I hesitate a bit to post this, but... on the Italian Python NG, somebody
was asking whether there was any way to convert an integer number x into
a string which represents it in an arbitrary base N (given a sequence
with a len of N that gives the digits to use) as "a single expression".
I haven't found a really general way, much less a clear one, but, the
best I have so far is...:
def number_in_base( x, N, digits, maxlen=99):
return '-'[x>=0:] + (
(x and ''.join([digits[k%N] for i in range(maxlen)
for k in [abs(x)//N**i] if k>0])[::-1]
) or digits[0])
Besides the lack of clarity, the obvious defect of this approach is that
darned 'maxlen' parameter -- but then, since I can have only a 'for',
not a 'while', in a list comprehension or generator expression, and I
don't think recursion qualifies as 'a single expression'...:-(
Anyway, improvements and suggestions welcome, thanks!
Alex
21  2130 
On Fri, 29 Oct 2004 23:58:47 +0200, al*****@yahoo.c om (Alex Martelli) wrote: I hesitate a bit to post this, but... on the Italian Python NG, somebody
was asking whether there was any way to convert an integer number x into
a string which represents it in an arbitrary base N (given a sequence
with a len of N that gives the digits to use) as "a single expression".
I haven't found a really general way, much less a clear one, but, the
best I have so far is...:
def number_in_base( x, N, digits, maxlen=99):
return '-'[x>=0:] + (
(x and ''.join([digits[k%N] for i in range(maxlen)
for k in [abs(x)//N**i] if k>0])[::-1]
) or digits[0])
Besides the lack of clarity, the obvious defect of this approach is that
darned 'maxlen' parameter -- but then, since I can have only a 'for',
not a 'while', in a list comprehension or generator expression, and I
don't think recursion qualifies as 'a single expression'...:-(
Anyway, improvements and suggestions welcome, thanks!
Maybe something useful in this? Not very tested (and not terribly clear either ;-) def number_in_base( x, N, digits):
... return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in iter(
... lambda qr=[abs(x),0]:qr[0] and (
... qr.__setslice__ (0,2,divmod(qr[0],N)) or digits[qr[1]])
... , 0)][::-1])
... number_in_base( 126 ,2,'0123456789A BCDEF')
'1111110' number_in_base( 126 ,8,'0123456789A BCDEF')
'176' number_in_base( 126 ,16,'0123456789 ABCDEF')
'7E' number_in_base( 1 ,16,'0123456789 ABCDEF')
'1' number_in_base( 0 ,16,'0123456789 ABCDEF')
'0' number_in_base(-126 ,16,'0123456789 ABCDEF')
'-7E' number_in_base(-126 ,2,'0123456789A BCDEF')
'-1111110'
Even less tested, and using a list subtype with overridden next to do the same:
def number_in_base( x, N, digits):
... return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in type('',(list,) ,{
... '__iter__':lamb da s:s, 'next':lambda s:(
... s[0] is 0 and iter([]).next() or
... s.__setslice__( 0,2,divmod(s[0],N)) or digits[s[1]])
... })([abs(x),0])][::-1])
... number_in_base(-126, 8, '01234567')
'-176' number_in_base(-126, 2, '01')
'-1111110' number_in_base( 126, 2, '01')
'1111110' number_in_base( 0 , 2, '01')
'0' number_in_base( 1 , 2, '01')
'1'
;-)
Regards,
Bengt Richter
On Fri, 29 Oct 2004 23:58:47 +0200, al*****@yahoo.c om (Alex Martelli) wrote: I hesitate a bit to post this, but... on the Italian Python NG, somebody
was asking whether there was any way to convert an integer number x into
a string which represents it in an arbitrary base N (given a sequence
with a len of N that gives the digits to use) as "a single expression".
I haven't found a really general way, much less a clear one, but, the
best I have so far is...:
def number_in_base( x, N, digits, maxlen=99):
return '-'[x>=0:] + (
(x and ''.join([digits[k%N] for i in range(maxlen)
for k in [abs(x)//N**i] if k>0])[::-1]
) or digits[0])
Besides the lack of clarity, the obvious defect of this approach is that
darned 'maxlen' parameter -- but then, since I can have only a 'for',
not a 'while', in a list comprehension or generator expression, and I
don't think recursion qualifies as 'a single expression'...:-(
Anyway, improvements and suggestions welcome, thanks!
