Hi Chris,
many thanks for the link to the stack overflow answer and in particular the PR
and also the elegant suggestion on how to address the problem with linear
programming.
I realized that I oversimplified the example though:
The problem I want to solve is a vector equation:
f_vec+a*x_vec+b*y_vec+n*s_vec=sh_vec+c*xsh_vec+d*ysh_vec
and I am looking for a solution with
0<=a,b,c,d<=1
I.e. there is more than one equation which need to be satisfied for the same x
and y:
print(sympy.solvers.inequalities.reduce_rational_inequalities([[x*5 + y*2
+z*3=5,x*2-y-z>5,x <= 1, x >= 0, y <= 1, y >= 0,z <= 1, z >= 0]], [x,y,z]))
I see no obvious way to apply your method to a set of multiple equations, but
it might due to my lack of experience with linear programming.
Thanks again
Rainer
Am Mittwoch, 10. August 2022, 23:03:29 CEST schrieb Chris Smith:
> You can't enter your expressions with `=` to create and Equality. You would
> have to reenter as Eq(5*x+2*y,10) or
> `parse_expr('5*x+2*y=10',transformations=T[1,9]')` (see
> [here](https://stackoverflow.com/a/73307040/1089161)).
>
> Past that, there is no SymPy function that will solve this, but in
> PR https://github.com/sympy/sympy/pull/22389 I added code today that will
> do so.
>
> Your equality will be treated like a function to maximize under the
>
> constrains that x<=1 and y<=1 (and both are nonnegative):
> >>> func = 5*x+2*y-10
> >>> cond = [x<=1, y<=1]
> >>> LP(func, cond, [x,y])[:2]
>
> (-3, {x: 1, y: 1})
>
> So that function has a maximum value of -3 when x and y are 1. Now negate
> the function and repeat
>
> >>> LP(-func, cond, [x,y])[:2]
>
> (10, {x: 0, y: 0})
>
> The max of the negated function is 10 when x and y are 0. So the min of the
> function is -10. You are interested in the case when the function is 0.
> Since the function is linear and has as bounds [-10, -3] which does not
> contain 0, it seems to me that this proves there is no solution.
>
> /c
>
> On Tuesday, August 9, 2022 at 10:46:55 AM UTC-5 m...@bokomoko.de wrote:
> > Hi Jeremy,
> >
> > thanks for sharing your link and thanks for compiling the documentation.
> > And
> > indeed it helped, with the information I could easily fix it:
> >
> > rd@h370:~/tmp.nobackup$ cat test-sympy.py
> > import sympy
> >
> > x, y, z = sympy.symbols('x y z')
> > sympy.init_printing(use_unicode=True)
> >
> > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2 >
> > 0]],
> > x))
> >
> >
> > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2 >
> > 0,x <
> > 5]], x))
> > rd@h370:~/tmp.nobackup$ python3 test-sympy.py
> > (-2 < x) & (x < oo)
> > (-2 < x) & (x < 5)
> > rd@h370:~/tmp.nobackup$
> >
> > I read through your page and posted some feedback at
> >
> > https://github.com/sympy/sympy/pull/23768
> >
> > My real problem is somewhat more complex though:
> >
> > I want to find out if
> >
> > f_vec+a*x_vec+b*y_vec+n*s_vec=sh_vec+c*xsh_vec+d*ysh_vec
> >
> > has a solution with
> >
> > 0<=a,b,c,d<=1
> >
> > All quantities with _vec are 3 dimensional vectors. I want to to find out
> > if
> > for a given set of vectors a solution exists or not.
> >
> > Extending my testcase in this direction does not work though:
> >
> > rd@h370:~/tmp.nobackup$ cat test-sympy.py
> > import sympy
> >
> > x, y, z = sympy.symbols('x y z')
> > sympy.init_printing(use_unicode=True)
> >
> > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2 >
> > 0]],
> > x))
> >
> > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x*5 + y*2
> > =
> > 10,x <= 1, x >= 0, y <= 1, y >= 0]], x))
> > rd@h370:~/tmp.nobackup$ python3 test-sympy.py
> > File "/home/rd/tmp.nobackup/test-sympy.py", line 9
> > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x*5 + y*2
> > = 10,x <= 1, x >= 0, y <= 1, y >= 0]], x))
> > ^
> > SyntaxError: invalid syntax
> > rd@h370:~/tmp.nobackup$
> >
> > I suspect that reduce_rational_inequalities is the wrong approach here,
> > but
> > what would the the right functions to use?
