Differents way to define a function in sagemath - python

I would like to know why these two "programs" produce different output
f(x)=x^2
f(90).mod(7)
and
def f(x):
return(x^2)
f(90).mod(7)
Thanks

Great question! Let's take a deeper look at the functions in question.
f(x)=x^2
def g(x):
return(x^2)
print type(g(90))
print type(f(90))
This yields
<type 'sage.rings.integer.Integer'>
<type 'sage.symbolic.expression.Expression'>
So what you are seeing is the difference between a symbolic function defined with the f(x) notation and a Python function using the def keyword. In Sage, the former has access to a lot of stuff (e.g. calculus) that plain old Sage integers won't have.
What I would recommend in this case, just for what you need, is
sage: a = f(90)
sage: ZZ(a).mod(7)
1
or actually the possibly more robust
sage: mod(a,7)
1
Longer explanation.
For symbolic stuff, mod isn't what you think. In fact, I'm not sure it will do anything (see the documentation for mod to see how to use it for polynomial modular work over ideals, though). Here's the code (accessible with x.mod??, documentation accessible with x.mod?):
from sage.rings.ideal import is_Ideal
if not is_Ideal(I) or not I.ring() is self._parent:
I = self._parent.ideal(I)
#raise TypeError, "I = %s must be an ideal in %s"%(I, self.parent())
return I.reduce(self)
And it turns out that for generic rings (like the symbolic 'ring'), nothing happens in that last step:
return f
This is why we need to, one way or another, ask it to be an integer again. See Trac 27401.

Related

How to check if a function is pure in Python?

A pure function is a function similar to a Mathematical function, where there is no interaction with the "Real world" nor side-effects. From a more practical point of view, it means that a pure function can not:
Print or otherwise show a message
Be random
Depend on system time
Change global variables
And others
All this limitations make it easier to reason about pure functions than non-pure ones. The majority of the functions should then be pure so that the program can have less bugs.
In languages with a huge type-system like Haskell the reader can know right from the start if a function is or is not pure, making the successive reading easier.
In Python this information may be emulated by a #pure decorator put on top of the function. I would also like that decorator to actually do some validation work. My problem lies in the implementation of such a decorator.
Right now I simply look the source code of the function for buzzwords such as global or random or print and complains if it finds one of them.
import inspect
def pure(function):
source = inspect.getsource(function)
for non_pure_indicator in ('random', 'time', 'input', 'print', 'global'):
if non_pure_indicator in source:
raise ValueError("The function {} is not pure as it uses `{}`".format(
function.__name__, non_pure_indicator))
return function
However it feels like a weird hack, that may or may not work depending on your luck, could you please help me in writing a better decorator?
I kind of see where you are coming from but I don't think this can work. Let's take a simple example:
def add(a,b):
return a + b
So this probably looks "pure" to you. But in Python the + here is an arbitrary function which can do anything, just depending on the bindings in force when it is called. So that a + b can have arbitrary side effects.
But it's even worse than that. Even if this is just doing standard integer + then there's more 'impure' stuff going on.
The + is creating a new object. Now if you are sure that only the caller has a reference to that new object then there is a sense in which you can think of this as a pure function. But you can't be sure that, during the creation process of that object, no reference to it leaked out.
For example:
class RegisteredNumber(int):
numbers = []
def __new__(cls,*args,**kwargs):
self = int.__new__(cls,*args,**kwargs)
self.numbers.append(self)
return self
def __add__(self,other):
return RegisteredNumber(super().__add__(other))
c = RegisteredNumber(1) + 2
print(RegisteredNumber.numbers)
This will show that the supposedly pure add function has actually changed the state of the RegisteredNumber class. This is not a stupidly contrived example: in my production code base we have classes which track each created instance, for example, to allow access via key.
The notion of purity just doesn't make much sense in Python.
(not an answer, but too long for a comment)
So if a function can return different values for the same set of arguments, it is not pure?
Remember that functions in Python are objects, so you want to check the purity of an object...
Take this example:
def foo(x):
ret, foo.x = x*x+foo.x, foo.x+1
return ret
foo.x=0
calling foo(3) repeatedly gives:
>>> foo(3)
9
>>> foo(3)
10
>>> foo(3)
11
...
Moreover, reading globals does not require to use the global statement, or the global() builtin inside your function. Global variables might change somewhere else, affecting the purity of your function.
All the above situation might be difficult to detect at runtime.

