[sage-devel] Re: Factorial syntax
Tom Boothby wrote: On Mon, Aug 31, 2009 at 10:38 AM, Robert Bradshawrober...@math.washington.edu wrote: As for the question at hand, I'm personally not convinced this is useful enough to merit another departure from pure Python. It also risks turning the valid Python expression x!=120 into an invalid one (unless the rule bah. That's easy to get around. is something like ! becomes factorial unless it's followed by one, but not two, equals signs...) And then people might expect x!! to be the double factorial instead of (x!)!. Agreed. If we were to implement this, we'd best look at other CAS's and see how they treat these issues. - Robert Em, I thought I'd try this in Mathematica In[1]:= 5! Out[1]= 120 In[2]:= 5!! Out[2]= 15 In[3]:= 5!!! Out[3]= 1307674368000 In[4]:= 5 Out[4]= 2027025 In[5]:= 5! spends a long time doing whatever it is trying to compute. Anyone like to guess what it's doing? --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
Dr. David Kirkby wrote: Em, I thought I'd try this in Mathematica In[1]:= 5! Out[1]= 120 In[2]:= 5!! Out[2]= 15 In[3]:= 5!!! Out[3]= 1307674368000 In[4]:= 5 Out[4]= 2027025 In[5]:= 5! spends a long time doing whatever it is trying to compute. Anyone like to guess what it's doing? Trying this in Wolfram Alpha http://www.wolframalpha.com/input/?i=5%21%21 reveals what Mathematica is doing. Apparently n!! is the double factorial http://reference.wolfram.com/mathematica/ref/Factorial2.html n!! = nx(n-2)x(n-2)x... As a non-mathematician I'd never herd of such a thing myself. --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
Dr. David Kirkby wrote: Dr. David Kirkby wrote: Em, I thought I'd try this in Mathematica In[1]:= 5! Out[1]= 120 In[2]:= 5!! Out[2]= 15 In[3]:= 5!!! Out[3]= 1307674368000 In[4]:= 5 Out[4]= 2027025 In[5]:= 5! spends a long time doing whatever it is trying to compute. Anyone like to guess what it's doing? Trying this in Wolfram Alpha http://www.wolframalpha.com/input/?i=5%21%21 reveals what Mathematica is doing. Apparently n!! is the double factorial http://reference.wolfram.com/mathematica/ref/Factorial2.html n!! = nx(n-2)x(n-2)x... As a non-mathematician I'd never herd of such a thing myself. Also relevant to the discussion is In[1]:= ?TrueQ TrueQ[expr] yields True if expr is True, and yields False otherwise. In[2]:= TrueQ[1==2] Out[2]= False In[3]:= TrueQ[5!=2] Out[3]= True In[4]:= TrueQ[5!=120] Out[4]= True In[5]:= TrueQ[5!=5] Out[5]= False And to work out the order of precedence on factorial and double-factorial. In[6]:= (5!)!! Out[6]= 959344498183598695489193994766932218518248994260838989636409419529429\ 5395488811817369600 In[7]:= 5!!! Out[7]= 1307674368000 In[8]:= (5!!)! Out[8]= 1307674368000 In[9]:= 5 Out[9]= 2027025 In[10]:= (5!!)!! Out[10]= 2027025 --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
Dr. David Kirkby wrote: Dr. David Kirkby wrote: Em, I thought I'd try this in Mathematica In[1]:= 5! Out[1]= 120 In[2]:= 5!! Out[2]= 15 In[3]:= 5!!! Out[3]= 1307674368000 In[4]:= 5 Out[4]= 2027025 In[5]:= 5! spends a long time doing whatever it is trying to compute. Anyone like to guess what it's doing? Trying this in Wolfram Alpha http://www.wolframalpha.com/input/?i=5%21%21 reveals what Mathematica is doing. Apparently n!! is the double factorial http://reference.wolfram.com/mathematica/ref/Factorial2.html n!! = nx(n-2)x(n-2)x... As a non-mathematician I'd never herd of such a thing myself. Wow, that seems totally ambiguous. Is 5!!! equal to (5!!)! or (5!)!! or ((5!)!)! The notation is pretty bad in this case. However note that: In[1]:= 5! ! Out[1]= 668950291344912705758811805409037258675274633313802981029567135230163\ 355724496298936687416527198498130815763789321409055253440858940812185989\ 848111438965000596496052125696 (note the space between the exclamation points) Jason -- Jason Grout --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
