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Maple should try harder...

Asked by: vv 14072
complex max rootof
February 08 2018
1  13
> 

restart;
> 

f:=5*x^3-5*x+1;

5*x^3-5*x+1

 (1)
> 

s:=[solve(f)]; evalf(%);  # All the roots are real

[(1/30)*(-2700+(300*I)*219^(1/2))^(1/3)+10/(-2700+(300*I)*219^(1/2))^(1/3), -(1/60)*(-2700+(300*I)*219^(1/2))^(1/3)-5/(-2700+(300*I)*219^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/30)*(-2700+(300*I)*219^(1/2))^(1/3)-10/(-2700+(300*I)*219^(1/2))^(1/3)), -(1/60)*(-2700+(300*I)*219^(1/2))^(1/3)-5/(-2700+(300*I)*219^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/30)*(-2700+(300*I)*219^(1/2))^(1/3)-10/(-2700+(300*I)*219^(1/2))^(1/3))]

  

[.8788850663-0.2e-9*I, -1.088033915-0.2598076212e-9*I, .2091488484+0.2598076212e-9*I]

 (2)
> 

max(s);  # ?

Error, (in simpl/max) complex argument to max/min: (1/30)*(-2700+(300*I)*219^(1/2))^(1/3)+10/(-2700+(300*I)*219^(1/2))^(1/3)

  
> 

type(s,list(realcons)); # Wrong, the type realcons should not be purely syntactic; or is it?

false

 (3)
> 

R:=convert(s,RootOf):
> 

max(R);  #  For nested RootOfs fails

Error, (in simpl/max) complex argument to max/min: (1/30)*RootOf(_Z^3+2700-300*RootOf(_Z^2+1, index = 1)*RootOf(_Z^2-73, index = 1)*RootOf(_Z^2-3, index = 1), index = 1)+10/RootOf(_Z^3+2700-300*RootOf(_Z^2+1, index = 1)*RootOf(_Z^2-73, index = 1)*RootOf(_Z^2-3, index = 1), index = 1)

  
> 

sort(s): evalf(%);  # Wrong

[.8788850663-0.2e-9*I, .2091488484+0.2598076212e-9*I, -1.088033915-0.2598076212e-9*I]

 (4)

 

Workaround

 

> 

S:=[seq(RootOf(f,x,index=i),i=1..3)];

[RootOf(5*_Z^3-5*_Z+1, index = 1), RootOf(5*_Z^3-5*_Z+1, index = 2), RootOf(5*_Z^3-5*_Z+1, index = 3)]

 (5)
> 

evalf(S);

[.2091488484, .8788850662, -1.088033915]

 (6)
> 

min(S);max(S);  # OK

RootOf(5*_Z^3-5*_Z+1, index = 3)

  

RootOf(5*_Z^3-5*_Z+1, index = 2)

 (7)
> 

sort(S);   # Wrong!

[RootOf(5*_Z^3-5*_Z+1, index = 1), RootOf(5*_Z^3-5*_Z+1, index = 2), RootOf(5*_Z^3-5*_Z+1, index = 3)]

 (8)
> 

################################
> 

r:=(sqrt(2)+I)^3 + (sqrt(2)-I)^3;

(2^(1/2)+I)^3+(2^(1/2)-I)^3

 (9)
> 

type(r,realcons);  # Purely syntactic?

false

 (10)
> 

type(expand(r),realcons);

true

 (11)
> 

max(r,13);  # Even for such a simple expression?

Error, (in simpl/max) complex argument to max/min: (2^(1/2)+I)^3+(2^(1/2)-I)^3

  
> 

 


Download TryHarder.mw

How to find a local extrema of a function?...

Asked by: Aaeru Michi 45
extrema
February 08 2018
2  7

So I've got a function and try to find an extrema (and there is one on the plot), but Maple gives me empty brackets.

First, earlier it gave me 2 x-coordinates with extrema (both empty), but now (after reloading) it gives one and empty.

Second, how do I set an interval, if I want to look for extrema from x=0 to x=1, for example? I tried extrema (V, {0,1}, x) and (V, {x=0, x=1}, x), but nothing seems to work.

2.mw

Grid:-Server doesn't work...

Asked by: mmcdara 7896
grid
February 08 2018
0  7

Hi everybody,

I use the Grid package to do intensive computations.

For some reason I'm ignorant about, the test case described in the Grid[Server][StartServer] 

 help page doesn't work with Maple 2015 (neither on Mac OS X, neither on Windows 7 ; here is the mw file run on MAC Os X)

Could someone explain me why (probably something I did not read with enough attention ... some license maybe) ?
Thanks in advance

GridServer.mw

Do I have enough propane for the winter?

by: AndrewG 195 Maple
propane
February 07 2018
6  3

Just a simple little worksheet to see if I have enough propane to heat my house for the rest of the winter.