Assign a numeric value that is returned from a function by using exec command

I need to assign a numeric value, which is returned from a function, to a variable name by using exec() command:
def func1(x,y):
return x+y
def main(x,y,n):
x=3; y=5; n=1
t = exec("func%s(%s,%s)" % (n,x,y))
return t**2
main(3,5,1)
I have many functions like "func1", "func2" and so on... I try to return t = func1(x,y) with theexec("func%s(%s,%s)" % (n,x,y)) statement. However, I cannot assign a value, returned fromexec().
There is a partly similar question on SE, but it is written for Python3 and is also not applicable to my case.
How can we resolve this problem or is there a more elegant way to perform such an operation, maybe without the use of'exec()'?
By the way, as "func%s(%s,%s)" % (n,x,y) is a statement, I used exec. Or should I better use eval?
It is almost always a really bad idea to get at functions and variables using their names as strings (or bits of their names as integers, as in the example code in the question). One reason why is that eval or exec can do literally anything and you generally want to avoid using code constructs whose behaviour is so hard to predict and reason about.
So here are two ways to get similar results with less pain.
First: Instead of passing around magic index numbers, like the 1 in the code above, pass the actual function which is, itself, a perfectly reasonable value for a variable in Python.
def main(x,y,f):
return f(x,y)**2
main(3, 5, func1)
(Incidentally, the definition of main in the question throws away the values of x,y,n that are passed in to it. That's probably a mistake.)
Second: Instead of making these mere functions, make them methods on classes, and pass around not the functions but either the classes themselves or instances of the classes.
class Solver:
def solve(self, x,y): return "eeeek, not implemented"
class Solver1:
def solve(self, x,y): return x+y
def main(x, y, obj):
return obj.solve(x,y)**2
main(3, 5, Solver1())
Which of these is the better approach depends on the details of your application. For instance, if you actually have multiple "parallel" sets of functions -- as well as your func1, func2, etc., there are also otherfunc1, otherfunc2 etc. -- then this is crying out for an object-oriented solution (the second approach above).
In general I would argue for the second approach; it tends to lead to cleaner code as your requirements grow.

Convert a string equation to an integer answer

If I have a string
equation = "1+2+3+4"
How do I change it into an int and equate the answer? I was thinking something like this but it would give an error.
answer = (int)equation
print(answer)
The equation could contain +-*/
If you are prepared to accept the risks, namely that you may be letting hostile users run whatever they like on your machine, you could use eval():
>>> equation = "1+2+3+4"
>>> eval(equation)
10
If your code will only ever accept input that you control, then this is the quickest and simplest solution. If you need to allow general input from users other than you, then you'd need to look for a more restrictive expression evaluator.
Update
Thanks to #roippi for pulling me up and pointing out that the code above executes in the environment of the calling code. So the expression would be evaluated with local and global variables available. Suppress that like so:
eval(equation, {'__builtins__': None})
This doesn't make the use of eval() secure. It just gives it a clean, empty environment in which to operate. A hostile user could still hose your system.
If we wanted to expose a calculator to the world, I'd be very interested to see if a cracker could work around this:
import string
def less_dangerous_eval(equation):
if not set(equation).intersection(string.ascii_letters + '{}[]_;\n'):
return eval(equation)
else:
print("illegal character")
return None
less_dangerous_eval('1*2/3^4+(5-6)')
returns:
3
I know that this can be broken by giving it bad syntax (fixable with a try/except block) or an operation that would take up all of the memory in the system (try/except catching this might be more iffy), but I am not currently aware of any way for someone to gain control.
This works if you only have digits and plusses:
answer = sum(float(i) for i in equation.split('+'))
or if you know they will only be integers
answer = sum(int(i) for i in equation.split('+'))
If you want to be able to evaluate more than that, I suggest you do your homework:
Look up the string module (which has string.digits)
the math module, which has your operations
create logic to perform the operations in proper order
Good luck!
I suggest you use eval and check the input:
def evaluate(s):
import string
for i in s:
if i not in "+-*/ " + string.digits:
return False # input is not valid
return eval(s)
As already mentioned, eval is unsafe, and very difficult to make safe. I remember seeing a very good blog post explaining this, does anyone know what it was? However ast.literal_eval is safe, it doesn't allow __import__ etc. I would strongly recomment using ast.literal_eval instead of eval whenever possible. Unfortunately, in this case it isn't possible. However, in a different case, e.g. one where you only need to support addition and multiplication, you could (and should) use literal_eval instead.
On the other hand, if this is homework with the intention for you to learn about parsing, then I would suggest doing this a different way. I know that if I was a teacher, I would respond to an answer using eval with "Very clever, but this won't help you pass a test on abstract syntax trees." (which are incidentally one thing that you should look at if you want to implement this "properly").

