Hi Jeremy, many thanks for the scipy link. I will experiment with it.
Rainer Am Dienstag, 16. August 2022, 06:03:16 CEST schrieb Jeremy Monat: > SymPy cannot (currently) reduce for multiple variables. As the draft guide > page > <https://output.circle-artifacts.com/output/job/99b313eb-c111-406f-81e3-22dc > f5d7c9fa/artifacts/0/doc/_build/html/guides/solving/solve-system-of-inequali > ties-algebraically.html> mentions, to reduce for more than one symbol, try > SciPy’s linprog() > <https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linpro > g.html#scipy.optimize.linprog>. (If there is no solution, obviously no > function will find one.) > > Jeremy > > On Mon, Aug 15, 2022 at 10:48 PM Chris Smith <smi...@gmail.com> wrote: > > 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 m...@bokomoko.de 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 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-a9 > >> 6 > >> > >> > > 9 > >> > >> 709f9293/artifacts/0/doc/_build/html/guides/solving/solve-system-of-inequ > >> a > >> > >> > > 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 > >> > > > >> > > > > "sympy" group. > >> > > > > To unsubscribe from this group and stop receiving emails from it, > >> > >> send > >> > >> > > an > >> > > > >> > > > > email to sympy+un...@googlegroups.com. > >> > > > > To view this discussion on the web visit > >> > > > > https://groups.google.com/d/msgid/sympy/4120287.OZXsGyJSKq%40h370 > >> > > > > . > >> > >> -- > >> 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 sympy+unsubscr...@googlegroups.com. > > To view this discussion on the web visit > > https://groups.google.com/d/msgid/sympy/6f40ebd5-46f0-4bd9-b5d4-1e703ff1db > > f2n%40googlegroups.com > > <https://groups.google.com/d/msgid/sympy/6f40ebd5-46f0-4bd9-b5d4-1e703ff1 > > dbf2n%40googlegroups.com?utm_medium=email&utm_source=footer> . -- Rainer Dorsch http://bokomoko.de/ -- You received this message because you are subscribed to the Google Groups "sympy" group. 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