On Sep 1, 2009, at 11:34 PM, Dr. David Kirkby wrote: Dr. David Kirkby wrote: Dr. David Kirkby wrote: Em, I thought I'd try this in Mathematica In[1]:= 5! Out[1]= 120 In[2]:= 5!! Out[2]= 15 In[3]:= 5!!! Out[3]= 1307674368000 In[4]:= 5 Out[4]= 2027025 In[5]:= 5! spends a long time doing whatever it is trying to compute. Anyone like to guess what it's doing? Trying this in Wolfram Alpha http://www.wolframalpha.com/input/?i=5%21%21 reveals what Mathematica is doing. Apparently n!! is the double factorial http://reference.wolfram.com/mathematica/ref/Factorial2.html n!! = nx(n-2)x(n-2)x... As a non-mathematician I'd never herd of such a thing myself. Also relevant to the discussion is In[1]:= ?TrueQ TrueQ[expr] yields True if expr is True, and yields False otherwise. In[2]:= TrueQ[1==2] Out[2]= False In[3]:= TrueQ[5!=2] Out[3]= True In[4]:= TrueQ[5!=120] Out[4]= True In[5]:= TrueQ[5!=5] Out[5]= False And to work out the order of precedence on factorial and double- factorial. In[6]:= (5!)!! Out[6]= 959344498183598695489193994766932218518248994260838989636409419529429\ 5395488811817369600 In[7]:= 5!!! Out[7]= 1307674368000 In[8]:= (5!!)! Out[8]= 1307674368000 In[9]:= 5 Out[9]= 2027025 In[10]:= (5!!)!! Out[10]= 2027025 If we support the ! notation, we should either have x!! == (x!)! or, preferably, x!!..! be the multi factorial (not limiting ourselves to single and double). - Robert --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
Hi! On Sep 2, 7:40 am, Jason Grout jason-s...@creativetrax.com wrote: Wow, that seems totally ambiguous. Is 5!!! equal to (5!!)! or (5!)!! or ((5!)!)! The notation is pretty bad in this case. [...] Yes, and this is why the very common notation 5! is bad syntax that should be avoided in a CAS, IMHO. Of course, one could say that 5! should mean factorial of 5 unless the following character is = as in 5!=3 or ! as in 5!!. But I wouldn't paint a bike shed in that way. Just imagine how much fun it is to find a bug like 5! ! (which probably is factorial(factorial (5))) versus 5!! (which probably is double_factorial(5)). If one starts like that, why not continue with [5] (quantum deformed integers) and [5]! (quantum factorial)? Or another very common notation: Should Sage really support d^2f(x,y)/ (dx*dy) to construct partial derivatives? I think that a CAS without a strong programming language is nothing but a simple pocket calculator. Therefore, if a mathematical notation interferes too much with the requirements of the underlying programming language, then the mathematical notation should be dropped. Compare this with the example given by Kwankyu: Rx=ZZ[] resembles a chain of inequalities, sage: 56=3 True and R[x] is not compatible with Python's syntax (if R is to be defined). Therefore, I think it is a very reasonable compromise to have the additional dot in R.x Cheers Simon --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
On Tue, 01 Sep 2009 at 11:42PM -0700, Robert Bradshaw wrote: If we support the ! notation, we should either have x!! == (x!)! or, preferably, x!!..! be the multi factorial (not limiting ourselves to single and double). I study combinatorics, and I'm fine with *not* supporting ! notation. Writing factorial(x) is obvious and unambiguous. If you want something shorter, you can do f = factorial. Then the mysterious and ambiguous examples above turn into something obvious: f(f(5)) or whatever. We already have multifactorial support: (5).multifactorial(2) equals 5 * 3 * 1, and so on. I don't see anyone strongly demanding ! notation, so I say we drop the idea. We have factorial() and .multifactorial(), they work perfectly well, and the syntax for using them is the same as in the rest of Sage. Dan -- --- Dan Drake - http://mathsci.kaist.ac.kr/~drake --- signature.asc Description: Digital signature
[sage-devel] Re: Factorial syntax
2009/9/2 Dan Drake dr...@kaist.edu: On Tue, 01 Sep 2009 at 11:42PM -0700, Robert Bradshaw wrote: If we support the ! notation, we should either have x!! == (x!)! or, preferably, x!!..! be the multi factorial (not limiting ourselves to single and double). I study combinatorics, and I'm fine with *not* supporting ! notation. Writing factorial(x) is obvious and unambiguous. If you want something shorter, you can do f = factorial. Then the mysterious and ambiguous examples above turn into something obvious: f(f(5)) or whatever. We already have multifactorial support: (5).multifactorial(2) equals 5 * 3 * 1, and so on. I don't see anyone strongly demanding ! notation, so I say we drop the idea. We have factorial() and .multifactorial(), they work perfectly well, and the syntax for using them is the same as in the rest of Sage. Dan To me at least writing 'factorial(n)' is a bit clumbersome, compared to what I would expect. Mathematica supports Plus[2,3] = 5 and Factorial[5] = 120 but I doubt I'd ever want to write 'Plus' or 'Factorial' out in full, which there are such commonly used symbols for this. But clearly Mathemaitca shows there is some ambiguity about how multiple exclamation marks are used. Dave --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