 

Do I have enough propane for the winter?

NULL

I've taken some measurements from my propane tank throughout the winter.  Now we can use Maple to see if we have enough to last the rest of the winter.

``

a := [["nov 27, 2017", 73.5], ["dec 9, 2017", 72], ["dec 16, 2017", 69], ["dec 31, 2017", 62], ["jan 12, 2018", 60], ["jan 19, 2018", 56], ["jan 26, 2018", 54], ["feb 4,2018", 51]]

[["nov 27, 2017", 73.5], ["dec 9, 2017", 72], ["dec 16, 2017", 69], ["dec 31, 2017", 62], ["jan 12, 2018", 60], ["jan 19, 2018", 56], ["jan 26, 2018", 54], ["feb 4,2018", 51]]

 (1)

with(Finance)  ``

pts := [seq([DayCount(a[1, 1], a[i, 1]), a[i, 2]], i = 1 .. nops(a))]

[[0, 73.5], [12, 72], [19, 69], [34, 62], [46, 60], [53, 56], [60, 54], [69, 51]]

 (2)

with(plots)

listplot(pts)

  

Adding a 30% and 20% level to the graph.  We probably shouldn't be too worried about the cold in June so DayCount("Nov 27, 2017", "Jun 1, 2018") = 186 we'll extend these reference lines out to 186.

plot({pts, [[0, 20], [186, 20]], [[0, 30], [186, 30]]}, view = [default, 0 .. 80])

  

 

30% is the recommended level your propane company wants you to fill up at.  The technician who installed the tank said 20% is all right.  It's up to you if you want to go to 10% but if you run out of propane the company has to come in and do a leak test on your system which is an added cost you don't want.  So let's predict at what point we need to start worrying about filling up our propane tank.  To do that, of course, all we need is a forecast line.  For that we'll just calculate a best fit.

 

a1 := [seq(DayCount(a[1, 1], a[i, 1]), i = 1 .. nops(a))]

[0, 12, 19, 34, 46, 53, 60, 69]

 (3)

a2 := a[() .. (), 2]

[73.5, 72, 69, 62, 60, 56, 54, 51]

 (4)

X := convert(a1, Vector)

Y := convert(a2, Vector)

with(Statistics)

L1 := LinearFit([1, x], X, Y, x)

HFloat(74.79237702730747)-HFloat(0.34416046490941915)*x

 (5)

Plotting it all together

plot({L1, pts, [[0, 20], [186, 20]], [[0, 30], [186, 30]]}, x = 0 .. 200, y = 0 .. 80, labels = ["Days", ""], tickmarks = [default, [seq(10*i = cat(10*i, "%"), i = 1 .. 8)]])

  

Projecting the line to 30% we get

solve(L1 = 30)

130.1496877

 (6)

AdvanceDate(a[1, 1], trunc(solve(L1 = 30)))

Record(monthDay = 6, month = 4, year = 2018, format = "%B %e, %Y", ModulePrint = proc (m) Finance:-FormatDate(m) end proc)

 (7)

April is still a bit chilly so maybe if we wait until 20%, of course it's getting warmer all this time so our usage should go down.  

AdvanceDate(a[1, 1], trunc(solve(L1 = 20)))

Record(monthDay = 5, month = (), year = 2018, format = "%B %e, %Y", ModulePrint = proc (m) Finance:-FormatDate(m) end proc)

 (8)

It isn't warm enough to turn off the furnace yet but it looks like we'll have enough to get us into the warm months

AdvanceDate(a[1, 1], trunc(solve(L1 = 10)))

Record(monthDay = 3, month = 6, year = 2018, format = "%B %e, %Y", ModulePrint = proc (m) Finance:-FormatDate(m) end proc)

 (9)

We'll hit 10% well into late spring and almost right into summer of course it's a rough estimate however it looks like we won't have to fill up during the high price winter season.  I can tell my wife to relax, we should have enough propane for the winter.

 

 

NULL


 

Download Propane_usage-.mw

calculate sum w2(x,y)...

Asked by: assma 75
February 07 2018
0  7

I need to calculate sum w2(x,y),

v2 := proc (x, y) options operator, arrow; sin(x)*cos(y) end proc;
u2 := proc (x, y) options operator, arrow; 3*sin(x)-cos(y) end proc;
w2 := proc (x, y) options operator, arrow; diff(v2(x, y), x)-(diff(u2(x, y), y)) end proc;
L1 := proc (x, y) option inline; abs(w2(x, y)) end proc; CodeTools:-Usage(evalhf(add(add(abs(w2(x, y)), x = 0 .. 10), y = 0 .. 10)));
Error, (in CodeTools:-Usage) unable to evaluate built-in function `diff` in evalhf

 but it is error , how  can be rewritten properly?

 

Find the intesection of two lines...

