Re: [sympy] Easy way to use S()

[Jonathan Gutow]

On Jul 13, 2023, at 5:23 AM, emanuel.c...@gmail.com 
 wrote:


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Le mercredi 12 juillet 2023 à 22:49:11 UTC+2, gu…@uwosh.edu a écrit :


Algebra_with_Sympy release 
v0.12.0 is now available. It now 
interprets numbers without decimals as sympy integers. This feature can be 
turned on and off.



Are you trying to reinvent Sage’s 
preparser
 ?

Not really. I have used Sage math in the past, maintained a local server that I 
used with students and even contributed code for 3D visualization when Sage was 
primarily using Jmol/JSmol for that. However, I found that Sage was less 
appropriate for use with my chemistry students and much more heavy-weight than 
a simple SymPy installation. Additionally, in my field instructors are sharing 
many notebooks based on SymPy that are only partially Sage compatible.

The features Algebra_with_SymPy layers on top of SymPy are those that the 
physical science community (physical chemistry in particular) have asked for. 
Most of the features do not involve the preparser and those that do and are 
similar to Sage’s features are only incidentally so. I have also been 
developing this with an eye towards it being useful for the Jupyter Physical 
Science Lab Project (https://jupyterphysscilab.github.io/Documentation/), which 
aims to be an electronic laboratory notebook which can support acquisition of 
analog data directly into the Jupyter notebooks along with symbolic math, 
numerical data analysis and textual notes, while being simple enough to use in 
introductory level college science courses. I also needed something that ran 
well on computers as low powered as the Raspberry Pi.

I have been trying to get approval to include the core feature of 
Algebra_with_Sympy (the Equation class) in SymPy, but the community has not 
reached a consensus on how some of the features should behave. See 
https://github.com/sympy/SymPEPs/pull/1/files.

Is there some feature overlap with Sage math? Yes. Do I wish to duplicate Sage 
math? No. For the use cases I primarily encounter I do not need the full power 
or complexity of Sage math, so I find the combination of Sympy + 
Algebra_with_Sympy is more appropriate. I like Sage and recommend it to people 
for more sophisticated uses than I have.

Jonathan
​

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Re: [sympy] Easy way to use S()

[emanuel.c...@gmail.com]

Le mercredi 12 juillet 2023 à 22:49:11 UTC+2, gu…@uwosh.edu a écrit :

Algebra_with_Sympy release v0.12.0 
 is now available. It now 
interprets numbers without decimals as sympy integers. This feature can be 
turned on and off.

Are you trying to reinvent Sage’s preparser 
 ?

On Saturday, July 8, 2023 at 11:39:45 PM UTC-5 gu...@uwosh.edu wrote:

David,

I hope this message is not a repeat. The one I wrote in reply seems to have 
been deleted.

So briefly:
1. Currently Algebra_with_Sympy does not interpret numbers without decimals 
as sympy integers, but I have got a working draft that does. I just need to 
finish updating the tests and documentation, before making a new release.
2. You can use Algebra_with_Sympy as a front-end for Sympy. You can ignore 
the `Equation` class and just do normal SymPy syntax. There are a some 
differences in what outputs look like. See the documentation about output 
formatting. 


Jonathan

On Saturday, July 8, 2023 at 5:39:46 AM UTC-4 da...@dbailey.co.uk wrote:

On 07/07/2023 23:23, gu...@uwosh.edu wrote: 
> David, 
> 
> I will work to get this into Algebra_with_Sympy quickly. I will post 
> when I complete the next release. 
> 
> Since these ease of use issues are not cleanly addressable within 
> SymPy proper, maybe you can think of Algebra_with_SymPy as your 
> interactive front-end for sympy. 
> 
I thought you wrote that you already wrapped integers in S() if the -i 
option was specified. Do you just mean that you would make -i the default? 

Can Algebra_with_SymPy operate as a frontend to SymPy in general? 

David 

​

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Re: [sympy] Easy way to use S()

[gu...@uwosh.edu]

Algebra_with_Sympy release v0.12.0 
 is now available. It now 
interprets numbers without decimals as sympy integers. This feature can be 
turned on and off.

