Ignore your equality `5*x + 2*y+3*z=5` and see if a solution exists for the
condition you specify:
>>> LP(
... x*2-y-z-5,[x <= 1, y <= 1,z <= 1,x>0,y>0,z>0],[x,y,z])
(-3, {x: 1, y: 0, z: 0}, _y0 + _y1 + _y2 - 5, [_y0 - _y3 - 2 >= 0, _y1 -
_y4 + 1 >= 0, _y2 - _y5 + 1 >= 0], {_y0: 2, _y1: 0, _y2: 0, _y3: 0, _y4: 0,
_y5: 0})
The maximum that 2*x - y - z - 5 can be is -3 but you want it to be greater
than 0. So there is no solution, is there?
/c
On Monday, August 15, 2022 at 3:30:43 AM UTC-5 [email protected] wrote:
> 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 [email protected] 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 <
> > > >
> > > > [email protected]> 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
> > >
> > > > > "sympy" group.
> > > > > To unsubscribe from this group and stop receiving emails from it,
> send
> > >
> > > an
> > >
> > > > > email to [email protected].
> > > > > To view this discussion on the web visit
> > > > > https://groups.google.com/d/msgid/sympy/4120287.OZXsGyJSKq%40h370.
>
>
> --
> Rainer Dorsch
> http://bokomoko.de/
>
>
>
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