Saalehorizontale

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How can I understand and work the Output...

Asked: Saalehorizontale 35 Product: Maple 2024

January 08 2025

1 0

Hey guys,

I have to solve a bunch of systems of polynomial equations und dome restrictions given by inequalitites. I have 8 variables, 8 equations and and 13 inequalitites. Since the simple solve or SemiAlgebraic command are not able to solve every system I tryd some other ways. Right now I try to bring the set of equations and ineqaulities in a better from or structure using RealTriangulize from the RegularChains library. Later on I want to take those results and use solve or SemiAlgebraic again, hoping, that Maple than finds the solutions and is not calculating for houres without a result. I already know, that you can have diffrent outputs for RealTriangularize (I know list, record, piecewise and zerodimensional, althought the last one is not really helpful). Since I want to go on wirking with the results I need to have them in a form, that I can read of the new equations and inequalities to put them into solve. Often that works totaly fine, but sometimes I get an output I dont understand. I understand what It means but I dont understand why Maple uses that type of output. If you have a look in the attached file you can see what I mean:

$restart; with(RegularChains); eq_5334 := {y*(m*x-m-n+1)+(-x+1)*n-x = 0, (-p+t)*k+p*y-t = 0, (k-x-y)*t-k*p+y = 0, (-x-y+1)*t+(-k+y)*n+x*s = 0, (-x-y+1)*p+m*y^2+x-y = 0, (x^2-x)*m+y*(t-1)-n+1 = 0, -k*n+s*x = 0, m*x*y-p = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; eq_5380 := {(-x-y+1)*p+m*x*y = 0, (-p+t)*k+p*y-t = 0, (k-x-y)*t-k*p+y = 0, (-x-y+1)*t+(-k+y)*n+x*s = 0, (m-1)*y^2+(-x+1)*y-p+x = 0, (x-1)*(m-1)*y-x^2-n+x = 0, m*x^2+(-m-n+1)*x+(-y+1)*n+t*y-1 = 0, -k*n+s*x = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; eq_5382 := {(-x-y+1)*p+m*x*y = 0, y*(m*x-m-n+1)+(-x+1)*n-x = 0, (-p+t)*k+p*y-t = 0, (k-x-y)*t-k*p+y = 0, (-x-y+1)*t+(-k+y)*n+x*s = 0, (-x-y+1)*p+m*y^2+x-y = 0, m*x^2+(-m-n+1)*x+(-y+1)*n+t*y-1 = 0, -k*n+s*x = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; sys := eq_5334; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5334 := RealTriangularize(sys, R, output = piecewise); sys := eq_5380; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5380 := RealTriangularize(sys, R, output = piecewise); sys := eq_5382; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5382 := RealTriangularize(sys, R, output = piecewise); sys := eq_5382; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5382_record := RealTriangularize(sys, R, output = record)$

`Non-fatal error while reading data from kernel.`

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I would like to get results like in dec_5334. I can easily go on working with this kind of form. In dec_5380 you can see a diffrent output. I dont see the point of giving me this output. the second line i basically epmty. and in the first line the solution is broken into peaces. when a certain solution just works under some inequalitites, why dont they put those four inequalities inside of the list in front of it? Is there a workaround for the "normal" output? Or is there a way to read off the lines from this kind of structure, with the open { in front ?

The same problem appears in dec_5382. WHy dont give me a list with to lists of equations and inequalities to show me both solutions?
In the last example dec_5382_record you can see the output when you change the corresponding option in RealTrinagularize. But here I again have the problem that I dont know how to read of the equations and inequalities from the open curly bracket.

If anyone could help me, I would be very glad. Thank yu in advance.

Regards

Felix

Download Output_of_RegularChains.mw

Can I trust the diffrent engines of Poly...

Asked: Saalehorizontale 35 Product: Maple 2024

December 18 2024

1 5

Hey Guys,

I have to solve multiple system of equations under some restrictions given as inequalities. Sometimes solve is not able to find the result in houres so I tryd to break the problem in half. So in the first step I just want to solve my 8 polynomial equations with 8 variables and in a second step I want so take the solutions, bring them together with the set of inequalities and solve it again. Since also some sets of equations are to hard for the simple solve command I got the advice from people of this plattform to try PolynomialSystem with the diffrent engines. However I have the feeling they make misstakes and now Im not sure If I can trust my results.

Attached you can find a file with an example. In the beginning I solve equations and restrictions together and there is a solutions. Then I tryd to solve only the equations with PolynomialSystem and the the four known engines and the eniges traditional and backsolve dont find the solution which as we saw before exist. When a soultions holds under restrictions it should always appear if I omit the restirctions. When I use the enige triade and groebner then the right solution is there.
However in some other cases it feels the other way round.
So to me it looks like no matter which engine I take, I can never 100% trust my results. Did I something wrong? Whats the reason for those mistakes? Furthermore backsolve gives me 7 solutions, but solutions 2 and 7 are the same. I also recognized, that there is a diffrence between putting in the variable vars as a list or a set. What happens, if I dont specify which engine should be used?