On Saturday, July 8, 2023 at 11:39:45 PM UTC-5 gu...@uwosh.edu wrote:

> David,
>
> I hope this message is not a repeat. The one I wrote in reply seems to 
> have been deleted.
>
> So briefly:
> 1. Currently Algebra_with_Sympy does not interpret numbers without 
> decimals as sympy integers, but I have got a working draft that does. I 
> just need to finish updating the tests and documentation, before making a 
> new release.
> 2. You can use Algebra_with_Sympy as a front-end for Sympy. You can ignore 
> the `Equation` class and just do normal SymPy syntax. There are a some 
> differences in what outputs look like. See the documentation about output 
> formatting. 
> 
>
> Jonathan
>
> On Saturday, July 8, 2023 at 5:39:46 AM UTC-4 da...@dbailey.co.uk wrote:
>
>> On 07/07/2023 23:23, gu...@uwosh.edu wrote: 
>> > David, 
>> > 
>> > I will work to get this into Algebra_with_Sympy quickly. I will post 
>> > when I complete the next release. 
>> > 
>> > Since these ease of use issues are not cleanly addressable within 
>> > SymPy proper, maybe you can think of Algebra_with_SymPy as your 
>> > interactive front-end for sympy. 
>> > 
>> I thought you wrote that you already wrapped integers in S() if the -i 
>> option was specified. Do you just mean that you would make -i the 
>> default? 
>>
>> Can Algebra_with_SymPy operate as a frontend to SymPy in general? 
>>
>> David 
>>
>>

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Re: [sympy] Easy way to use S()

[gu...@uwosh.edu]

David,

I hope this message is not a repeat. The one I wrote in reply seems to have 
been deleted.

So briefly:
1. Currently Algebra_with_Sympy does not interpret numbers without decimals 
as sympy integers, but I have got a working draft that does. I just need to 
finish updating the tests and documentation, before making a new release.
2. You can use Algebra_with_Sympy as a front-end for Sympy. You can ignore 
the `Equation` class and just do normal SymPy syntax. There are a some 
differences in what outputs look like. See the documentation about output 
formatting. 


Jonathan

On Saturday, July 8, 2023 at 5:39:46 AM UTC-4 da...@dbailey.co.uk wrote:

> On 07/07/2023 23:23, gu...@uwosh.edu wrote:
> > David,
> >
> > I will work to get this into Algebra_with_Sympy quickly. I will post 
> > when I complete the next release.
> >
> > Since these ease of use issues are not cleanly addressable within 
> > SymPy proper, maybe you can think of Algebra_with_SymPy as your 
> > interactive front-end for sympy.
> >
> I thought you wrote that you already wrapped integers in S() if the -i 
> option was specified. Do you just mean that you would make -i the default?
>
> Can Algebra_with_SymPy operate as a frontend to SymPy in general?
>
> David
>
>

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Re: [sympy] Easy way to use S()

[David Bailey]

On 07/07/2023 23:23, gu...@uwosh.edu wrote:

David,

I will work to get this into Algebra_with_Sympy quickly. I will post 
when I complete the next release.


Since these ease of use issues are not cleanly addressable within 
SymPy proper, maybe you can think of Algebra_with_SymPy as your 
interactive front-end for sympy.


I thought you wrote that you already wrapped integers in S() if the -i 
option was specified. Do you just mean that you would make -i the default?


Can Algebra_with_SymPy operate as a frontend to SymPy in general?

David

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Re: [sympy] Easy way to use S()

[gu...@uwosh.edu]

David,

I will work to get this into Algebra_with_Sympy quickly. I will post when I 
complete the next release.

Since these ease of use issues are not cleanly addressable within SymPy 
proper, maybe you can think of Algebra_with_SymPy as your interactive 
front-end for sympy.

Jonathan

On Friday, July 7, 2023 at 4:41:07 PM UTC-4 da...@dbailey.co.uk wrote:

> On 07/07/2023 10:09, Isuru Fernando wrote:
> > Hi David,
> >
> > You could write a simple converter to convert all ints to sympy Integers
> > if you are writing the code inside a function. See code below.
> >
> > Isuru
> >
> Thanks, I can solve this problem to my satisfaction, but my main 
> concern, as a pointed out to Aaron, is that SymPy may get a bad 
> reputation among those who explore it cursorily. The point is, it can 
> give peculiar answers, which is analogous to my friend's problem with 
> his Sinclair calculator. The Sinclair folk could (presumably) explain in 
> detail why that result was bad, but my friend wasn't keen on using his 
> new flashy gadget any more. I think they were the first cheap 
> calculators to provide a full set of transcendental functions, so it was 
> very unfortunate.
>
> David
>
>

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Re: [sympy] Easy way to use S()

[David Bailey]

On 07/07/2023 10:09, Isuru Fernando wrote:

Hi David,

You could write a simple converter to convert all ints to sympy Integers
if you are writing the code inside a function. See code below.

