Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello!

 

When I use simplify((t-1)/(-1+2*t)) it returns the same thing I entered, how come Maple doesn't return the actual simplified version that is (1/2)-(1/(2*(2*t-1))), even when using expand, it doesn't return anything really that good.

 

Do anyone know a good idea to get the desired result via Maple? Thank you. 

I am stumped with this trivial puzzle.  Let
z := arctan(x/sqrt(a^2-x^2));
                    
How do we simplify z to.

I tried all sorts of tricks with simplify(...) and convert(...), with assumptions, but did not get anywhere.  Any clues?

Versions: Maple 2016 and 2017.

I was trying to answer a question by torabi 25, August 14, 2017 to speed up his calculations. I got this idea of converting the original code to a procedure - that was not easy, run the procedure and obtain a value of time() to establish a baseline, and making sure the answer from the procedure was the same as from torabi 25. So far so good. Then I would compile the procedure, execute it, and get another value for time(). Hopefully the compiled procedure will be faster than the uncompiled procedure. I am close, but - please see if you can fix my compiler error. Thanks!


 

restart

pa := proc (k::integer, h::float, N::float, nu::float, E_m::float, E_c::float, rho_m::float, rho_c::float, d::(Matrix()))::float; local lambda_m::float, lambda_c::float, mu_m::float, mu_c::float, Z::float, U::float, S::float, e2::float, f::float, W::float, z::float, b::integer, alpha::integer, beta::integer; lambda_m := nu*E_m/((1+nu)*(1-2*nu)); lambda_c := nu*E_c/((1+nu)*(1-2*nu)); mu_m := E_m/(2+2*nu); mu_c := E_c/(2+2*nu); Z := rho_m+(rho_c-rho_m)*(1/2+z/h)^N; U := lambda_m+(lambda_c-lambda_m)*(1/2+z/h)^N; S := mu_m+(mu_c-mu_m)*(1/2+z/h)^N; e2 := 0.; for alpha from 0 to k-2 do for b from 0 to k-2 do for beta from 0 to k-1 do f := 2*S*d[beta+1, alpha+1]*W(beta)*sqrt(alpha+1/2)*orthopoly:-P(alpha, z)*d[2, b+1]*sqrt(b+1/2)*orthopoly:-P(b, z); e2 := e2-(int(f, z = -(1/2)*h .. (1/2)*h)) end do end do end do end proc

NULL

k := 6; h := 1.; N := .5; nu := .3; E_m := 7.0*10^10; E_c := 3.80*10^11; rho_m := 2702.; rho_c := 3800.; d := Matrix([evalf([0, 0, 0, 0, 0, 0, 0, 0]), evalf([sqrt(3), 0, 0, 0, 0, 0, 0, 0]), evalf([0, sqrt(15), 0, 0, 0, 0, 0, 0]), evalf([sqrt(7), 0, sqrt(35), 0, 0, 0, 0, 0]), evalf([0, sqrt(27), 0, sqrt(63), 0, 0, 0, 0]), evalf([sqrt(11), 0, sqrt(55), 0, sqrt(99), 0, 0, 0]), evalf([0, sqrt(39), 0, sqrt(91), 0, sqrt(143), 0, 0]), evalf([sqrt(15), 0, sqrt(75), 0, sqrt(135), 0, sqrt(195), 0])], datatype = float[8])

time(pa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d))

2.156

(1)

pa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d)

-0.3192307695e12*W(1)+0.4396880666e12*W(3)-0.1474586302e12*W(5)-0.9235575679e11*W(2)+0.1979090107e12*W(4)

(2)

# Original Answer:        -3.192307692*10^11*W(1)+4.396880662*10^11*W(3)-1.474586301*10^11*W(5)-9.235575669*10^10*W(2)+1.979090105*10^11*W(4);NULL

cpa := Compiler:-Compile(pa)

Error, (in Compiler:-Compile) Array parameter types must specify a hardware datatype

 

time(cpa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d))

0.

(3)

cpa(k, h, N, nu, E_m, E_c, rho_m, rho_c, d)

NULL


 

Download for_(5).mw

 

Is there a routine available to derive the variable (i.e for any given z) for the standard normal loss function, L(z)?