But clearly Mathemaitca shows there is some ambiguity about how multiple exclamation marks are used. Yes, unfortunately math is filled with such contextual ambiguity and/ or conflicting conventions (for instance, is i an indexing integer or a root of -1?). I'm usually all for multiple modes, but this is one place where even I would draw the line. - kcrisman --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
2009/9/2 kcrisman kcris...@gmail.com: But clearly Mathemaitca shows there is some ambiguity about how multiple exclamation marks are used. Yes, unfortunately math is filled with such contextual ambiguity and/ or conflicting conventions (for instance, is i an indexing integer or a root of -1?). I'm usually all for multiple modes, but this is one place where even I would draw the line. - kcrisman 'i' is current. 'j' is the square root of -1 (to us electrical engineers anyway!) Dave --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
On Tue, Sep 1, 2009 at 11:34 PM, Dr. David Kirkbydavid.kir...@onetel.net wrote: In[7]:= 5!!! Out[7]= 1307674368000 In[8]:= (5!!)! Out[8]= 1307674368000 In[9]:= 5 Out[9]= 2027025 In[10]:= (5!!)!! Out[10]= 2027025 Yuck. -1 to compatibility with this. All or nothing -- if you're going to support double factorial, you should support any multifactorial. Reasonably, we can't expect to support arbitrary math input. We don't support |A| where len(A) does the job, and we don't accept half-open interval notation, either. I've made up my mind, I don't support the factorial notation. -1. --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
I think that a CAS without a strong programming language is nothing but a simple pocket calculator. Therefore, if a mathematical notation interferes too much with the requirements of the underlying programming language, then the mathematical notation should be dropped. I vote +1 for this argument Compare this with the example given by Kwankyu: Rx=ZZ[] resembles a chain of inequalities, sage: 56=3 True and R[x] is not compatible with Python's syntax (if R is to be defined). Therefore, I think it is a very reasonable compromise to have the additional dot in R.x This explanation makes sense. Thank you. Kwankyu --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
On Mon, Aug 31, 2009 at 10:38 AM, Robert Bradshawrober...@math.washington.edu wrote: On Mon, 31 Aug 2009, William Stein wrote: On Mon, Aug 31, 2009 at 8:23 AM, rjf fate...@gmail.com wrote: You can either (a) adhere to Python syntax. (b) adhere to Python except for a few changes that are so subtle that no one would even notice. (c) adhere to Python except for a few more changes that you tell everyone about and hope that the discrepancy between Sage and Python (and Cython) will not be noticed by critics, and so you can continue to claim Sage is just Python and everyone knows and loves Python. (d) use Python as a base, and add whatever you want, because you now have your own preparser and can add, say, postfix !. And now you probably should tell your users that the Sage language is python inspired. (e) use your own parser for your own made up language that looks like some mathematical notation. Maxima/Macsyma is in category (d) or (e): it uses its own parser for Algol 60 as a base and added things to it, but also has a syntax- extension feature so that the parser can be changed by the user. e.g. commands to add new post-fix operators etc. (At run-time). One of the premises and alleged great advantages of Sage was, I thought, that it is just Python, and you seem to be casually tossing that idea into