Isuru

Thanks, I can solve this problem to my satisfaction, but my main 
concern, as a pointed out to Aaron, is that SymPy may get a bad 
reputation among those who explore it cursorily. The point is, it can 
give peculiar answers, which is analogous to my friend's problem with 
his Sinclair calculator. The Sinclair folk could (presumably) explain in 
detail why that result was bad, but my friend wasn't keen on using his 
new flashy gadget any more. I think they were the first cheap 
calculators to provide a full set of transcendental functions, so it was 
very unfortunate.


David

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Re: [sympy] Easy way to use S()

[Isuru Fernando]

Hi David,

You could write a simple converter to convert all ints to sympy Integers
if you are writing the code inside a function. See code below.

Isuru


import sympy
from sympy.interactive.session import int_to_Integer
import inspect
import types

def use_sympy_ints(f):
# https://stackoverflow.com/q/57480368/4768820
source = inspect.getsource(f)
source = '\n'.join(source.splitlines()[1:]) # remove the decorator
first line.
old_code_obj = f.__code__
new_ast= int_to_Integer(source)
new_code_obj = compile(new_ast, old_code_obj.co_filename, 'exec')
g = dict(f.__globals__)
g['Integer'] = sympy.Integer
new_f = types.FunctionType(new_code_obj.co_consts[0], g)
return new_f

@use_sympy_ints
def foo(x):
return x + 1 / 2

On Fri, Jul 7, 2023 at 3:32 AM Aaron Meurer  wrote:

> On Thu, Jul 6, 2023 at 4:15 PM David Bailey  wrote:
> >
> > On 05/07/2023 21:40, Aaron Meurer wrote:
> > > For interactive use, just passing a string to S() (or equivalently
> > > sympify() or parse_expr()) is the simplest way to deal with this.
> > > However, I would avoid this for non-interactive usage (i.e., any code
> > > that gets saved to be executed later). Putting your expression in a
> > > string breaks the ability for Python to parse it directly, meaning
> > > things like simple syntax errors won't be caught until the code gets
> > > run.
> > >
> > > You should also be very careful when doing this if you use
> > > assumptions. S("x + 1") will create a symbol x with the default
> > > assumptions. If you already defined x with assumptions, like
> > >
> > > x = symbols('x', real=True)
> > >
> > > then this will be a *different* symbol. For example:
> >
> > Thanks for that caution, Aaron,
> >
> > This whole problem reminds me vaguely of a friend of mine that bought an
> > early Sinclair calculator. He discovered that ln(2) was seriously
> > inaccurate, so he wrote to them. They replied that there was nothing
> > wrong with his calculator, he had just chosen an unfortunate example!
> >
> > What I'm trying to say is that there must be people out there who gave
> > given up on SymPy after discovering what it does to 1/2*x, or worse
> > still, got an error in their work (particularly if using Python 2).
>
> No one should be using Python 2 at this point. So fortunately that
> particular headache is behind us.
>
> >
> > Thinking about it, I can see how hard it is to do something really
> > effective about this problem, but couldn't you prevail on the Python
> > term to insert a hook in the Python parser to make it possible to change
> > an input string before Python parses it and applies its integer division
> > rule?
>
> That particular way of solving the problem would very likely be
> rejected. It's basically equivalent to adding macros to the language,
> which has been rejected multiple times before.
>
> I have wondered if it wouldn't be possible for Python to keep track of
> how purely numeric constants are created at compile time and store
> that information on the constant. Since it would only apply to pure
> numbers and would only happen at compile time, it would have basically
> no runtime penalties. That would also allow something like
> 1.001, which automatically truncates to 1.0, to create
> sympy.Float('1.001'). But it's only a vague idea I've
> ruminated on and I haven't written to the core Python team about it.
>
> Aaron Meurer
>
> >
> > David
> >
> > --
> > You received this message because you are subscribed to the Google
> Groups "sympy" group.
> > To unsubscribe from this group and stop receiving emails from it, send
> an email to sympy+unsubscr...@googlegroups.com.
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> https://groups.google.com/d/msgid/sympy/d6b19b21-d61c-e4f8-3116-f5f64ac6ab48%40dbailey.co.uk
> .
>
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> .
>

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Re: [sympy] Easy way to use S()

[Aaron Meurer]