Asked by: Richard Poor 15
rootfinding homework plotting
February 07 2018
0  1

I created the following plot

plot([BesselJ(0, x), BesselJ(1, x)], x = 0 .. 10, color = [red, blue]);
 

What I want to do mext is calculate all x values on this interval wherethe two paths intersect

 Calculate all x values on this interval where

About LinearAlgebra "Add"command...

Asked by: qilianshan 65
February 07 2018
1  1

I have a question as this：

Examples as following：(come from MAPLE‘s help ) 
with(LinearAlgebra);
Ax := <1.00004, 1.99987, -0.12e-3>;
b := <1., 2., 0.>;
Add(Ax, b, 1, -1);

result is this：[0.400000000000400e-4, -0.129999999999963e-3, -0.120000000000000e-3]'

I think result is :[0.400000000000400e-4, -0.13e-3, -0.120000000000000e-3]' 

Is this a bug of MAPLE?



 

How to convert Pi to a numerical answer....

Asked by: Richard Poor 15
February 07 2018
1  3

I am trying to solve the function


f :=  sqrt(1-x2)
L := int(sqrt(1+(diff(f(x), x))2), x = 0 .. 5)

Maple is returning an answer with Pi:  (1/2)*Pi+I*ln(5+2*sqrt(6))

How do I convert this into a numerical format?  

 

Time consuming integration...

Asked by: maple2015 145
February 07 2018
0  2

 

Dear Friends
Is there a way to solve a complicated integration in less possible time?

Thanks

_________________________________________________________________________________
 

restart;
Digits := 100:
tm := time():
with(LinearAlgebra):

m := 6:
a := 0.1:
b := 10*a:
E := 1:
h := 1:
nu := 0.3:

w := (r-b)^2*(r-a)^2*add(add(W[n, i]*r^n*t^(i-n), n = 0 .. i), i = 0 .. m):
ur := -z*(diff(w, r)):
ut := -z*(diff(w, t))/r:
er := diff(ur, r)+(1/2)*(diff(w, r))^2:
et := ur/r+(diff(ut, t))/r+(diff(w, t))^2/(2*r^2):
grt := diff(ut, r)-ut/r+(diff(ur, t))/r+(diff(diff(w, t), r))/r:
u := -(1/2)*E*(2*er*et*nu+er^2+et^2)/(nu^2-1)+(1/2)*E*grt^2/(2*(1+nu)):

PI := int(int(int(u*r, z = -(1/2)*h .. (1/2)*h), t = 0 .. 2*Pi), r = a .. b)-0.5*P*(int(int(r*(diff(w, r))^2, r = a .. b), t = 0 .. 2*Pi)):

Time = time()-tm;

Batch File for Window run Maple Input File ...

Asked by: panke 145
windows script batch
February 07 2018
1  1

I am looking for a window bat file to run my maple input file.mw

all roots of a function...

Asked by: mahdi1625 10
rootfinding
February 06 2018
0  3

How can I find all roots of sin(sqrt(x)) as the search interval is not constant and depens on x for this function?

3D globe for Maple?...

Asked by: Rouben Rostamian 8586
February 06 2018
2  11

Is there a 3D globe available for Maple?  Specifically, a globe depicting the Earth's continents and oceans, that can be grabbed and rotated with the mouse like any other 3D Maple plot?

Why can't I solve for a variable?...

Asked by: exality 45
solve
February 06 2018
2  5

I can't believe I've just spent a half hour trying to do the simplest thing:

The second example is copied straight out of Tutorial 2.  I'm doing just what the tutorial says: right-click, Solve, Solve for Variable.  I've tried disabling everything in my startup profile, recalculating, restarting, etc.  Why in the world can't I do this simple thing?

Solve_for_variable.mw

arctan(a(x),b(x)) = arctan(a(x)/b(x) as long as x...

Asked by: Frederik160400 5
February 06 2018
1  8

Is it possible that the two-variable arctan function arctan(a(x),b(x)) could be could be equal to arctan(a(x)/b(x)) as long as x>0? And why?

arctan(a(x),b(x))=arctan(a(x)/b(x) as long as x>0 ?

Thank's for any replies :)

Plotting from a Matrix...

Asked by: mela 20
matrix fsolve plotting
February 06 2018
0  3

Hi,

Please I would like to find out if it is possible to plot from a matrix, for example

1) Plot the first and second rows of a matrix, where y-axis is the first row and x-axis is the second row

2) Plot a 3-D diagram using,e.g., first, second and third rows from a matrix. Or

3) Plot the first row of the matrix on the y-axis and then let the x-axis be a time period (e.g. quarters 1, 2, 3, 4).

I attached my Maple file which is solved using FSOLVE. I would like to (i) plot variable A and parameter T  And (ii) plot variables A and F against parameter T in a 3-D form. 

Your help is highly appreciated.

 

Regards,

 

Mela

 

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