Recipe for anonymous functions in python?

I'm looking for the best recipie to allow inline definition of functions, or multi-line lambda, in python.
For example, I'd like to do the following:
def callfunc(func):
func("Hello")
>>> callfunc(define('x', '''
... print x, "World!"
... '''))
Hello World!
I've found an example for the define function in this answer:
def define(arglist, body):
g = {}
exec("def anonfunc({0}):\n{1}".format(
arglist,
"\n".join(" {0}".format(line) for line in body.splitlines())), g)
return g["anonfunc"]
This is one possible solution, but it is not ideal. Desireable features would be:
be smarter about indentation,
hide the innards better (e.g. don't have anonfunc in the function's scope)
provide access to variables in the surrounding scope / captures
better error handling
and some things I haven't thought of. I had a really nice implementation once that did most of the above, but I lost in unfortunately. I'm wondering if someone else has made something similar.
Disclaimer:
I'm well aware this is controversial among Python users, and regarded as a hack or unpythonic. I'm also aware of the discussions regaring multi-line-lambdas on the python-dev mailing list, and that a similar feature was omitted on purpose. However, from the same discussions I've learned that there is also interest in such a function by many others.
I'm not asking whether this is a good idea or not, but instead: Given that one has decided to implement this, (either out of fun and curiosity, madness, genuinely thinking this is a nice idea, or being held at gunpoint) how to make anonymous define work as close as possible to def using python's (2.7 or 3.x) current facilities?
Examples:
A bit more as to why, this can be really handy for callbacks in GUIs:
# gtk example:
self.ntimes = 0
button.connect('clicked', define('*a', '''
self.ntimes += 1
label.set_text("Button has been clicked %d times" % self.ntimes)
''')
The benefit over defining a function with def is that your code is in a more logical order. This is simplified code taken from a Twisted application:
# twisted example:
def sayHello(self):
d = self.callRemote(HelloCommand)
def handle_response(response):
# do something, this happens after (x)!
pass
d.addCallback(handle_response) # (x)
Note how it seems out of order. I usually break stuff like this up, to keep the code order == execution order:
def sayHello_d(self):
d = self.callRemote(HelloCommand)
d.addCallback(self._sayHello_2)
return d
def _sayHello_2(self, response):
# handle response
pass
This is better wrt. ordering but more verbose. Now, with the anonymous functions trick:
d = self.callRemote(HelloCommand)
d.addCallback(define('response', '''
print "callback"
print "got response from", response["name"]
'''))
If you come from a javascript or ruby background, python's abilities to deal with anonymous functions may indeed seem limited, but this is for a reason. Python designers decided that clarity of code is more important than conciseness. If you don't like that, you probably don't like python at all. There's nothing wrong about that, there are many other choices - why not to try a language that tastes better to you?
Putting chunks of code into strings and interpreting them on the fly is definitely a wrong way to "extend" a language, just because none of tools you're working with - from syntax highlighters to the python interpreter itself - would be able to deal with "stringified" code in a sensible way.
To answer the question as asked: what you're doing there is essentially an attempt to construct some better-than-python programming language and compile it to python on the fly. The idea is not new in the world of scripting languages and can be productive or not (CoffeeScript is an example of a successful implementation), but your very approach is wrong. format() not the tool you're looking for when working with code. If you're writing a compiler, do it properly: use a parser (e.g. pyparsing) to read your code in an AST, walk through the AST to generate python code (or even bytecode), catch syntax errors as you go and take measures to provide better runtime feedback (e.g. error context, line numbers etc). Finally, make sure your compiler works across different python versions and implementations.
Or just use ruby.