On Thu, Jul 6, 2023 at 4:15 PM David Bailey  wrote:
>
> On 05/07/2023 21:40, Aaron Meurer wrote:
> > For interactive use, just passing a string to S() (or equivalently
> > sympify() or parse_expr()) is the simplest way to deal with this.
> > However, I would avoid this for non-interactive usage (i.e., any code
> > that gets saved to be executed later). Putting your expression in a
> > string breaks the ability for Python to parse it directly, meaning
> > things like simple syntax errors won't be caught until the code gets
> > run.
> >
> > You should also be very careful when doing this if you use
> > assumptions. S("x + 1") will create a symbol x with the default
> > assumptions. If you already defined x with assumptions, like
> >
> > x = symbols('x', real=True)
> >
> > then this will be a *different* symbol. For example:
>
> Thanks for that caution, Aaron,
>
> This whole problem reminds me vaguely of a friend of mine that bought an
> early Sinclair calculator. He discovered that ln(2) was seriously
> inaccurate, so he wrote to them. They replied that there was nothing
> wrong with his calculator, he had just chosen an unfortunate example!
>
> What I'm trying to say is that there must be people out there who gave
> given up on SymPy after discovering what it does to 1/2*x, or worse
> still, got an error in their work (particularly if using Python 2).

No one should be using Python 2 at this point. So fortunately that
particular headache is behind us.

>
> Thinking about it, I can see how hard it is to do something really
> effective about this problem, but couldn't you prevail on the Python
> term to insert a hook in the Python parser to make it possible to change
> an input string before Python parses it and applies its integer division
> rule?

That particular way of solving the problem would very likely be
rejected. It's basically equivalent to adding macros to the language,
which has been rejected multiple times before.

I have wondered if it wouldn't be possible for Python to keep track of
how purely numeric constants are created at compile time and store
that information on the constant. Since it would only apply to pure
numbers and would only happen at compile time, it would have basically
no runtime penalties. That would also allow something like
1.001, which automatically truncates to 1.0, to create
sympy.Float('1.001'). But it's only a vague idea I've
ruminated on and I haven't written to the core Python team about it.

Aaron Meurer

>
> David
>
> --
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Re: [sympy] Easy way to use S()

[David Bailey]

On 05/07/2023 21:40, Aaron Meurer wrote:

For interactive use, just passing a string to S() (or equivalently
sympify() or parse_expr()) is the simplest way to deal with this.
However, I would avoid this for non-interactive usage (i.e., any code
that gets saved to be executed later). Putting your expression in a
string breaks the ability for Python to parse it directly, meaning
things like simple syntax errors won't be caught until the code gets
run.

You should also be very careful when doing this if you use
assumptions. S("x + 1") will create a symbol x with the default
assumptions. If you already defined x with assumptions, like

x = symbols('x', real=True)

then this will be a *different* symbol. For example:


Thanks for that caution, Aaron,

This whole problem reminds me vaguely of a friend of mine that bought an 
early Sinclair calculator. He discovered that ln(2) was seriously 
inaccurate, so he wrote to them. They replied that there was nothing 
wrong with his calculator, he had just chosen an unfortunate example!


What I'm trying to say is that there must be people out there who gave 
given up on SymPy after discovering what it does to 1/2*x, or worse 
still, got an error in their work (particularly if using Python 2).


Thinking about it, I can see how hard it is to do something really 
effective about this problem, but couldn't you prevail on the Python 
term to insert a hook in the Python parser to make it possible to change 
an input string before Python parses it and applies its integer division 
rule?


David

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Re: [sympy] Easy way to use S()

[Aaron Meurer]

For interactive use, just passing a string to S() (or equivalently
sympify() or parse_expr()) is the simplest way to deal with this.
However, I would avoid this for non-interactive usage (i.e., any code
that gets saved to be executed later). Putting your expression in a
string breaks the ability for Python to parse it directly, meaning
things like simple syntax errors won't be caught until the code gets
run.

You should also be very careful when doing this if you use
assumptions. S("x + 1") will create a symbol x with the default
assumptions. If you already defined x with assumptions, like

x = symbols('x', real=True)

then this will be a *different* symbol. For example:

>>> x = symbols('x', real=True)
>>> expr = S("x + 1")
>>> x + expr
x + x + 1

This can lead to all sorts of confusion. So really only use string
input if you are very careful about these issues.