I am happy about any advice. Thank you in advance.

Regards

Felix

$restart; equations := {-y*(m-p) = 0, ((-x-y+1)*k+x)*n+s*y-t = 0, (k-x-y)*t-k*p+y = 0, (-m+n+y)*x+m-1 = 0, -(x+y-1)*(p-t)*k+(-x-y+1)*t+x*p = 0, y^2+(-m-1)*y+1+x*(p-1) = 0, (-x-y+1)*t+(-m+1)*x+y*n+m-1 = 0, -k*n+s*x = 0}; restrictions := {0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; vars := indets(equations); evalf(solve(`union`(equations, restrictions), vars)); Sol_w := SolveTools:-PolynomialSystem(equations, vars); Sol_traditional := SolveTools:-PolynomialSystem(equations, vars, engine = traditional); nops([Sol_traditional]); Sol_backsolve := SolveTools:-PolynomialSystem(equations, vars, engine = backsolve); nops([Sol_backsolve]); Sol_triade_1 := SolveTools:-PolynomialSystem(equations, vars, engine = triade); nops([Sol_triade_1]); Sol_groebner := SolveTools:-PolynomialSystem(equations, vars, engine = groebner); nops([Sol_groebner])$

${-y*(m-p) = 0, ((-x-y+1)*k+x)*n+s*y-t = 0, (k-x-y)*t-k*p+y = 0, (-m+n+y)*x+m-1 = 0, -(x+y-1)*(p-t)*k+(-x-y+1)*t+x*p = 0, y^2+(-m-1)*y+1+x*(p-1) = 0, (-x-y+1)*t+(-m+1)*x+y*n+m-1 = 0, -k*n+s*x = 0}$

${k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = 1, m = 1, n = 0, p = 1, s = t, t = t, x = 0, y = 1}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = -(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(2/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(16/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-7/9, m = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, n = (11/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(53/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(55/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(152/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-61/3, p = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, s = -(8/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(40/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(35/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2-(127/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+58/9, t = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(7/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+1/3, x = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+4/3, y = RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)}$

{k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = s, t = s, x = 0, y = 1}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}

${k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}, {k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = t, t = t, x = 0, y = 1}, {k = -(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(2/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(16/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-7/9, m = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, n = (11/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(53/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(55/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(152/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-61/3, p = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, s = -(8/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(40/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(35/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2-(127/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+58/9, t = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(7/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+1/3, x = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+4/3, y = RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}$

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$evalf(allvalues({k = -(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+2*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/9)+16*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/9)+(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-7/9, m = 4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/3)-20*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-17*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, n = 11*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/3)-53*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-55*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+152*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/3)-61/3, p = 4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/3)-20*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-17*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, s = -8*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/9)+40*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/9)+35*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/9)-127*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/9)+58/9, t = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-8*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+7*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/3)+1/3, x = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-8*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/3)+4/3, y = RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)}))$

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Can_I_trust_the_diffrent_eniges_of_Polynomial_Systems.mw

Why do I get this error when solving a u...

Asked: Saalehorizontale 35 Product: Maple 2024

December 08 2024

0 4

Hey guys,

in the attached file you can see my problem. Since Maple was not able to calculate my set with 8 equations, 8 variables and 13 inequalities I had to split in into two steps. Here you can see how I try to take one solutions of what I got with solve onto 8 equations with 8 variables and to solve this together with my inequalities. It never was a problem before. So ow I get a weird error I dont understand.

$restart; inequalities := {0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(p-1)*s, 0 < (m*y-1)*n+(m*x-m+1)*(1-p), 0 < (m*x-m-s+1)*p+m*y*(s-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; solve(`union`({k = (x*(1-sqrt(x))+sqrt(x)-2*x)/((x^2-3*x+1)*x), m = (sqrt(x)+x)/(x-1), n = (sqrt(x)+x)/(x-1), p = (-1-sqrt(x))/(x-1), s = (-1-sqrt(x))/(x-1), t = (2*x*(1-sqrt(x))+1+sqrt(x)-5*x)/(x^2-3*x+1), y = 1-sqrt(x)}, inequalities)); inequalities := {0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(p-1)*s, 0 < (m*y-1)*n+(m*x-m+1)*(1-p), 0 < (m*x-m-s+1)*p+m*y*(s-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}$

Error, (in unknown) invalid input: SolveTools:-Inequality expects its 1st argument, eqns, to be of type {list, set}({`<`, `<=`, `=`}), but received [p < 1, -p < 0, And(2*argument((p-1)/p) <= Pi,-Pi < 2*argument((p-1)/p))]