Maybe something useful in this? Not very tested (and not terribly clear either ;-) def number_in_base( x, N, digits):
... return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in iter(
... lambda qr=[abs(x),0]:qr[0] and (
... qr.__setslice__ (0,2,divmod(qr[0],N)) or digits[qr[1]])
... , 0)][::-1])
... number_in_base( 126 ,2,'0123456789A BCDEF')
'1111110' number_in_base( 126 ,8,'0123456789A BCDEF')
'176' number_in_base( 126 ,16,'0123456789 ABCDEF')
'7E' number_in_base( 1 ,16,'0123456789 ABCDEF')
'1' number_in_base( 0 ,16,'0123456789 ABCDEF')
'0' number_in_base(-126 ,16,'0123456789 ABCDEF')
'-7E' number_in_base(-126 ,2,'0123456789A BCDEF')
'-1111110'
Even less tested, and using a list subtype with overridden next to do the same:
def number_in_base( x, N, digits):
... return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in type('',(list,) ,{
... '__iter__':lamb da s:s, 'next':lambda s:(
... s[0] is 0 and iter([]).next() or
... s.__setslice__( 0,2,divmod(s[0],N)) or digits[s[1]])
... })([abs(x),0])][::-1])
... number_in_base(-126, 8, '01234567')
'-176' number_in_base(-126, 2, '01')
'-1111110' number_in_base( 126, 2, '01')
'1111110' number_in_base( 0 , 2, '01')
'0' number_in_base( 1 , 2, '01')
'1'
;-)
Regards,
Bengt Richter
On Sat, 30 Oct 2004 06:07:23 GMT, bo**@oz.net (Bengt Richter) wrote:
[...] Maybe something useful in this? Not very tested (and not terribly clear either ;-)
def number_in_base( x, N, digits): ... return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in iter(
... lambda qr=[abs(x),0]:qr[0] and (
... qr.__setslice__ (0,2,divmod(qr[0],N)) or digits[qr[1]])
... , 0)][::-1])
...
Alternatively, a little more compactly (though I feel guilty about the -1 ;-):
def number_in_base( x, N=10, digits='0123456 789ABCDEF'):
... return '-'[:x<0] + ''.join(list(it er(lambda qr=[abs(x),-1]: (qr[0] or qr[1]<0) and (
... qr.__setslice__ (0,2,divmod(qr[0],N)) or digits[qr[1]]), False))[::-1])
... number_in_base( 126,2,'01')
'1111110' number_in_base( 126, 8,'01234567')
'176' number_in_base(-126, 8,'01234567')
'-176' number_in_base( -1, 2,'01234567')
'-1' number_in_base( 1, 2,'01234567')
'1' number_in_base( 0, 2,'01234567')
'0'
Regards,
Bengt Richter
<ex*****@divmod .com> wrote:
... def number_in_base( x, N, digits, maxlen=99):
return '-'[x>=0:] + (
(x and ''.join([digits[k%N] for i in range(maxlen)
for k in [abs(x)//N**i] if k>0])[::-1]
) or digits[0])
... range(maxlen) can be replaced with range(int(math. log(x) / math.log(N))
+ 1).
Right! I had missed that because I was focusing on builtin names only.
Thanks!
Also, and perhaps you are already aware, number_in_base( x, 1, '0')
Yes, I was aware that the pre condition N>=2 (as well as other
preconditions, such as len(digits) >= N) are not checked; sorry for not
making that clear.
doesn't produce the correct output with the above algorithm, although I
believe it will if you switch to using math.log().
With math.log it raises a ZeroDivisionErr or -- arguably more correct
than a bunch of 0's, yes. It's interesting that the math.log
application does catch such errors as N<2;-).
Alex
On Sat, 30 Oct 2004 07:48:34 GMT, bo**@oz.net (Bengt Richter) wrote: On Sat, 30 Oct 2004 06:07:23 GMT, bo**@oz.net (Bengt Richter) wrote:
[...]Maybe something useful in this? Not very tested (and not terribly clear either ;-)
>>> def number_in_base( x, N, digits):
... return x==0 and digits[0] or '-'[:x<0] + ''.join([d for d in iter(
... lambda qr=[abs(x),0]:qr[0] and (
... qr.__setslice__ (0,2,divmod(qr[0],N)) or digits[qr[1]])
... , 0)][::-1])
...
Alternativel y, a little more compactly (though I feel guilty about the -1 ;-):
def number_in_base( x, N=10, digits='0123456 789ABCDEF'): ... return '-'[:x<0] + ''.join(list(it er(lambda qr=[abs(x),-1]: (qr[0] or qr[1]<0) and (
... qr.__setslice__ (0,2,divmod(qr[0],N)) or digits[qr[1]]), False))[::-1])
...
Yet another, prefixing digits instead of joining reversed list:
def number_in_base( x, N=10, digits='0123456 789ABCDEF'):
... return '-'[:x<0]+reduce(lambda s,c:c+s, iter(lambda qr=[abs(x),-1]: (qr[0] or qr[1]<0)
... and (qr.__setslice_ _(0,2,divmod(qr[0],N)) or digits[qr[1]]), False))
... number_in_base( 0 , 2, '01')
'0' number_in_base( 1 , 2, '01')
'1' number_in_base( 126, 2, '01')
'1111110' number_in_base(-126, 2, '01')
'-1111110'
Regards,
Bengt Richter
On Fri, 29 Oct 2004 23:34:42 GMT, ex*****@divmod. com wrote: range(maxlen) can be replaced with range(int(math. log(x) / math.log(N)) + 1).