Aaron Meurer

On Mon, Jul 3, 2023 at 6:25 AM Oscar Benjamin
 wrote:
>
> On Mon, 3 Jul 2023 at 00:16, David Bailey  wrote:
> >
> > On 02/07/2023 23:44, Oscar Benjamin wrote:
> > > On Sun, 2 Jul 2023 at 23:06, David Bailey  wrote:
> > >> Dear Group,
> > >>
> > >> If I want to enter m+1/2, I define m as a symbol and write:
> > >>
> > >>m+S(1)/2.
> > >>
> > >> However if I have a complicated expression with lots of fractions, such 
> > >> as:
> > >>
> > >> 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m + 1)*(2*m + 
> > >> 2))
> > >>
> > >> it would be much neater if I could automatically wrap all the integers
> > >> in S so that no floating point numbers get introduced.
> > >>
> > >> Is that feasible? I did try wrapping the whole expression in S, but that
> > >> does not work.
> > > You can wrap the whole expression in nsimplify:
> > >
> > >   >>> e = 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m
> > > + 1)*(2*m + 2))
> > >   >>> print(e)
> > >   x**2*(m + 0.5)*(m + 1.5)/((2*m + 2)*(4*m + 2)) + x*(m + 0.5)/(2*m + 1) 
> > > + 1
> > >   >>> print(nsimplify(e))
> > >   x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) 
> > > + 1
> > >
> > > The nsimplify function will attempt to guess what rational number a
> > > float represents. In your example this is easy because all floats are
> > > exactly represented in binary (having only twos in the denominator)
> > > but otherwise the conversion can be inexact:
> > >
> > >   >>> f = 1/3
> > >   >>> f
> > >   0.
> > >   >>> print(Rational(f))  # exact value of the binary float
> > >   6004799503160661/18014398509481984
> > >   >>> nsimplify(f)  # probably the value that the float was intended to 
> > > have
> > >   1/3
> > >
> > Thanks Oscar for that incredibly fast reply, but I'm not super keen on
> > algebra that is only probably correct!
>
> Agreed but that means that you need to avoid creating floats in the
> first place. Many users find it awkward to do this and prefer to use
> nsimplify.
>
> Another option is to call S with a string::
>
> In [27]: s = '1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m +
> 3/2)/(2*(2*m + 1)*(2*m + 2))'
>
> In [28]: print(S(s))
> x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1
>
> --
> Oscar
>
> --
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Re: [sympy] Easy way to use S()

[gu...@uwosh.edu]

3e4 in sympy pretty printing is output as a decimal number. At somewhere 
greater that 10^10 pretty printing switches to scientific notation with a • 
in sympy.

In the code cells I insist on using * for multiplication to avoid any 
questions about implicit multiplication and multi-character variable names. 
I think I will continue to do that.

Entering 3.2e4 as (3.2*10**4) also works. If you are running with integer 
recognition and the mantissa is entered as an integer the value will be 
treated as an integer in the case where you write it out.

Jonathan

On Monday, July 3, 2023 at 11:05:27 AM UTC-5 da...@dbailey.co.uk wrote:

I mean 3e4 looks very confusing in an algebraic expression, and if you 
permit implicit multiplication as in hand algebra it is ambiguous. Anyway 
performing algebra with expressions containing real numbers is decidedly 
dangerous. 

Davis

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Re: [sympy] Easy way to use S()

[David Bailey]

On 03/07/2023 14:44, gu...@uwosh.edu wrote:

David,

I want to make sure I understand the behavior you would prefer, 
because I think I can implement it in algebra-with-sympy 
. 
The package already does some pre-parsing, so I think I could handle 
it there.


Here is what I think you are asking for:
1. Any number that is not in scientific notation and does not contain 
a decimal point would be considered an integer and be converted to S().

2. All other numerical values would be treated as they normally are.



Yes, that describes what I want completely!

I wonder if you should ban exponential notation completely from your 
tool except for a final step in which real numbers might be substituted 
into an expression?


I mean 3e4 looks very confusing in an algebraic expression, and if you 
permit implicit multiplication as in hand algebra it is ambiguous. 
Anyway performing algebra with expressions containing real numbers is 
decidedly dangerous.


Davis

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Re: [sympy] Easy way to use S()

[David Bailey]

On 03/07/2023 13:24, Oscar Benjamin wrote:

Another option is to call S with a string::
In [27]: s = '1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m +
3/2)/(2*(2*m + 1)*(2*m + 2))'

In [28]: print(S(s))
x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1

--
Oscar


Thanks Oscar, that is a much more useful feature!


BTW, I couldn't see it mentioned in the documentation for S(), and I 
think it should definitely also be mentioned in the section of of the 
SymPy documentation that discusses the problem with Python evaluating 
expressions like 1/2 in an unhelpful way.


David

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Re: [sympy] Easy way to use S()

[gu...@uwosh.edu]

The documentation for  isympy mode is not good. When I search the sympy 
docs I find this
https://docs.sympy.org/latest/modules/interactive.html. I am do not find 
anything about the -i option on this page.

