sum([p for p in range(1,10) if is_prime(p)])
︡e7533239-cd5c-4519-ab22-a5fdf0cf49c5︡
︠80fefcbe-be48-427b-a451-8d6d03e520bai︠
%html
Exercise: Find the sume of the non-even primes from $1$ to $100$.
︡7840813f-8c0e-4751-938a-38cedf165782︡{"done":true,"html":"Exercise: Find the sume of the non-even primes from $1$ to $100$."}
︠4fcd0b7f-84b7-40ab-9b52-92c9080c4c98︠
# Try it yourself!
︡e47bc3f4-6c9b-4498-a3f2-58e91ab08022︡
︠beae0550-104d-44a5-a944-37bde4f1dd30i︠
%html
Wait, it gets better.... Nesting!
We can nest these lists in order to construct lists of tuples, dictionaries, matrices, etc.
︡82ff61c3-b331-4a98-9706-6fd8a03f93cf︡{"done":true,"html":"\n Wait, it gets better.... Nesting!\n
\nWe can nest these lists in order to construct lists of tuples, dictionaries, matrices, etc."}
︠c7f1e2d9-f25c-4553-b5d9-c33645ba5eebs︠
[(x,y,z) for x in range(1,3) for y in range(1,3) for z in range (1,3)]
︡c19798d9-818b-41f5-aedf-7048f0291c44︡
︠38e716ca-ec8e-48e1-8d11-60f5310e44c3s︠
[[i^j for j in range(1,3)] for i in range(1,5)]
︡b880e6ba-ee07-4292-9b73-6af1649f0024︡
︠c4148dec-e9e6-4d1d-b6ed-ee2b3beceec6︠
︡601fdf43-4e9c-4092-9b81-4d599401aea1︡
︠7475f674-64ac-4420-ad55-5164e7cf9402s︠
matrix([[i^j for j in range(1,3)] for i in range(1,5)])
︡d37f24ad-413e-46b9-8f6c-5ce432531a6b︡
︠fd296d75-c7da-42d5-9952-ab6297d9b785i︠
%html
These special lists also allow us to grab the keys/values of dictionaries!
︡229704dc-2f5a-4194-afc8-2e97b85d8670︡{"done":true,"html":"\n These special lists also allow us to grab the keys/values of dictionaries!\n
"}
︠fdcf292c-94c8-47e7-8e73-e0ea8906730fs︠
D = {2:1, 3:2, 4:3}
[value for value in D.itervalues()]
︡d5146111-faef-4712-8871-1e403bba766a︡
︠d28a51c2-214e-41c5-85c9-bd0a5f01ae95s︠
[key for key in D.iterkeys()]
︡fd107c90-8624-4381-9056-413454c2739d︡
︠70e55f28-b8f5-4aa9-b766-07475535eef1s︠
[(key,value) for key,value in D.iteritems()]
︡564f3cf4-2ffc-4b73-b811-69c513c899ec︡
︠1499a03e-d01c-43a1-98e1-801e18845178i︠
%html
Integers vs ints
Revisited
︡09310eb0-2ce5-4eac-bfed-698c1557ef8e︡{"done":true,"html":"Integers vs ints
\nRevisited
"}
︠b3b54567-787d-4be2-baf8-7ef499baf03e︠
matrix(QQ, [[i/j for i in range(1,10)] for j in range(1,10)])
︡b99f9565-0849-4f9a-a1d3-95f7e76a4345︡
︠b8848356-0318-4015-b3a9-31294fee9bbd︠
matrix(QQ, [[i/j for i in srange(1,10)] for j in srange(1,10)])
︡a928b098-6fa2-42c9-af11-321fe261f466︡
︠a7881b01-1c60-4a4e-b12c-cb61c7b4c1a1i︠
%html
Part $2^2$:
Functions
Functions are defined using the def statement. We can return things from functions using the return keyword.