If we know the value of L(z), how can z be determined?

There seems to be a bug with indefinite integration:

integrate(cos(t)*exp(-x*t),t=-infinity..infinity)

gives

0

Substituting any number for x, or assuming x >= 0  (or x<=0) does give the correct result,

The problem also persists when assuming x>-1 (or x>-Maple_floats(MIN_FLOAT))

mathcontainerUses_Doubt.mw
 

restart; d[1] := [2.36, 26.90], [2.75, 30.0], [3.14, 31.9], [3.53, 32.8], [3.93, 33.4], [4.32, 32.8], [4.71, 31.9]

[2.36, 26.90], [2.75, 30.0], [3.14, 31.9], [3.53, 32.8], [3.93, 33.4], [4.32, 32.8], [4.71, 31.9]

(1)

NULL

d[2] := [2.36, 32.40], [2.75, 34.90], [3.14, 36.90], [3.53, 38.00], [3.93, 38.40], [4.32, 37.8], [4.71, 36.5]

[2.36, 32.40], [2.75, 34.90], [3.14, 36.90], [3.53, 38.00], [3.93, 38.40], [4.32, 37.8], [4.71, 36.5]

(2)

d[3] := [2.36, 27.9], [2.75, 28.3], [3.14, 30.0], [3.53, 30.9], [3.93, 31.3], [4.32, 30.8], [4.71, 29.7]

[2.36, 27.9], [2.75, 28.3], [3.14, 30.0], [3.53, 30.9], [3.93, 31.3], [4.32, 30.8], [4.71, 29.7]

(3)

y := a*x^2+b*x+c; for i to 3 do d[i] := [d[i]]; c[i] := CurveFitting[LeastSquares](d[i], x, curve = y) end do

HFloat(8.047886108501745)+HFloat(11.793324911833839)*x-HFloat(1.5172878997894277)*x^2

(4)

 

curve1 := [c[1], c[2]]; k[1] := [1, 2]; curve1p := [d[1], d[2]]; l[1] := "plot 1"

"plot 1"

(5)

curve2 := [c[2], c[3]]; k[2] := [2, 3]; curve2p := [d[2], d[3]]; l[2] := "plot 2"

"plot 2"

(6)

curve3 := [c[1], c[3]]; k[3] := [1, 3]; curve3p := [d[1], d[3]]; l[3] := "plot 3"

"plot 3"

(7)
Table 1

 

xlabel := "Brake Power"; ylabel := "Efficiency"

"Efficiency"

(8)

p1 := plot(curve1, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve1p, style = point, color = [black], symbol = [soliddiamond, box], symbolsize = 10); plots:-display(p1, p2)

 

p1 := plot(curve2, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve2p, style = point, color = [black], symbol = [box, point], symbolsize = 10); plots:-display(p1, p2)

 

p1 := plot(curve3, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve3p, style = point, color = [black], symbol = [soliddiamond, point], symbolsize = 10); plots:-display(p1, p2)

 

 

"for j from 1 to 3 do  print( Report on l[j]); for i in k[j] do x1(i):=solve((&DifferentialD;)/(&DifferentialD; x)c[i]);  y1(i):=eval( c[i], [x = x1(i)]):  print( Maximum brake thermal efficiency of,y1(i) "%"occurs at brake power value of , x1(i)kW);  end do;  end do;"

Maximum*brake*thermal*efficiency*of, HFloat(30.964188366461613)*"%"*occurs*at*brake*power*value*of, 3.886317459*kW

(9)

NULL


 

Download mathcontainerUses_Doubt.mw

Can any one state the uses of mathcontainer?

1. It can store only one algebraic expression at a time?

2. Can it handle list of algebraic expressions?

3. Can it store list data points (x,y) for a list of curves?

4. Can there be any use for click to edit this component?

More than a simple Yes or No a simple example for each yes answer would be very helpful.

I enclose a document with list of coordinates for for three curves, expression for curve fitting, three expressions derived for these plot points (coordinates), a command for optimum y for each of the three curves (maximum y and corresponding x value), 

Thanks for answering.