the trash. (The idea that the user-language and the implementation-language for a computer algebra system has been a topic for discussion at least since the early 1970s, so the idea that all those clever people just missed the boat -- the solution is Python; Python does it all; seemed a bit simplistic. So I'm not surprised at the slippage, to a pre-parser and Cython and now , oh, let's add a postfix !.) Wow, you are truly the master of flamebait! I don't consider this flamebait, I think it's a rather accurate (though blunt) assessment of the uneasieness some people have regarding the preparser. I agree... though I'd describe it as overly dramatic, not blunt. I'm frequently annoyed by the preprocessor and certain symbolic constructs. I prefer to use Sage as a library about 90% of the time. OTOH, what rjf seems to be missing is that we aren't breaking compatibility with Python -- I generally support features that (a) would be syntax errors anyway (b) don't slow the preprocessor down, and (c) are wildly useful. (a) and (b) are satisfied by this feature request... but I'm not sure about (c). I'd say Sage is between (c) and (d)--just the fact that we're having this discussion means we're not willing to just go and add stuff to the preparser left and right. As for the question at hand, I'm personally not convinced this is useful enough to merit another departure from pure Python. It also risks turning the valid Python expression x!=120 into an invalid one (unless the rule bah. That's easy to get around. is something like ! becomes factorial unless it's followed by one, but not two, equals signs...) And then people might expect x!! to be the double factorial instead of (x!)!. Agreed. If we were to implement this, we'd best look at other CAS's and see how they treat these issues. - Robert --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
Hi, Out of curiosity, I want to ask why Sage has the syntax R.x = QQ[] rather than Rx = QQ[]? It seems to me that the dot is redundant. Is it something the preparser cann't do? Kwankyu --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
You can either
(a) adhere to Python syntax.
(b) adhere to Python except for a few changes that are so subtle that
no one would even notice.
(c) adhere to Python except for a few more changes that you tell
everyone about and hope that the discrepancy between Sage and Python
(and Cython) will not be noticed by critics, and so you can continue
to claim Sage is just Python and everyone knows and loves Python.
(d) use Python as a base, and add whatever you want, because you now
have your own preparser and can add, say, postfix !. And now you
probably should tell your users that the Sage language is python
inspired.
(e) use your own parser for your own made up language that looks like
some mathematical notation.
Maxima/Macsyma is in category (d) or (e): it uses its own parser for
Algol 60 as a base and added things to it, but also has a syntax-
extension feature so that the parser can be changed by the user. e.g.
commands to add new post-fix operators etc. (At run-time).
One of the premises and alleged great advantages of Sage was, I
thought, that it is just Python, and you seem to be casually tossing
that idea into the trash.
(The idea that the user-language and the implementation-language for a
computer algebra system has been a topic for discussion at least since
the early 1970s, so the idea that all those clever people just missed
the boat -- the solution is Python; Python does it all; seemed a bit
simplistic. So I'm not surprised at the slippage, to a pre-parser
and Cython and now , oh, let's add a postfix !.)
But what I think is appropriate here is an explicit formulation about
what you are doing, either (a)(e) or something else, and the
consequences.
RJF
On Aug 29, 10:13 am, William Stein wst...@gmail.com wrote:
On Sat, Aug 29, 2009 at 10:10 AM, Jason Grout
jason-s...@creativetrax.comwrote:
Fredrik Johansson wrote:
Hi,
How about supporting n! as a shortcut for factorial(n)? This syntax is
very convenient and makes a huge difference for combinatorial
expressions with many factorials. MM (Maple Mathematica) allow this
notation, as do many scientific calculators.
