Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

Hello MaplePrimes, 

So, I have used the discont=true option in the past and it has worked fine for me but for some reason with these functions I am using now the plots are still containing the veritcal asymptotes. Anyone spot something I am forgetting or doing incorrectly?

I have attached my maple file for easy viewing. 

Thanks. 

DiscontQuestion.mw

 

See A342180 in OEIS. Two codes have been written for this, one in Python (17 terms found), the other in Mathematica (33 terms). Could a Maple code go beyond a(33), assuming higher terms exist? 

This question may be a little dumb, but how can I calculate the resultant of two homogeneous polynomials with two variables according to these variables? Say resultant(f,g,{x,y}), where f(x,y) and g(x,y) are homogeneous polynomials with degree m and n, respectively. Any help would be greatly appreciated!

RootOfQuestion.mw

Hi Everyone, so i understand (to the best of my knowledge) the purpose of RootOf and I have worked with them before but now for some reason when i try to use allvalues to express the solution explicitly it does not express it, instead just keeps as RootOf expression. 

I have attached the maple file I am working with. 

I have also tried solve(expr, explicit) as well as convert(expr, radical) and still nothing. 

Am I missing something small? 

here is my try

for ploting points of data ( d(n(, sum(n))

new.mw

Here is my try to integrate the expression L with trapozoid or simpson 

numerical_int.mw

I am trying to solve this type of problem:

I thought I could double check my answers by creating a RandomVariable and calculating the probablity using the Probability function.

But from the RandomVariables documentation,  it seems only univariate random variables are supported.

Is there really no way to define a RandomVariable given a joint distribution?

Requesting a procedure to calculate primes p for which there exists a prime q <= p such that pi(p)=q-pi(q), where pi is the prime counting function. If possible options to select output as p, or as (p,q).

p list starts:2,13,17,29,31,43.....

q list starts: 2,11,13,17,19,23...

Thanks in advance,

David.

The input

f(x) := x^2;

n := evalf(int(f(x)^2, x = 0 .. 1));

f(x) :=  f(x)/n;

plot(f(x), x = 0 .. 1)

leads to the error

Error, (in f) too many levels of recursion
I need to reassign the function as itself divided by n that depends on the old f...

A piece of code like this is supposed to be inside a loop, so creating f_new(x):=f(x)/n doesn't solve the issue.

If it was a cpp code I'd write something like f(x)/=n for every x. How can I do it in Maple?

Thank you in advance for you answers!

I have two functions, f(x) and g(x).

Based the plot, I can see that they intersect around x equals 0, 1, around 4.5 and 10.

So I tried to find the numerical solution by solving f(x) -  g(x) for x assuming x is real.

I'm stuck here because the aswer involves RootOf and _Z and I don't know what to do next.

This is what I've tried so far:
 

``

``

"f(x):=18*log10(x)"

proc (x) options operator, arrow; 18*log10(x) end proc

(1)

"g(x):=1/(2) x^(3)-8*x^(2)+(69/(2))^()*x-27"

proc (x) options operator, arrow; (1/2)*x^3-8*x^2+(69/2)*x-27 end proc

(2)

plot([f(x), g(x)], x = -1 .. 11)

 

``

`assuming`([solve(f(x)-g(x), x)], [x::real])

exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z))

(3)

allvalues(exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z)))

exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, 1.505446443)), exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, -3.291052648)), exp(RootOf(-(exp(_Z))^3*ln(10)+16*(exp(_Z))^2*ln(10)-69*exp(_Z)*ln(10)+54*ln(10)+36*_Z, 2.302585093)), 1

(4)

``

``


 

Download intersect_curve.mw

 

I know there's an answer to this because I can get the expected answer from Wolfram Alpha (see here).

How can I accomplish this in Maple? 

Hi friends!

I have the following problem.

I'm trying to generate a matrix given a certain lenght n and a polynomial g(x) of degree r as follows:

If n=10, g(x)=x^4+3x^3+x^2+2x+1 and r=degree(g(x))=4, then the resulting matrix will be

 

 

 

 

 

i.e. a matrix with 10 columns, n-r=6 lines, and whose inputs are the coefficients of the polynomial, as follows:

Any help will be very appreciated.

Thank you!

Hi,

I have questions about linestyle in maple, how to change solid and Dash whatever  to line with cross or line with plus 

Please see a plot attached.