>	$restart; solve(`union`({k = (x(1-sqrt(x))+sqrt(x)-2x)/((x^2-3x+1)x), m = (sqrt(x)+x)/(x-1), n = (sqrt(x)+x)/(x-1), p = (-1-sqrt(x))/(x-1), s = (-1-sqrt(x))/(x-1), t = (2x(1-sqrt(x))+1+sqrt(x)-5x)/(x^2-3x+1), y = 1-sqrt(x)}, {0 < x, 0 < y}))$

${k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), 3/2+(1/2)*5^(1/2) < p}, {k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), 1 < p, p < 3/2+(1/2)*5^(1/2)}, {k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), 1/2 < p, p < (1/2)*5^(1/2)-1/2}, {k = p^3/(p^3-2*p+1), m = -p+1, n = -p+1, s = p, t = (3*p-2)*p/(p^2+p-1), x = (p^2-2*p+1)/p^2, y = 1-((p^2-2*p+1)/p^2)^(1/2), p < 1, (1/2)*5^(1/2)-1/2 < p}$

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>	$restart; solve(`union`({k = (x(1-sqrt(x))+sqrt(x)-2x)/((x^2-3x+1)x), m = (sqrt(x)+x)/(x-1), n = (sqrt(x)+x)/(x-1), p = (-1-sqrt(x))/(x-1), s = (-1-sqrt(x))/(x-1), t = (2x(1-sqrt(x))+1+sqrt(x)-5x)/(x^2-3x+1), y = 1-sqrt(x)}, {0 < s, 0 < x, 0 < y}))$

Error, (in unknown) invalid input: SolveTools:-Inequality expects its 1st argument, eqns, to be of type {list, set}({`<`, `<=`, `=`}), but received [-p < 0, And(2*argument((p-1)/p) <= Pi,-Pi < 2*argument((p-1)/p))]

So my question is why does this error occur? And what does it mean? the "but received..." argument in the error makes no sense to me. Why does it happen when I add 0<s but 0<x,0<y is okay?

Thank you in advance

Download Why_this_error.mw

How to make solving of system of polynom...

Asked: Saalehorizontale 35 Product: Maple 2024

December 04 2024

2 0

Hey guys,

I am working with Maple 2024. I have to solve many systems of polynomial equations symbolically. I have 8 equations, 8 variables and 14 inequalities (which also implies that I only want real solutions). In my opinion the equations are not too difficult. However there is a maximum of up to 4 variables multiplied together which could be a problem. Since I have to solve thousand of those systems I need to reduce the amount of time needed. While many of the systmes only take a few seconds, there are a few systems (10%) that need way to much time (multiple houres, sometimes I stop the process before the computation is over).

In my attached file you can see the kind of equations I have. While "equations_500 union inequalities" only needs a few seconds, "equations_1162 union inequalities" needs more than 2 houres (than I stopped).
I also tryed a second approach. At first I just solved the 8 equations. Then I took every solution, combined it with the set of inequalities and solved it again. Not only does it not work for equations_1162 eather, but it also sometimes brings the warning "solutions may have been lost" which is not really convincing. For that process I also used "with(RealDomain) since I only want to find real solutions when solving the eight equations in the first step.

I figured out, that for the normal and simpel solve command it cqn help to rename the variables so the lexigraphic order as the initial situation playes a role. But when I understood the pages explaining SolveTools or Groebner, this optimal order of the variables is completed automatically inside these environments.

So my question is: Is there any way to accelerate the process (in this case for equations_1162)? Waiting some minutes isfine, but I cant wait houres for one solution.

Thank you in advance.

solve_system_of_polynomials_with_inequalities.mw

problems with solve - disjoint sets of s...

Asked: Saalehorizontale 35 Product: Maple 2024

October 15 2024

1 2

Download problems_with_solve_15.10.24.mw

Hey guys,

I'm working with Maple to solve sets of 8 equations and 14 inequalities. I use the command solve to get values for my 8 variables. Often there is no solution, sometimes we have one single solution or like a parametric solution. However sometimes this procedure fails to finish the calculation, that means I stop the calculation after a certain time (multiple houres). So now I am looking for some other ways to get the solution. For example I try a two-stage solve-attemp. In the first round I use the solve coammand only for the set of 8 equations. In the second round I take each of the solutions I found in the step before and combine them with the set of inequalities. Then I use solve again for this set.

However I found out that the two ways I described above lead to diffrent solutions. In my opinion the solutions of solve(equations union inequalities) should be a subset of solve(equations), since all the solutions we find with equations union inequalities has to fullfill the 8 equations we want put into solve(equations). As you can see in the attached file that is not the case. The sets of solutions of solve(equalities union inequalites) and the set of solutions of solve(equalities) is disjoint, so no subset.
Since I have disjoint sets in the step between, the solutions of solve(equations union inequalities) and the solutions of solve((solve equations) union inequalities) are disjoint as well, so I think the problem is already in the step before.

I would be really glad if anyone can help me. Either explain me, where my argumentation above went wrong or why I find those solutions which dont fit together.

Regards
Felix

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