Although Python doesn't have any other postfix operators, I don't
think there's any ambiguity as ! is unused in Python except for the !=
operator. The worst I can come up with is x!=y, but given that =
denotes assignment and not equality, this still only has one possible
meaning.
In an attempt to find places that ! could be used, I found the
following interesting thing.
sage: var('x!')
x!
sage: _^2
x!^2
sage: x!
File ipython console, line 1
x!
^
SyntaxError: invalid syntax
Maybe Sage symbolic variables should be restricted to identifiers that
are legal in python...
Yes, definitely +1 to that. I think this used to be the case at some point.
William
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[sage-devel] Re: Factorial syntax
On Mon, Aug 31, 2009 at 8:23 AM, rjf fate...@gmail.com wrote: You can either (a) adhere to Python syntax. (b) adhere to Python except for a few changes that are so subtle that no one would even notice. (c) adhere to Python except for a few more changes that you tell everyone about and hope that the discrepancy between Sage and Python (and Cython) will not be noticed by critics, and so you can continue to claim Sage is just Python and everyone knows and loves Python. (d) use Python as a base, and add whatever you want, because you now have your own preparser and can add, say, postfix !. And now you probably should tell your users that the Sage language is python inspired. (e) use your own parser for your own made up language that looks like some mathematical notation. Maxima/Macsyma is in category (d) or (e): it uses its own parser for Algol 60 as a base and added things to it, but also has a syntax- extension feature so that the parser can be changed by the user. e.g. commands to add new post-fix operators etc. (At run-time). One of the premises and alleged great advantages of Sage was, I thought, that it is just Python, and you seem to be casually tossing that idea into the trash. (The idea that the user-language and the implementation-language for a computer algebra system has been a topic for discussion at least since the early 1970s, so the idea that all those clever people just missed the boat -- the solution is Python; Python does it all; seemed a bit simplistic. So I'm not surprised at the slippage, to a pre-parser and Cython and now , oh, let's add a postfix !.) Wow, you are truly the master of flamebait! -- William --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
We have not actually had any +1 votes for a new postfix ! operator, so
it's bit premature to criticise that decision be fore it hasn't been
made. (William's +1 was for a different suggestion, that Sage's
symbolic variables should not be allowed to be wider than python's.
Again, keeping to python conventions if at all possible.
John
(a veteran Algol 68 programmer, though not Algol 60!)
2009/8/31 rjf fate...@gmail.com:
You can either
(a) adhere to Python syntax.
(b) adhere to Python except for a few changes that are so subtle that
no one would even notice.
(c) adhere to Python except for a few more changes that you tell
everyone about and hope that the discrepancy between Sage and Python
(and Cython) will not be noticed by critics, and so you can continue
to claim Sage is just Python and everyone knows and loves Python.
(d) use Python as a base, and add whatever you want, because you now
have your own preparser and can add, say, postfix !. And now you
probably should tell your users that the Sage language is python
inspired.
(e) use your own parser for your own made up language that looks like
some mathematical notation.
Maxima/Macsyma is in category (d) or (e): it uses its own parser for
Algol 60 as a base and added things to it, but also has a syntax-
extension feature so that the parser can be changed by the user. e.g.
commands to add new post-fix operators etc. (At run-time).
One of the premises and alleged great advantages of Sage was, I
thought, that it is just Python, and you seem to be casually tossing
that idea into the trash.
(The idea that the user-language and the implementation-language for a
computer algebra system has been a topic for discussion at least since
the early 1970s, so the idea that all those clever people just missed
the boat -- the solution is Python; Python does it all; seemed a bit
simplistic. So I'm not surprised at the slippage, to a pre-parser
and Cython and now , oh, let's add a postfix !.)
But what I think is appropriate here is an explicit formulation about
what you are doing, either (a)(e) or something else, and the
consequences.
RJF
On Aug 29, 10:13 am, William Stein wst...@gmail.com wrote:
On Sat, Aug 29, 2009 at 10:10 AM, Jason Grout
jason-s...@creativetrax.comwrote:
Fredrik Johansson wrote:
Hi,
How about supporting n! as a shortcut for factorial(n)? This syntax is
very convenient and makes a huge difference for combinatorial
expressions with many factorials. MM (Maple Mathematica) allow this
notation, as do many scientific calculators.