A general web search turns up this old command line doc which also does not 
document the -i option. The only thing that is clear is some predefined 
symbols and automatic symbol creation.
https://www.mankier.com/1/isympy
None of the other links from the search are any better.

It looks like isympy is close to the sensible convenience mode I am 
suggesting. However, it needs to be identified and documented much more 
clearly. It probably should be in the introductory material.

>I normally use sympy through the command line isympy interface which 
is a wrapper around ipython that provides an environment automatically 
set up for using sympy. I don't use this myself but isympy has a -i 
flag to interpret integer literals as sympy Integers (and therefore 
integer division as rational division): 

>$ isympy -i 

On Monday, July 3, 2023 at 8:44:07 AM UTC-5 gu...@uwosh.edu wrote:

> David,
>
> I want to make sure I understand the behavior you would prefer, because I 
> think I can implement it in algebra-with-sympy 
> . The 
> package already does some pre-parsing, so I think I could handle it there.
>
> Here is what I think you are asking for:
> 1. Any number that is not in scientific notation and does not contain a 
> decimal point would be considered an integer and be converted to S().
> 2. All other numerical values would be treated as they normally are.
>
> Is that all you are asking for or do you need something more sophisticated?
>
> As more of these usage questions come up, I am beginning to wonder if 
> sympy needs an interactive mode that implements sensible/useful extensions 
> and defaults that would get in the way of sympy's use as a symbolic 
> manipulation back-end? The idea would be to have these features only turned 
> on in the interactive mode.
>
> Jonathan
>
> On Monday, July 3, 2023 at 7:25:00 AM UTC-5 Oscar wrote:
>
>> On Mon, 3 Jul 2023 at 00:16, David Bailey  wrote: 
>> > 
>> > On 02/07/2023 23:44, Oscar Benjamin wrote: 
>> > > On Sun, 2 Jul 2023 at 23:06, David Bailey  
>> wrote: 
>> > >> Dear Group, 
>> > >> 
>> > >> If I want to enter m+1/2, I define m as a symbol and write: 
>> > >> 
>> > >> m+S(1)/2. 
>> > >> 
>> > >> However if I have a complicated expression with lots of fractions, 
>> such as: 
>> > >> 
>> > >> 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m + 
>> 1)*(2*m + 2)) 
>> > >> 
>> > >> it would be much neater if I could automatically wrap all the 
>> integers 
>> > >> in S so that no floating point numbers get introduced. 
>> > >> 
>> > >> Is that feasible? I did try wrapping the whole expression in S, but 
>> that 
>> > >> does not work. 
>> > > You can wrap the whole expression in nsimplify: 
>> > > 
>> > > >>> e = 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m 
>> > > + 1)*(2*m + 2)) 
>> > > >>> print(e) 
>> > > x**2*(m + 0.5)*(m + 1.5)/((2*m + 2)*(4*m + 2)) + x*(m + 0.5)/(2*m + 
>> 1) + 1 
>> > > >>> print(nsimplify(e)) 
>> > > x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 
>> 1) + 1 
>> > > 
>> > > The nsimplify function will attempt to guess what rational number a 
>> > > float represents. In your example this is easy because all floats are 
>> > > exactly represented in binary (having only twos in the denominator) 
>> > > but otherwise the conversion can be inexact: 
>> > > 
>> > > >>> f = 1/3 
>> > > >>> f 
>> > > 0. 
>> > > >>> print(Rational(f)) # exact value of the binary float 
>> > > 6004799503160661/18014398509481984 
>> > > >>> nsimplify(f) # probably the value that the float was intended to 
>> have 
>> > > 1/3 
>> > > 
>> > Thanks Oscar for that incredibly fast reply, but I'm not super keen on 
>> > algebra that is only probably correct! 
>>
>> Agreed but that means that you need to avoid creating floats in the 
>> first place. Many users find it awkward to do this and prefer to use 
>> nsimplify. 
>>
>> Another option is to call S with a string:: 
>>
>> In [27]: s = '1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 
>> 3/2)/(2*(2*m + 1)*(2*m + 2))' 
>>
>> In [28]: print(S(s)) 
>> x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 
>> 1 
>>
>> -- 
>> Oscar 
>>
>

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Re: [sympy] Easy way to use S()

[gu...@uwosh.edu]

David,

I want to make sure I understand the behavior you would prefer, because I 
think I can implement it in algebra-with-sympy 
. The 
package already does some pre-parsing, so I think I could handle it there.

Here is what I think you are asking for:
1. Any number that is not in scientific notation and does not contain a 
decimal point would be considered an integer and be converted to S().
2. All other numerical values would be treated as they normally are.