Look forward to hearing from you as soon as possible.

Regards,

Mathastr

plots.pdf

Hello Everyone,

I have an equation system which is under-determined and thus yields infinite solutions. 
These usually come in the form of "_t1[1]" or similar variables. Mostly one, sometimes even two.
I am also working on a script for automated solving of a buckling problem and the solution yields of course these t-variables.
Everytime the code run, I get a different t-variable, which makes automation harder.

Please see attached code. (Of course simplified, not my actual code.)

It starts with a random matrix and a solution vector for the equation system.
The system is solved and its coefficients transfered to an equation.
However every time I hit "Enter" on the LinearSolve command, the name of the _t4[1] variable changes.

Is there a way to keep getting the same variable name? How do you work with this?

Best Regards,
Lennart

A := Matrix(4, 4, {(1, 1) = 1, (1, 2) = 3, (1, 3) = 4.5, (1, 4) = 7, (2, 1) = 0, (2, 2) = 2, (2, 3) = 5, (2, 4) = 9, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0}); B := Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0}); C := LinearAlgebra[LinearSolve](A, B)

Vector[column](%id = 18446746248681490062)

(1)

W1 := C[1]; W2 := C[2]; W3 := C[3]; W4 := C[4]; Q := W1*x^4+W2*x^3+W3*x^2+W1

(HFloat(3.0)*_t4[2]+HFloat(6.5)*_t4[1])*x^4+(-HFloat(2.5)*_t4[2]-HFloat(4.5)*_t4[1])*x^3+_t4[2]*x^2+HFloat(3.0)*_t4[2]+HFloat(6.5)*_t4[1]

(2)

restart

``


 

Download MultipleTCoefficients.mw

Hello Everyone,

I am currently trying to tidy up my worksheet and hide all of the script/code that I wrote in the Maple 2D-Math within the execution script of buttons etc.
Was going well so far until I started transferring code where I was using a lot of symbolic math (if I understood correctly)
There is one instance where I have a variable chi which equals x divided by a.
a being a number, e.g. 5000, while x is and remains a variable.
No problem in 2D-Math as the unknown x is dragged through all following equations.

Not so in the code editor, I think. Doing the calculation results not in x/5000, but in this:


It keeps getting worse because this term will be derived, assembled into a matrix, etc. where the expressions are getting ridiculous:


Without getting into the details of what my script should do, I believe this is a very general issue, not specific to my code.

Is the code editor / "Code when Used/Clicked" not capable of symbolic math? Oder is there some setting that could potentially help me?

Best Regards,
Lennart
 

Hello Everyone,

Me Again... So I have been working do create a procedure, but I started the coding without encasing it in the proc() / end proc; brackets, thinking I could add it later.
What the script does is take parameters and create a matrix and determines the determinant of that matrix.
When I let the script run on its own, it is working perfectly, but when I activate the proc() / end proc; brackets it suddenly gives me a number of errors, telling me the matrix is not square or that the if-loop misses its 2nd argument.

I am kind of suspecting this happens because I take the variable "NumberPlies" from a Table that exists outside the proc(), but on the same work sheet, but I am not 100% sure.
I have uploaded the code, so one of you experts could perhaps have a look and tell me where I am wrong. Why is the script behaving differently on its own compared to when I call it as a procedure?

Any help would be fantastic!

Best Regards,
Lennart
 

Download Test_GetDet_MaplePrimes.mw
 

Maple*des*zur*Berechnung*Beulverhaltens*Composite*Programm*symmetrischer-LEVY*Platten*nach
Anzahl Lagen des Laminates (Ohne Mittellage, eine Seite der Symmetrie):


Lastfall-Definition:

Maple*des*zur*Berechnung*Beulverhaltens*Composite*Programm*symmetrischer-LEVY*Platten*nach

(1)