Although Python doesn't have any other postfix operators, I don't
think there's any ambiguity as ! is unused in Python except for the !=
operator. The worst I can come up with is x!=y, but given that =
denotes assignment and not equality, this still only has one possible
meaning.
In an attempt to find places that ! could be used, I found the
following interesting thing.
sage: var('x!')
x!
sage: _^2
x!^2
sage: x!
File ipython console, line 1
x!
^
SyntaxError: invalid syntax
Maybe Sage symbolic variables should be restricted to identifiers that
are legal in python...
Yes, definitely +1 to that. I think this used to be the case at some point.
William
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[sage-devel] Re: Factorial syntax
On Mon, 31 Aug 2009, William Stein wrote: On Mon, Aug 31, 2009 at 8:23 AM, rjf fate...@gmail.com wrote: You can either (a) adhere to Python syntax. (b) adhere to Python except for a few changes that are so subtle that no one would even notice. (c) adhere to Python except for a few more changes that you tell everyone about and hope that the discrepancy between Sage and Python (and Cython) will not be noticed by critics, and so you can continue to claim Sage is just Python and everyone knows and loves Python. (d) use Python as a base, and add whatever you want, because you now have your own preparser and can add, say, postfix !. And now you probably should tell your users that the Sage language is python inspired. (e) use your own parser for your own made up language that looks like some mathematical notation. Maxima/Macsyma is in category (d) or (e): it uses its own parser for Algol 60 as a base and added things to it, but also has a syntax- extension feature so that the parser can be changed by the user. e.g. commands to add new post-fix operators etc. (At run-time). One of the premises and alleged great advantages of Sage was, I thought, that it is just Python, and you seem to be casually tossing that idea into the trash. (The idea that the user-language and the implementation-language for a computer algebra system has been a topic for discussion at least since the early 1970s, so the idea that all those clever people just missed the boat -- the solution is Python; Python does it all; seemed a bit simplistic. So I'm not surprised at the slippage, to a pre-parser and Cython and now , oh, let's add a postfix !.) Wow, you are truly the master of flamebait! I don't consider this flamebait, I think it's a rather accurate (though blunt) assessment of the uneasieness some people have regarding the preparser. I'd say Sage is between (c) and (d)--just the fact that we're having this discussion means we're not willing to just go and add stuff to the preparser left and right. As for the question at hand, I'm personally not convinced this is useful enough to merit another departure from pure Python. It also risks turning the valid Python expression x!=120 into an invalid one (unless the rule is something like ! becomes factorial unless it's followed by one, but not two, equals signs...) And then people might expect x!! to be the double factorial instead of (x!)!. - Robert --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
I also don't consider Fateman's comments flamebait. This kind of syntactic-philosopy discussion comes up frequently on CA mailing lists. I've had an offline discussion about supporting the quantum mechanical ket operator with the syntax of |state. One possible implementation is to consider the vert and less-than symbols to be syntactic sugar for ( and ) However, supporting |state would involve Axiom parser changes. There appear to be three target audiences, the programmers, the mathematicians, and the computational mathematicians. Sage has clearly been singing to the programmers. A postfix ! would appeal more to the mathematicians. Fateman, being in the computational mathematician category has a clear understanding of the range of tradeoffs. I suspect his blunt tone is due to the fact that, as he says, this has been debated since the 1970s. However, he's being quite clear about the range of possible philosophical responses. -Tim On Aug 31, 1:38 pm, Robert Bradshaw rober...@math.washington.edu wrote: On Mon, 31 Aug 2009, William Stein wrote: On Mon, Aug 31, 2009 at 8:23 AM, rjf fate...