Is that all you are asking for or do you need something more sophisticated?

As more of these usage questions come up, I am beginning to wonder if sympy 
needs an interactive mode that implements sensible/useful extensions and 
defaults that would get in the way of sympy's use as a symbolic 
manipulation back-end? The idea would be to have these features only turned 
on in the interactive mode.

Jonathan

On Monday, July 3, 2023 at 7:25:00 AM UTC-5 Oscar wrote:

> On Mon, 3 Jul 2023 at 00:16, David Bailey  wrote:
> >
> > On 02/07/2023 23:44, Oscar Benjamin wrote:
> > > On Sun, 2 Jul 2023 at 23:06, David Bailey  wrote:
> > >> Dear Group,
> > >>
> > >> If I want to enter m+1/2, I define m as a symbol and write:
> > >>
> > >> m+S(1)/2.
> > >>
> > >> However if I have a complicated expression with lots of fractions, 
> such as:
> > >>
> > >> 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m + 
> 1)*(2*m + 2))
> > >>
> > >> it would be much neater if I could automatically wrap all the integers
> > >> in S so that no floating point numbers get introduced.
> > >>
> > >> Is that feasible? I did try wrapping the whole expression in S, but 
> that
> > >> does not work.
> > > You can wrap the whole expression in nsimplify:
> > >
> > > >>> e = 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m
> > > + 1)*(2*m + 2))
> > > >>> print(e)
> > > x**2*(m + 0.5)*(m + 1.5)/((2*m + 2)*(4*m + 2)) + x*(m + 0.5)/(2*m + 1) 
> + 1
> > > >>> print(nsimplify(e))
> > > x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) 
> + 1
> > >
> > > The nsimplify function will attempt to guess what rational number a
> > > float represents. In your example this is easy because all floats are
> > > exactly represented in binary (having only twos in the denominator)
> > > but otherwise the conversion can be inexact:
> > >
> > > >>> f = 1/3
> > > >>> f
> > > 0.
> > > >>> print(Rational(f)) # exact value of the binary float
> > > 6004799503160661/18014398509481984
> > > >>> nsimplify(f) # probably the value that the float was intended to 
> have
> > > 1/3
> > >
> > Thanks Oscar for that incredibly fast reply, but I'm not super keen on
> > algebra that is only probably correct!
>
> Agreed but that means that you need to avoid creating floats in the
> first place. Many users find it awkward to do this and prefer to use
> nsimplify.
>
> Another option is to call S with a string::
>
> In [27]: s = '1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m +
> 3/2)/(2*(2*m + 1)*(2*m + 2))'
>
> In [28]: print(S(s))
> x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1
>
> --
> Oscar
>

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Re: [sympy] Easy way to use S()

[Oscar Benjamin]

On Mon, 3 Jul 2023 at 00:16, David Bailey  wrote:
>
> On 02/07/2023 23:44, Oscar Benjamin wrote:
> > On Sun, 2 Jul 2023 at 23:06, David Bailey  wrote:
> >> Dear Group,
> >>
> >> If I want to enter m+1/2, I define m as a symbol and write:
> >>
> >>m+S(1)/2.
> >>
> >> However if I have a complicated expression with lots of fractions, such as:
> >>
> >> 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m + 1)*(2*m + 
> >> 2))
> >>
> >> it would be much neater if I could automatically wrap all the integers
> >> in S so that no floating point numbers get introduced.
> >>
> >> Is that feasible? I did try wrapping the whole expression in S, but that
> >> does not work.
> > You can wrap the whole expression in nsimplify:
> >
> >   >>> e = 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m
> > + 1)*(2*m + 2))
> >   >>> print(e)
> >   x**2*(m + 0.5)*(m + 1.5)/((2*m + 2)*(4*m + 2)) + x*(m + 0.5)/(2*m + 1) + 1
> >   >>> print(nsimplify(e))
> >   x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1
> >
> > The nsimplify function will attempt to guess what rational number a
> > float represents. In your example this is easy because all floats are
> > exactly represented in binary (having only twos in the denominator)
> > but otherwise the conversion can be inexact:
> >
> >   >>> f = 1/3
> >   >>> f
> >   0.
> >   >>> print(Rational(f))  # exact value of the binary float
> >   6004799503160661/18014398509481984
> >   >>> nsimplify(f)  # probably the value that the float was intended to have
> >   1/3
> >
> Thanks Oscar for that incredibly fast reply, but I'm not super keen on
> algebra that is only probably correct!