Ramakrishnan V

Hey there. 

I recently had to install maple 2017, because the licensens for 2016 had expired. 

And in the new version, whenever i want to copy a matrix from a result, it gives me an _rtable, and a number. The result is the same, but it makes it harder to read and i am not able to edit values in this copied matrix. 

How do i change this?

I have an two arrays of elements Op1[i,j] with -5 <= i,j <= 5 and Op2[i,j] with 5<=i,j<= 35 . When I use surfdata like

surfdata({0p1,Op2})

it produces a plot with both the range of Op1 and Op2 between 0 and 1 (see Fig1).

I tried surfdata({0p1,Op2},-5..35,-5..35) but this only gave the range of the figure from -5 to 35, -5 to 35 but with both plots scaled so that they cover the whole range(see Fig2).

How do i make surfdata use different ranges on the same plot for both arrays?

Please can someone help with maple comand to obtain Jacobian elliptic functions particularly in code editing region?

I have an excel data file where data are in floating points of different decimals. I have made the following command which worked once. Second time it gives an error stating that one argumnet is expected, but receives three. How do I solve this problem. I want the data to be imported to data table in two decimal formats.

Export_TO_Maple1.xlsxExport_TO_Maple2.xlsxDOUBT.mw

M1 := Import(evalf[2]("E:/A_PhD2017/Export_TO_Maple1.xlsx", "Sheet1", "A2:U8"));

Is it possible to compare two maple files, given that there are small changes between them?

in the steps below, it is not fluent to do, and appear diff(1,t)

KineticEnergy := 1/2*m*diff(x(t), t)^2;
PotentialEnergy := subs(x=x(t),int((1/R^2)^2,x));
Action := KineticEnergy - PotentialEnergy;
AA := diff(Action,x(t)) - diff(diff(Action, diff(x(t),t)),t) = 0 <-------- Dsolve this
AA := eval(subs(diff(1,t)=0,diff(Action,x(t))) - Diff(subs(p=Diff(x(t),t),diff(subs(Diff(x(t),t)=p, Action), p)),t)) = 0
dsolve(AA, x(t));
 

Where R is constant

The following image shows a .mw file on two monitors (1 = right side) (2 = left side).  

Distortion occurs when I try to drag-and-drop an open file from monitor 1 to monitor 2.  Transfer from one monitor to another works fine on all other applications (.pdf, .docx, web stuff, graphic files like .png, and .xlsx.  Only .mw files distort when I try to open them or move them to monitor 2.  I was able to move, open, etc. any .mw file for over a year, then a couple of days ago the files started to distort.  I had a 32-bit version of Maple (Maple 2015.2 build ID 1097895—deleted it.  Also deleted and reinstalled Maple 2015.0, build 1022128.  I checked and updated my video card, updated the 2-monitor settings on Windows 7.  All this to no avail, the Maple 2015.0 program works on monitor 1, but it can not be opened or dragged-and-dropped to monitor 2.

Help, advice, suggestions welcomed—many thanks in advance.

Les

 

Hello.

 

I have been trying to create a code to solve a structure by using FEM, but I keep getting an error that stops me from moving on.

 

Everytime I run my code, Maple gives me the error in the Title of my question:
"Error, number of indices exceeds rank"

 

Unfortunately I can't find any help in Maplesoft support for such error, and I need immediate help for that.

Can someone help me with that? Should I post my entire code?

Thanks!

Hi everyone, 

I often get the error 'cannot save points as a float matrix' while I'm trying to plot with the spacecurve command.

loodl2 is a 4 component vector, loodl2c is the 3 component variant.

loodl2:=T1.<loodl,1>: loodl2c:=<loodl2[1], loodl2[2], loodl2[3]>
loodlpl:=spacecurve(loodl2c, k=-10..10, color=red):

also with this syntax:
loodl2c:=loodl2[1..3]

and this syntax:

l2c1:= 2*k: l2c2:=0, l2c3:=8-k:
spacecurve([l2c1, l2c2, l2c3], k=-10..10, color=red):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

It will only plot if I do this:
loodl2c:=<2*k, 0, 8-k>
Can someone help me?
 

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