 

restart; interface(warnlevel = 0); with(DocumentTools); with(LinearAlgebra); with(DocumentTools); with(LinearAlgebra); E1 := 125000; E2 := 10000; v12 := .3; G12 := 5000; t := .25; v21 := E2*v12/E1; Q11 := E1/(-v12*v21+1); Q22 := E2/(-v12*v21+1); Q12 := v21*E1/(-v12*v21+1); Q66 := G12; NumberPlies := GetProperty('ComboBox1', 'selectedindex'); A11 := 0; A12 := 0; A16 := 0; A21 := 0; A22 := 0; A26 := 0; A61 := 0; A62 := 0; A66 := 0; B11 := 0; B12 := 0; B16 := 0; B21 := 0; B22 := 0; B26 := 0; B61 := 0; B62 := 0; B66 := 0; D11 := 0; D12 := 0; D16 := 0; D21 := 0; D22 := 0; D26 := 0; D61 := 0; D62 := 0; D66 := 0; for i to NumberPlies do CurrentAngle := PlyTable1[i, 1]; CurrentHeight := t*i; CurrentHeight := CurrentHeight-.5*t*NumberPlies; CurrentAngleRad := (1/180)*Pi*CurrentAngle; CurrentQMatrix := Matrix(3, 3, {(1, 1) = Q11, (1, 2) = Q12, (1, 3) = 0, (2, 1) = Q12, (2, 2) = Q22, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Q66}); TurnMatrix := Matrix(3, 3, {(1, 1) = cos(CurrentAngleRad)^2, (1, 2) = sin(CurrentAngleRad)^2, (1, 3) = -2*cos(CurrentAngleRad)*sin(CurrentAngleRad), (2, 1) = sin(CurrentAngleRad)^2, (2, 2) = cos(CurrentAngleRad)^2, (2, 3) = 2*cos(CurrentAngleRad)*sin(CurrentAngleRad), (3, 1) = -2*cos(CurrentAngleRad)*sin(CurrentAngleRad), (3, 2) = 2*cos(CurrentAngleRad)*sin(CurrentAngleRad), (3, 3) = cos(CurrentAngleRad)^2-sin(CurrentAngleRad)^2}); CurrentQMatrixTurned := Multiply(TurnMatrix, Multiply(CurrentQMatrix, Transpose(TurnMatrix))); Q_11 := CurrentQMatrixTurned[1, 1]; Q_12 := CurrentQMatrixTurned[1, 2]; Q_16 := CurrentQMatrixTurned[1, 3]; Q_21 := CurrentQMatrixTurned[2, 1]; Q_22 := CurrentQMatrixTurned[2, 2]; Q_26 := CurrentQMatrixTurned[2, 3]; Q_61 := CurrentQMatrixTurned[3, 1]; Q_62 := CurrentQMatrixTurned[3, 2]; Q_66 := CurrentQMatrixTurned[3, 3]; A11 := A11+Q_11*(CurrentHeight-CurrentHeight+t); A12 := A12+Q_12*(CurrentHeight-CurrentHeight+t); A16 := A16+Q_16*(CurrentHeight-CurrentHeight+t); A21 := A21+Q_21*(CurrentHeight-CurrentHeight+t); A22 := A22+Q_22*(CurrentHeight-CurrentHeight+t); A26 := A26+Q_26*(CurrentHeight-CurrentHeight+t); A61 := A61+Q_61*(CurrentHeight-CurrentHeight+t); A62 := A62+Q_62*(CurrentHeight-CurrentHeight+t); A66 := A66+Q_66*(CurrentHeight-CurrentHeight+t); B11 := B11+.5*Q_11*(CurrentHeight^2-(CurrentHeight-t)^2); B12 := B12+.5*Q_12*(CurrentHeight^2-(CurrentHeight-t)^2); B16 := B16+.5*Q_16*(CurrentHeight^2-(CurrentHeight-t)^2); B21 := B21+.5*Q_21*(CurrentHeight^2-(CurrentHeight-t)^2); B22 := B22+.5*Q_22*(CurrentHeight^2-(CurrentHeight-t)^2); B26 := B26+.5*Q_26*(CurrentHeight^2-(CurrentHeight-t)^2); B61 := B61+.5*Q_61*(CurrentHeight^2-(CurrentHeight-t)^2); B62 := B62+.5*Q_62*(CurrentHeight^2-(CurrentHeight-t)^2); B66 := B66+.5*Q_66*(CurrentHeight^2-(CurrentHeight-t)^2); D11 := D11+(1/3)*Q_11*(CurrentHeight^3-(CurrentHeight-t)^3); D12 := D12+(1/3)*Q_12*(CurrentHeight^3-(CurrentHeight-t)^3); D16 := D16+(1/3)*Q_16*(CurrentHeight^3-(CurrentHeight-t)^3); D21 := D21+(1/3)*Q_21*(CurrentHeight^3-(CurrentHeight-t)^3); D22 := D22+(1/3)*Q_22*(CurrentHeight^3-(CurrentHeight-t)^3); D26 := D26+(1/3)*Q_26*(CurrentHeight^3-(CurrentHeight-t)^3); D61 := D61+(1/3)*Q_61*(CurrentHeight^3-(CurrentHeight-t)^3); D62 := D62+(1/3)*Q_62*(CurrentHeight^3-(CurrentHeight-t)^3); D66 := D66+(1/3)*Q_66*(CurrentHeight^3-(CurrentHeight-t)^3) end do; A = (Matrix(3, 3, {(1, 1) = A11, (1, 2) = A12, (1, 3) = A16, (2, 1) = A21, (2, 2) = A22, (2, 3) = A26, (3, 1) = A61, (3, 2) = A62, (3, 3) = A66})); B = (Matrix(3, 3, {(1, 1) = B11, (1, 2) = B12, (1, 3) = B16, (2, 1) = B21, (2, 2) = B22, (2, 3) = B26, (3, 1) = B61, (3, 2) = B62, (3, 3) = B66})); D = (Matrix(3, 3, {(1, 1) = D11, (1, 2) = D12, (1, 3) = D16, (2, 1) = D21, (2, 2) = D22, (2, 3) = D26, (3, 1) = D61, (3, 2) = D62, (3, 3) = D66})); Nx := 200; Ny := 0; Nxy := 0; a := 500; b := 500; m := 1; chi := x/a; eta := y/b; alpha := a/b; alphaD := a*(D22/D11)^(1/4)/b; betaM := m*Pi/alphaD; betaD := (D12+2*D66)/sqrt(D11*D22); etaD := D12/sqrt(D11*D22); nyD := etaD/betaD; kx := Nx*b^2/(Pi^2*sqrt(D11*D22)); ky := Ny*b^2/(Pi^2*D22); kxy := Nxy*b^2/(Pi^2*(D11*D22^3)^(1/4)); Omega := betaD^2-1+kx*(alphaD/m)^2; if kx > (m/alphaD)^2 then lambda1 := m*Pi*sqrt(betaD+sqrt(Omega))/alphaD; lambda3 := m*Pi*sqrt(sqrt(Omega)-betaD)/alphaD; GenFunc := W1*cosh(lambda1*eta)+W2*sinh(lambda1*eta)+W3*cos(lambda3*eta)+W4*sin(lambda3*eta); Status := 1 elif kx < (m/alphaD)^2*(-betaD^2+1) then omegaklein := sqrt(.5*(sqrt(betaD^2-Omega)+betaD)); phi := sqrt(.5*(sqrt(betaD^2-Omega)-betaD)); GenFunc := W1*cosh(omegaklein*eta)*cos(phi*eta)+W2*sinh(omegaklein*eta)*cos(phi*eta)+W3*cosh(omegaklein*eta)*sin(phi*eta)+W4*sinh(omegaklein*eta)*sin(phi*eta); Status := 5 elif (m/alphaD)^2 > kx then if kx > (m/alphaD)^2*(-betaD^2+1) then lambda1 := m*Pi*sqrt(betaD+sqrt(Omega))/alphaD; lambda3 := m*Pi*sqrt(sqrt(Omega)-betaD)/alphaD; GenFunc := W1*cosh(lambda1*eta)+W2*sinh(lambda1*eta)+W3*cosh(lambda3*eta)+W4*sinh(lambda3*eta); Status := 3 end if end if; y := 0; EQ1 := GenFunc = 0; unassign('y'); GenFunc; EQHelp := diff(GenFunc, `$`(y, 1)); y := 0; EQ2 := EQHelp = 0; unassign('y')*GenFunc; y := b; EQ3 := GenFunc = 0; unassign('y'); GenFunc; EQHelp2 := diff(GenFunc, `$`(y, 1)); y := b; EQ4 := EQHelp2 = 0; unassign('y'); Test := GenerateMatrix({EQ1, EQ2, EQ3, EQ4}, {W1, W2, W3, W4}); Determinant(Test[1]); return Determinant(Test[1])

HFloat(-0.2442128895120277)

(2)

GetDet

GetDet

(3)

GetDet()

Error, (in LinearAlgebra:-Determinant) matrix must be square

 

``


 

Download Test_GetDet_MaplePrimes.mw

 

Test_GetDet_MaplePrimes.mw

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