︡db7f52cd-3141-4b6f-aff0-da4e17e21e3b︡{"done":true,"html":"\n Part $2^2$:\n
\n\n Functions\n
\nFunctions are defined using the def statement. We can return things from functions using the return keyword."}
︠9eadf5b2-317a-4b4a-9043-14df1017a96bs︠
def f(x):
return x^2
f(2)
︡f70ede9d-2b90-450c-b0da-6462fcd49b2b︡
︠0758c4f8-9e8d-415a-aade-9453ddbc5b81i︠
%html
Recursion - Catalan Numbers
$C_0 = 1$
$C_{n} = \frac{2(2n-1)}{n+1} C_{n-1}$
︡107e4557-526b-4926-a1fd-64c0a1474d92︡{"done":true,"html":"\n Recursion - Catalan Numbers\n
\n$C_0 = 1$
\n$C_{n} = \\frac{2(2n-1)}{n+1} C_{n-1}$"}
︠d0948dc0-8645-4af7-8d62-1c9e4938eb53s︠
def catalanNumber(x):
if x == 0:
return 1
else:
return (2 * (2 * x - 1) / (x+1)) * catalanNumber(x-1)
[catalanNumber(n) for n in range(0,10)]
︡2ab35f5b-d700-48d6-bb69-a33e2ae04603︡
︠0656473b-8c5a-48fe-9354-3d6d43dba3bfi︠
%html
Complicated recursion - Catalan Numbers part 2
$C_0 = 1$
$C_n = \sum_{i = 0}^{n-1} C_{i} C_{n-1-i}$
︡d0161207-c47c-4d79-b3bd-e52fa9b0c222︡{"done":true,"html":"\n Complicated recursion - Catalan Numbers part 2\n
\n$C_0 = 1$
\n$C_n = \\sum_{i = 0}^{n-1} C_{i} C_{n-1-i}$"}
︠2cd8b43d-e7f7-4aaa-88f8-c2df2e400bccs︠
def catalanNumber(x):
if x == 0:
return 1
else:
return sum([ (catalanNumber(i) * catalanNumber(x-1 - i)) for i in range(0,x)])
[catalanNumber(n) for n in range(0,10)]
︡854b5f9f-7217-4868-8440-bda014040da9︡
︠5b79ca00-a8a5-478a-b9bd-0cadc555068ei︠
%html
Exercise: Create a function for the fibonacci series and display the first $20$.
︡ac503a3e-1893-46d1-ba2e-c9504b73b4f9︡{"done":true,"html":"Exercise: Create a function for the fibonacci series and display the first $20$."}
︠059ef14d-0778-48bd-9173-cab1ce34b8d3︠
# Try it!
︡b079af0e-2242-4871-ae4d-7a01869ed122︡
︠9191de02-9f96-47f1-bced-84e9c483a85ai︠
%html
Functions can also have default values.
︡32dc7c47-23ef-445a-bcef-66d531183dc3︡{"done":true,"html":"\n Functions can also have default values.\n
"}
︠a25ef25d-590f-445d-97fd-95adef0f8a3fs︠
# By default we choose 1
def choose(n, k = 1):
return binomial(n,k)
choose(5)
choose(5,2)
︡c82448c0-c11d-4aff-a08a-31e247886070︡
︠7af4051f-2ff1-41b2-b624-1ef3a3e34ea5i︠
%html
Functions can also return multiple values if desired.
︡e9266950-7971-4368-bfb4-76da274d4b9d︡{"done":true,"html":"\n Functions can also return multiple values if desired.\n
"}
︠0ce67677-7479-483f-ad38-b924228b051as︠
def fibAndCat(n):
return fibonacci(n), catalan_number(n)
F, C = fibAndCat(5)
F
C
︡2f7b3bad-16a9-43d8-945f-7a64520082f4︡
︠86b988c0-7ffb-42a6-9307-6ca62a627c57s︠
[fibAndCat(i) for i in range(0,10)]
︡3ba7b1c9-e785-40c5-afe8-d3579447dbf8︡
︠44afaa96-5047-4b94-bdb2-375cf65758d5i︠
%html
Digraphs!
Sage allows us to construct digraphs using dictionaries. Let's take a sidestep and look at how to construct digraphs and some operations we can do on them.
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\n\n Sage allows us to construct digraphs using dictionaries. Let's take a sidestep and look at how to construct digraphs and some operations we can do on them.\n
"}
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D = {0:[1,2,3], 1:[0,3], 2:[3,4], 4:[5,5,5,1], 5:[5]}
G = DiGraph(D)
G.plot()
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G.adjacency_matrix()
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Exercise: Plot your favourite digraph.
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