Agreed but that means that you need to avoid creating floats in the
first place. Many users find it awkward to do this and prefer to use
nsimplify.

Another option is to call S with a string::

In [27]: s = '1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m +
3/2)/(2*(2*m + 1)*(2*m + 2))'

In [28]: print(S(s))
x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1

--
Oscar

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Re: [sympy] Easy way to use S()

[David Bailey]

On 02/07/2023 23:44, Oscar Benjamin wrote:

On Sun, 2 Jul 2023 at 23:06, David Bailey  wrote:

Dear Group,

If I want to enter m+1/2, I define m as a symbol and write:

   m+S(1)/2.

However if I have a complicated expression with lots of fractions, such as:

1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m + 1)*(2*m + 2))

it would be much neater if I could automatically wrap all the integers
in S so that no floating point numbers get introduced.

Is that feasible? I did try wrapping the whole expression in S, but that
does not work.

You can wrap the whole expression in nsimplify:

  >>> e = 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m
+ 1)*(2*m + 2))
  >>> print(e)
  x**2*(m + 0.5)*(m + 1.5)/((2*m + 2)*(4*m + 2)) + x*(m + 0.5)/(2*m + 1) + 1
  >>> print(nsimplify(e))
  x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1

The nsimplify function will attempt to guess what rational number a
float represents. In your example this is easy because all floats are
exactly represented in binary (having only twos in the denominator)
but otherwise the conversion can be inexact:

  >>> f = 1/3
  >>> f
  0.
  >>> print(Rational(f))  # exact value of the binary float
  6004799503160661/18014398509481984
  >>> nsimplify(f)  # probably the value that the float was intended to have
  1/3

Thanks Oscar for that incredibly fast reply, but I'm not super keen on 
algebra that is only probably correct!


David

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Re: [sympy] Easy way to use S()

[Oscar Benjamin]

On Sun, 2 Jul 2023 at 23:06, David Bailey  wrote:
>
> Dear Group,
>
> If I want to enter m+1/2, I define m as a symbol and write:
>
>   m+S(1)/2.
>
> However if I have a complicated expression with lots of fractions, such as:
>
> 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m + 1)*(2*m + 2))
>
> it would be much neater if I could automatically wrap all the integers
> in S so that no floating point numbers get introduced.
>
> Is that feasible? I did try wrapping the whole expression in S, but that
> does not work.

You can wrap the whole expression in nsimplify:

 >>> e = 1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m
+ 1)*(2*m + 2))
 >>> print(e)
 x**2*(m + 0.5)*(m + 1.5)/((2*m + 2)*(4*m + 2)) + x*(m + 0.5)/(2*m + 1) + 1
 >>> print(nsimplify(e))
 x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1

The nsimplify function will attempt to guess what rational number a
float represents. In your example this is easy because all floats are
exactly represented in binary (having only twos in the denominator)
but otherwise the conversion can be inexact:

 >>> f = 1/3
 >>> f
 0.
 >>> print(Rational(f))  # exact value of the binary float
 6004799503160661/18014398509481984
 >>> nsimplify(f)  # probably the value that the float was intended to have
 1/3

https://docs.sympy.org/latest/modules/simplify/simplify.html#sympy.simplify.simplify.nsimplify

I normally use sympy through the command line isympy interface which
is a wrapper around ipython that provides an environment automatically
set up for using sympy. I don't use this myself but isympy has a -i
flag to interpret integer literals as sympy Integers (and therefore
integer division as rational division):

 $ isympy -i
 ...
 In [1]: 1/3
 Out[1]: 1/3

 In [2]: print(1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m +
3/2)/(2*(2*m + 1)*(2*m + 2)))
 x**2*(m + 1/2)*(m + 3/2)/((2*m + 2)*(4*m + 2)) + x*(m + 1/2)/(2*m + 1) + 1

I think that previous versions of SymPy Live would reinterpret 1/3 as
rational division in a similar way but that does not seem to be true
of the current version (maybe that was missed in the move to pyodide):

https://live.sympy.org/

--
Oscar

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[sympy] Easy way to use S()

[David Bailey]

Dear Group,

If I want to enter m+1/2, I define m as a symbol and write:

 m+S(1)/2.

However if I have a complicated expression with lots of fractions, such as:

1 + x*(m + 1/2)/(2*m + 1) + x**2*(m + 1/2)*(m + 3/2)/(2*(2*m + 1)*(2*m + 2))

it would be much neater if I could automatically wrap all the integers 
in S so that no floating point numbers get introduced.


Is that feasible? I did try wrapping the whole expression in S, but that 
does not work.


Best wishes,

David

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