What are the important language features (idioms) of Python to learn early on [duplicate]

This question already has answers here:
The Zen of Python [closed]
(22 answers)
Python: Am I missing something? [closed]
(16 answers)
Closed 8 years ago.
I would be interested in knowing what the StackOverflow community thinks are the important language features (idioms) of Python. Features that would define a programmer as Pythonic.
Python (pythonic) idiom - "code expression" that is natural or characteristic to the language Python.
Plus, Which idioms should all Python programmers learn early on?
Thanks in advance
Related:
Code Like a Pythonista: Idiomatic Python
Python: Am I missing something?
Python is a language that can be described as:
"rules you can fit in the
palm of your hand with a huge bag of
hooks".
Nearly everything in python follows the same simple standards. Everything is accessible, changeable, and tweakable. There are very few language level elements.
Take for example, the len(data) builtin function. len(data) works by simply checking for a data.__len__() method, and then calls it and returns the value. That way, len() can work on any object that implements a __len__() method.
Start by learning about the types and basic syntax:
Dynamic Strongly Typed Languages
bool, int, float, string, list, tuple, dict, set
statements, indenting, "everything is an object"
basic function definitions
Then move on to learning about how python works:
imports and modules (really simple)
the python path (sys.path)
the dir() function
__builtins__
Once you have an understanding of how to fit pieces together, go back and cover some of the more advanced language features:
iterators
overrides like __len__ (there are tons of these)
list comprehensions and generators
classes and objects (again, really simple once you know a couple rules)
python inheritance rules
And once you have a comfort level with these items (with a focus on what makes them pythonic), look at more specific items:
Threading in python (note the Global Interpreter Lock)
context managers
database access
file IO
sockets
etc...
And never forget The Zen of Python (by Tim Peters)
Beautiful is better than ugly.
Explicit is better than implicit.
Simple is better than complex.
Complex is better than complicated.
Flat is better than nested.
Sparse is better than dense.
Readability counts.
Special cases aren't special enough to break the rules.
Although practicality beats purity.
Errors should never pass silently.
Unless explicitly silenced.
In the face of ambiguity, refuse the temptation to guess.
There should be one-- and preferably only one --obvious way to do it.
Although that way may not be obvious at first unless you're Dutch.
Now is better than never.
Although never is often better than *right* now.
If the implementation is hard to explain, it's a bad idea.
If the implementation is easy to explain, it may be a good idea.
Namespaces are one honking great idea -- let's do more of those!
This page covers all the major python idioms: http://python.net/~goodger/projects/pycon/2007/idiomatic/handout.html
An important idiom in Python is docstrings.
Every object has a __doc__ attribute that can be used to get help on that object. You can set the __doc__ attribute on modules, classes, methods, and functions like this:
# this is m.py
""" module docstring """
class c:
"""class docstring"""
def m(self):
"""method docstring"""
pass
def f(a):
"""function f docstring"""
return
Now, when you type help(m), help(m.f) etc. it will print the docstring as a help message.
Because it's just part of normal object introspection this can be used by documention generating systems like epydoc or used for testing purposes by unittest.
It can also be put to more unconventional (i.e. non-idiomatic) uses such as grammars in Dparser.
Where it gets even more interesting to me is that, even though doc is a read-only attribute on most objects, you can use them anywhere like this:
x = 5
""" pseudo docstring for x """
and documentation tools like epydoc can pick them up and format them properly (as opposed to a normal comment which stays inside the code formatting.
Decorators get my vote. Where else can you write something like:
def trace(num_args=0):
