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Min is bigger than max???...

Sotto 60 Maple 2022
optimization minimize
September 05 2024
3 3

Hello

in this example Untitled.mw Maple 2022 on MacOs  'finds' a minimum bigger than the maximum.

It looks like something is wrong...

Best Nicola

minimize a polynomial function...

Sotto 60 Maple 2022
minimize
July 24 2024
2 4

Dear all,

I am trying to minimize this polynomial function G on [0,1]x[0,1]:

Maple 2022 seems unable to find the (approximate) minimum. Even adding _EnvExplicit:=true, as suggested here on a previous post, does not fix the issue.

Any suggestion?

Thanks, Nicola

> 

restart:
> 

_EnvExplicit:=true:
> 

G := (x, y) -> ((-1)*38.87*y^4 + 39.7800000000000*y^3 + (-1)*6.76000000000000*y^2 + 10.4000000000000*y - 3.90000000000000)*x^4 + (39.78*y^4 + (-1)*40.4600000000000*y^3 + 6.80000000000000*y^2 + (-1)*10.2000000000000*y + 3.40000000000000)*x^3 + ((-1)*6.76*y^4 + 6.80000000000000*y^3 + (-1)*1.12000000000000*y^2 + 1.60000000000000*y - 0.400000000000000)*x^2 + (10.4*y^4 + (-1)*10.2000000000000*y^3 + 1.60000000000000*y^2 + (-1)*2.00000000000000*y)*x + 1. + (-1)*3.9*y^4 + (-1)*0.4*y^2 + 3.4*y^3

proc (x, y) options operator, arrow; (-38.87*y^4+39.7800000000000*y^3-6.76000000000000*y^2+10.4000000000000*y-3.90000000000000)*x^4+(39.78*y^4-40.4600000000000*y^3+6.80000000000000*y^2-10.2000000000000*y+3.40000000000000)*x^3+(-6.76*y^4+6.80000000000000*y^3-1.12000000000000*y^2+1.60000000000000*y-.400000000000000)*x^2+(10.4*y^4-10.2000000000000*y^3+1.60000000000000*y^2-2.00000000000000*y)*x+1.-3.9*y^4-.4*y^2+3.4*y^3 end proc

 (1)
> 

minimize(G(x,y),x=0..1,y=0..1)
 

NULL

Download Untitled.mw

Explore a surface...

Sotto 60 Maple 2022
explore plotting
July 15 2024
0 1

Dear all,

I'd like to explore graphically a polynomial surface depending on two parameters a and b.

The problem is that, as soon as I start playing with the sliders, Maple freezes and I have to 'force quit'.

Can you please tell me if you have the same problem with this example?

Thanks.

> 

restart:
> 

with(plots):
> 

K := 1 - y*x - (1 - x)*(b*x^3 + a*x^2 + x + 1)*(1 - y)*(b*y^3 + a*y^2 + y + 1)

1-y*x-(1-x)*(b*x^3+a*x^2+x+1)*(1-y)*(b*y^3+a*y^2+y+1)

 (1)
> 

Explore(plot3d(K, x=0..1, y=0..1,  font= [Times, bold, 20], labels= ['x', 'y','z'],   labelfont= [Times, bold, 40],  title = "K(x,y)"), b = 0..1., a=0..1.);
 

 

Download Explore.mw

Error with minimize/maximize...

Sotto 60 Maple 2022
minimize
July 13 2024
1 7

Dear all,

I have this polynomial function

G(x, y) := (-0.14*y^3 + 1.20000000000000*y^2 - 1.26000000000000*y + 0.200000000000000)*x^3 + (1.20*y^3 - 10.0800000000000*y^2 + 10.0800000000000*y - 1.20000000000000)*x^2 + (-8.82*y + 10.08*y^2 - 1.26*y^3)*x + 1. - 1.2*y^2 + 0.2*y^3

I don't understand why the command

minimize(G(x,y),x=0..1,y=0..1);

produces the error

Error, (in RootOf/RootOf:-algnum_in_range) invalid input: RootOf/RootOf:-rootof_in_range expects its 1st argument, rt, to be of type ('RootOf')(polynom(rational,_Z),identical(index) = posint), but received RootOf(7*_Z^3-93*_Z^2+327*_Z-187)

Thanks for your advices, Nicola

Double integrals...

Sotto 60 Maple 2022
integration syntax numeric
July 11 2024
2 2

Dear all

I have a function like 

F[1] := (x, y) -> x*y/(1 + 10.35841093*(1 - x)*((-1)*0.9*x + 1)*(1 - y)*((-1)*0.9*y + 1))

This function is continuous on D = [0,1]x[0,1]. I'm interested in the (approximate) value of the double integral over D.

Unfortunately the entry

int(int(F[1](x,y),x=0..1.),y=0..1.)

produces Float(infinity). 

Thanks Nicola

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