> >
> > Any hint is welcome :-)
> >
> > Many thanks
> > Rainer
> >
> > PS: Also thanks for hint towards less-verbose function calls. I typically
> > write it verbose, since I am not writing Python code too frequently, and
> > for
> > me the verbose version is something like a documentation, since I see
> > where
> > the functions come from.
> >
> > Am Samstag, 6. August 2022, 17:19:45 CEST schrieb Jeremy Monat:
> > > Hi Ranier,
> > >
> > > Here's a way to do it:
> > > >>> import sympy
> > > >>> x, y, z = sympy.symbols('x y z')
> > > >>> sympy.solvers.inequalities.reduce_inequalities([x + 2 > 0, x < 5],
> > > >>> x)
> > >
> > > (-2 < x) & (x < 5)
> > >
> > > reduce_inequalities is the top-level inequality reducer, which will call
> > > other lower-level functions (such as reduce_rational_inequalities) as
> > > needed. reduce_inequalities takes a simple list, rather than a nested
> >
> > list,
> >
> > > of inequalities.
> > >
> > > I'm actually drafting a guide page on this topic now; glad to know it's
> >
> > of
> >
> > > interest! You can access the draft
> > > <
> >
> > https://output.circle-artifacts.com/output/job/a1f8297d-6be8-4627-9f47-a96
> > 9
> >
> > 709f9293/artifacts/0/doc/_build/html/guides/solving/solve-system-of-inequa
> > li>
> > > ties-algebraically.html>, and I'd appreciate any feedback (either here
> >
> > or on
> >
> > > the pull request <https://github.com/sympy/sympy/pull/23768> on GitHub).
> > >
> > > Best,
> > > Jeremy
> > >
> > > P.S. If you like, you can use less-verbose function calls by importing
> > >
> > > reduce_inequalities and symbols from SymPy:
> > > >>> from sympy import reduce_inequalities, symbols
> > > >>> x, y, z = symbols('x y z')
> > > >>> reduce_inequalities([x + 2 > 0, x < 5], x)
> > >
> > > (-2 < x) & (x < 5)
> > >
> > > On Sat, Aug 6, 2022 at 3:31 AM 'Rainer Dorsch' via sympy <
> > >
> > > sy...@googlegroups.com> wrote:
> > > > Hi,
> > > >
> > > > I just started with sympy, and try to understand how to tell sympy,
> >
> > what I
> >
> > > > want. I tried
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2
> > > > >
> > > > 0],[x
> > > > < 5]], x))
> > > > and expected
> > > > (-2 < x) & (x < 5)
> > > > but got
> > > > (-oo < x) & (x < oo)
> > > > Can anybody tell how I can tell sympy that x should satisfy both
> > > > inequalities
> > > > the same time?
> > > > For me it seems sympy rather interprets the set of equations rather as
> >
> > an
> >
> > > > "or"
> > > > and not an "and"
> > > >
> > > > Here is the full example
> > > >
> > > > rd@h370:~/tmp.nobackup$ cat test-sympy.py
> > > > import sympy
> > > >
> > > > x, y, z = sympy.symbols('x y z')
> > > > sympy.init_printing(use_unicode=True)
> > > >
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2
> > > > >
> > > > 0]],
> > > > x))
> > > >
> > > >
> > > > print(sympy.solvers.inequalities.reduce_rational_inequalities([[x + 2
> > > > >
> > > > 0],[x
> > > > < 5]], x))
> > > > rd@h370:~/tmp.nobackup$ python3 test-sympy.py
> > > > (-2 < x) & (x < oo)
> > > > (-oo < x) & (x < oo)
> > > > rd@h370:~/tmp.nobackup$
> > > >
> > > >
> > > > Any hint is welcome.
> > > >
> > > > Thanks
> > > > Rainer
> > > >
> > > >
> > > > --
> > > > Rainer Dorsch
> > > > http://bokomoko.de/
> > > >
> > > >
> > > > --
> > > > You received this message because you are subscribed to the Google
> >
> > Groups
> >
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> >
> > > > email to sympy+un...@googlegroups.com.
> > > > To view this discussion on the web visit
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--
Rainer Dorsch
http://bokomoko.de/
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