@gmail.com wrote: You can either (a) adhere to Python syntax. (b) adhere to Python except for a few changes that are so subtle that no one would even notice. (c) adhere to Python except for a few more changes that you tell everyone about and hope that the discrepancy between Sage and Python (and Cython) will not be noticed by critics, and so you can continue to claim Sage is just Python and everyone knows and loves Python. (d) use Python as a base, and add whatever you want, because you now have your own preparser and can add, say, postfix !. And now you probably should tell your users that the Sage language is python inspired. (e) use your own parser for your own made up language that looks like some mathematical notation. Maxima/Macsyma is in category (d) or (e): it uses its own parser for Algol 60 as a base and added things to it, but also has a syntax- extension feature so that the parser can be changed by the user. e.g. commands to add new post-fix operators etc. (At run-time). One of the premises and alleged great advantages of Sage was, I thought, that it is just Python, and you seem to be casually tossing that idea into the trash. (The idea that the user-language and the implementation-language for a computer algebra system has been a topic for discussion at least since the early 1970s, so the idea that all those clever people just missed the boat -- the solution is Python; Python does it all; seemed a bit simplistic. So I'm not surprised at the slippage, to a pre-parser and Cython and now , oh, let's add a postfix !.) Wow, you are truly the master of flamebait! I don't consider this flamebait, I think it's a rather accurate (though blunt) assessment of the uneasieness some people have regarding the preparser. I'd say Sage is between (c) and (d)--just the fact that we're having this discussion means we're not willing to just go and add stuff to the preparser left and right. As for the question at hand, I'm personally not convinced this is useful enough to merit another departure from pure Python. It also risks turning the valid Python expression x!=120 into an invalid one (unless the rule is something like ! becomes factorial unless it's followed by one, but not two, equals signs...) And then people might expect x!! to be the double factorial instead of (x!)!. - Robert --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
2009/8/29 Fredrik Johansson fredrik.johans...@gmail.com: Hi, How about supporting n! as a shortcut for factorial(n)? This syntax is very convenient and makes a huge difference for combinatorial expressions with many factorials. MM (Maple Mathematica) allow this notation, as do many scientific calculators. Although Python doesn't have any other postfix operators, I don't think there's any ambiguity as ! is unused in Python except for the != operator. The worst I can come up with is x!=y, but given that = denotes assignment and not equality, this still only has one possible meaning. I seem to remember this coming up before, and the consensus being that we want to avoid adding stuff to the preparser unless it is really crucial. I could not find that discussion though, so I may be forgetting the arguments. John --~--~-~--~~~---~--~~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-devel] Re: Factorial syntax
Fredrik Johansson wrote:
Hi,
How about supporting n! as a shortcut for factorial(n)? This syntax is
very convenient and makes a huge difference for combinatorial
expressions with many factorials. MM (Maple Mathematica) allow this
notation, as do many scientific calculators.
Although Python doesn't have any other postfix operators, I don't
think there's any ambiguity as ! is unused in Python except for the !=
operator. The worst I can come up with is x!=y, but given that =
denotes assignment and not equality, this still only has one possible
meaning.
In an attempt to find places that ! could be used, I found the
following interesting thing.
sage: var('x!')
x!
sage: _^2
x!^2
sage: x!
File ipython console, line 1
x!
^
SyntaxError: invalid syntax
Maybe Sage symbolic variables should be restricted to identifiers that
are legal in python...
Jason
--
Jason Grout
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[sage-devel] Re: Factorial syntax
On Sat, Aug 29, 2009 at 10:10 AM, Jason Grout
jason-s...@creativetrax.comwrote:
Fredrik Johansson wrote:
Hi,
How about supporting n! as a shortcut for factorial(n)? This syntax is
very convenient and makes a huge difference for combinatorial
expressions with many factorials. MM (Maple Mathematica) allow this
notation, as do many scientific calculators.
Although Python doesn't have any other postfix operators, I don't
think there's any ambiguity as ! is unused in Python except for the !=
operator. The worst I can come up with is x!=y, but given that =
denotes assignment and not equality, this still only has one possible
meaning.
In an attempt to find places that ! could be used, I found the
following interesting thing.
sage: var('x!')
x!
sage: _^2
x!^2
sage: x!
File ipython console, line 1
x!
^
SyntaxError: invalid syntax
Maybe Sage symbolic variables should be restricted to identifiers that
are legal in python...
Yes, definitely +1 to that. I think this used to be the case at some point.
William
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