def wrapper(func):
def new_f(*a,**k):
print_args = ''
if num_args > 0:
print_args = str.join(',', [str(x) for x in a[0:num_args]])
print('entering %s(%s)' %(f.__name__,print_args))
rc = f(*a,**k)
if rc is not None:
print('exiting %s(%s)=%s' %(f.__name__,str(rc)))
else:
print('exiting %s(%s)' %(f.__name__))
return rc
return new_f
return wrapper
#trace(1)
def factorial(n):
if n < 2:
return 1
return n * factorial(n-1)
factorial(5)
and get output like:
entering factorial(5)
entering factorial(4)
entering factorial(3)
entering factorial(2)
entering factorial(1)
entering factorial(0)
exiting factorial(0)=1
exiting factorial(1)=1
exiting factorial(2)=2
exiting factorial(3)=6
exiting factorial(4)=24
exiting factorial(5)=120
Everything connected to list usage.
Comprehensions, generators, etc.
Personally, I really like Python syntax defining code blocks by using indentation, and not by the words "BEGIN" and "END" (as in Microsoft's Basic and Visual Basic - I don't like these) or by using left- and right-braces (as in C, C++, Java, Perl - I like these).
This really surprised me because, although indentation has always been very important to me, I didn't make to much "noise" about it - I lived with it, and it is considered a skill to be able to read other peoples, "spaghetti" code. Furthermore, I never heard another programmer suggest making indentation a part of a language. Until Python! I only wish I had realized this idea first.
To me, it is as if Python's syntax forces you to write good, readable code.
Okay, I'll get off my soap-box. ;-)
From a more advanced viewpoint, understanding how dictionaries are used internally by Python. Classes, functions, modules, references are all just properties on a dictionary. Once this is understood it's easy to understand how to monkey patch and use the powerful __gettattr__, __setattr__, and __call__ methods.
Here's one that can help. What's the difference between:
[ foo(x) for x in range(0, 5) ][0]
and
( foo(x) for x in range(0, 5) ).next()
answer:
in the second example, foo is called only once. This may be important if foo has a side effect, or if the iterable being used to construct the list is large.
Two things that struck me as especially Pythonic were dynamic typing and the various flavors of lists used in Python, particularly tuples.
Python's list obsession could be said to be LISP-y, but it's got its own unique flavor. A line like:
return HandEvaluator.StraightFlush, (PokerCard.longFaces[index + 4],
PokerCard.longSuits[flushSuit]), []
or even
return False, False, False
just looks like Python and nothing else. (Technically, you'd see the latter in Lua as well, but Lua is pretty Pythonic in general.)
Using string substitutions:
name = "Joe"
age = 12
print "My name is %s, I am %s" % (name, age)
When I'm not programming in python, that simple use is what I miss most.
Another thing you cannot start early enough is probably testing. Here especially doctests are a great way of testing your code by explaining it at the same time.
doctests are simple text file containing an interactive interpreter session plus text like this:
Let's instantiate our class::
>>> a=Something(text="yes")
>>> a.text
yes
Now call this method and check the results::
>>> a.canify()
>>> a.text
yes, I can
If e.g. a.text returns something different the test will fail.
doctests can be inside docstrings or standalone textfiles and are executed by using the doctests module. Of course the more known unit tests are also available.
I think that tutorials online and books only talk about doing things, not doing things in the best way. Along with the python syntax i think that speed in some cases is important.
Python provides a way to benchmark functions, actually two!!
One way is to use the profile module, like so:
import profile
def foo(x, y, z):
return x**y % z # Just an example.
profile.run('foo(5, 6, 3)')
Another way to do this is to use the timeit module, like this:
import timeit
def foo(x, y, z):
return x**y % z # Can also be 'pow(x, y, z)' which is way faster.
timeit.timeit('foo(5, 6, 3)', 'from __main__ import *', number = 100)
# timeit.timeit(testcode, setupcode, number = number_of_iterations)

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