Log accepts the base as second argument.
def number_in_base( x, N=10, digits="0123456 789ABCDEF"):
return '-'[x>=0:]+"".join(
[digits[abs(x)/N**i%N]
for i in xrange(1+int(ma th.log(abs(x)+1 ,N)))
if N**i<=abs(x)][::-1]) or digits[0]
Also, and perhaps you are already aware, number_in_base( x, 1, '0') doesn't produce the correct output with the above algorithm, although I believe it will if you switch to using math.log().
It doesn't handle roman numerals either... but so ?
You can't count using base 1 with positional systems.
Andrea
On Sat, 30 Oct 2004 12:12:36 +0000, Andrea Griffini wrote: You can't count using base 1 with positional systems.
Well, you can, sort of. You end up with the integers, obviously, and the
result has a rather striking resemblance to the modern foundations of
number theory, in which there is only one number, 0, and the "increment"
function which returns a number one larger. If you want three, it is
expressed increment(incre ment(increment( 0))), which is rather similar to
the base-1 number "111".
Zero in this system would probably be a null string, making increment this:
def increment(numbe r):
return "1" + number
(And abracadabra, I'm back on topic for the newsgroup, albeit tenuously :-) )
Some people say base 2 is the most natural base in the universe. But you
can certainly make a claim for base 1, based on its correspondence to
number theory, from which we build the rest of math. (Most people never
dig this deep; it was one of my favorite classes in Comp. Sci., though,
and we're probably the only people other than mathematicians to offer the
course.)
Hi all,
warning: off topic nitpicking below!
Jeremy Bowers said unto the world upon 2004-10-30 13:29: On Sat, 30 Oct 2004 12:12:36 +0000, Andrea Griffini wrote:
You can't count using base 1 with positional systems.
Well, you can, sort of. You end up with the integers, obviously, and the
result has a rather striking resemblance to the modern foundations of
number theory, in which there is only one number, 0, and the "increment"
function which returns a number one larger. If you want three, it is
expressed increment(incre ment(increment( 0))), which is rather similar to
the base-1 number "111".
I take it you didn't mean 0 was the only number, but rather the only
primitive number. (Alternatively " '0' is the only individual constant"
in the cant I prefer.)
I am also surprised to see "increment" -- I come to that material with
working in Philosophy of Mathematics and Logic, but almost every
presentation I have ever seen uses "successor" . (I'm going off of
philosophical and mathematical logic presentations.)
I do so wish that terminology is the whole area would just stabilize
already!
Zero in this system would probably be a null string, making increment this:
def increment(numbe r):
return "1" + number
(And abracadabra, I'm back on topic for the newsgroup, albeit tenuously :-) )
Some people say base 2 is the most natural base in the universe. But you
can certainly make a claim for base 1, based on its correspondence to
number theory, from which we build the rest of math. (Most people never
dig this deep; it was one of my favorite classes in Comp. Sci., though,
and we're probably the only people other than mathematicians to offer the
course.)
I've never taken a single comp. sci. course, so I will both claim and
commit disciplinary bias: serious undergrad logic/foundations of maths
courses do happen in Philosophy, too :-)
On the other hand, I'm a bit surprised that these things get taught in
comp. sci. This past summer when teaching Intro to Logic, I encountered
at least one fourth-year comp. sci. student who had no idea what an
axiomatic system was :-|
print "We now return you to your usual programing"
Best to all,
Brian vdB
On Sat, 30 Oct 2004 16:06:04 -0400, Brian van den Broek wrote: I take it you didn't mean 0 was the only number, but rather the only
primitive number. (Alternatively " '0' is the only individual constant"
in the cant I prefer.)
*shrug* Can't say I get worked up over the difference there. Regardless,
you "can't" write "3". (Of course you can define it, but that's true of
everything.)
I am also surprised to see "increment" -- I come to that material with
working in Philosophy of Mathematics and Logic, but almost every
presentation I have ever seen uses "successor" . (I'm going off of
philosophical and mathematical logic presentations.)
Yeah, that would be right. Couldn't recall the exact name.
number theory, from which we build the rest of math. (Most people never
dig this deep; it was one of my favorite classes in Comp. Sci., though,
and we're probably the only people other than mathematicians to offer the
course.)
I've never taken a single comp. sci. course, so I will both claim and
commit disciplinary bias: serious undergrad logic/foundations of maths
courses do happen in Philosophy, too :-)
Gonna nit pick myself here: "Most people". I think adding Philosophers and
dilettantes and the rare electrical engineer isn't likely to change the
"most".
On the other hand, I'm a bit surprised that these things get taught in
comp. sci. This past summer when teaching Intro to Logic, I encountered
at least one fourth-year comp. sci. student who had no idea what an
axiomatic system was :-|
Graduate level. And many of the grads hated it. There is a chasm between
the average Comp. Sci. student and the average professor; it isn't so bad
at the grad level but it is still there. I'm not sure if it's worse than
most disciplines, but I am inclined to believe it is, since Comp Sci
typically can't really work out if it is math or engineering (wide
consensus is that while there are scientific aspects to it, it probably
shouldn't have it in the name), and there are, in my experience, fairly
clean divisions of each student and professor into one camp or another. I
was one of the exceedingly rare students who could do both quite well, and
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