MaplePrimes Questions

When I try to get a higher resolution plot using numpoints, the lines are jagged and look lower resolution.

plot(sin(x),x=-10..10,numpoints=3000,resolution=10000)plot(sin(x),x=-10..10,numpoints=400,resolution=10000)

 

You can see the difference, the first does not look anti-aliased whil ethe second does(although the 2nd looks far better on my comp)

A way to define a N *N matrix with the help of loop 

with(inttrans):
sinc := x->piecewise(x = 0, 1, sin(Pi*x)/x/Pi):
S := x->sinc(x):
SE := x->sinc(x)*exp(-x^2):
plot(abs(fourier(SE(x),x,s)),s=0..5)

 

works fine for S but when trying to plot SE I get

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

 

I simply want to plot the fourier transform of a function so I can see it's frequency response. Maple seems to be breaking for more complex functions. It seems to be doing this when it can't evaluate the function exactly, which I don't care for plots.

 

Hi

Let s_n be the number of ternary strings (of 0s, 1s and 2s) of length n that have no
adjacent even digits.
For example, s_0 = 1 (the empty string),
s1 = 3 (the strings 0, 1 and 2),

while s2 = 5:  01; 10; 11; 12; 21;

We can compute by hand  Find s3; and we obtain 11
My question how can use maple to get a general recurrence relation for s_n. 

many think for your help

Give the following functions find Domain, Range, Possible Asymptotes, Intercepts, Critical Points, Intervals of Increase, Decrease, Relative and Absolute Extrema, and Concavity.

A) f(x)=x(x^2-6x+8)

B) f(x) =x^3/4 -3x

After two days of trying to take the Jacobian of a multi-variable mapping in Maple, I'm still finding no way. Here is an example of what I mean by "multi-variable mapping":

(x,y) -> x^2-y^2

Every AP high-school student knows how to take the partial derivatives of that, but Maple's "Jacobian" feature doesn't work on mappings. It only works on expressions.

So I spent today trying to leverage off the "D" feature, only to find it rendered useless by bugs: https://mapleprimes.com/questions/227007-How-To-Take-Partial-Derivative-Of-A-Mapping

It took me less than two days to do it in Mathematica, by way of comparison.

On the website, they show a photo of a man elated to be doing math in Maple, but that's not how it's gone for me. I'm cursing outloud, and my blood pressure is high. I'm angry that I lost money on a product that can't take the Jacobian of a mapping, and I'm angry that I lost two days of my life doing tedious debugging while paying money instead of getting paid for my work.

Maple pays math PhD's to release a commercial CAS that can't take the Jacobian of a mapping. So much for the value of a PhD.

I need to find the intersection of 3 planes.

x+3*y-5*z=0
x+4*y-8*z=0
-2*x-7*y+13*z=0

I managed to get the intersection using LinearSolve but I keep getting an error when I try to plot out the planes using plot3d. What can I change in the commands for it to work?
 

with(LinearAlgebra)

[`&x`, Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix, BidiagonalForm, BilinearForm, CARE, CharacteristicMatrix, CharacteristicPolynomial, Column, ColumnDimension, ColumnOperation, ColumnSpace, CompanionMatrix, CompressedSparseForm, ConditionNumber, ConstantMatrix, ConstantVector, Copy, CreatePermutation, CrossProduct, DARE, DeleteColumn, DeleteRow, Determinant, Diagonal, DiagonalMatrix, Dimension, Dimensions, DotProduct, EigenConditionNumbers, Eigenvalues, Eigenvectors, Equal, ForwardSubstitute, FrobeniusForm, FromCompressedSparseForm, FromSplitForm, GaussianElimination, GenerateEquations, GenerateMatrix, Generic, GetResultDataType, GetResultShape, GivensRotationMatrix, GramSchmidt, HankelMatrix, HermiteForm, HermitianTranspose, HessenbergForm, HilbertMatrix, HouseholderMatrix, IdentityMatrix, IntersectionBasis, IsDefinite, IsOrthogonal, IsSimilar, IsUnitary, JordanBlockMatrix, JordanForm, KroneckerProduct, LA_Main, LUDecomposition, LeastSquares, LinearSolve, LyapunovSolve, Map, Map2, MatrixAdd, MatrixExponential, MatrixFunction, MatrixInverse, MatrixMatrixMultiply, MatrixNorm, MatrixPower, MatrixScalarMultiply, MatrixVectorMultiply, MinimalPolynomial, Minor, Modular, Multiply, NoUserValue, Norm, Normalize, NullSpace, OuterProductMatrix, Permanent, Pivot, PopovForm, ProjectionMatrix, QRDecomposition, RandomMatrix, RandomVector, Rank, RationalCanonicalForm, ReducedRowEchelonForm, Row, RowDimension, RowOperation, RowSpace, ScalarMatrix, ScalarMultiply, ScalarVector, SchurForm, SingularValues, SmithForm, SplitForm, StronglyConnectedBlocks, SubMatrix, SubVector, SumBasis, SylvesterMatrix, SylvesterSolve, ToeplitzMatrix, Trace, Transpose, TridiagonalForm, UnitVector, VandermondeMatrix, VectorAdd, VectorAngle, VectorMatrixMultiply, VectorNorm, VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip]

(1)

A := `<|>`(`<,>`(1, 1, -2), `<,>`(3, 4, -7), `<,>`(-5, -8, 13))

Matrix(%id = 18446745896624469046)

(2)

b := `<,>`(0, 0, 0)

Vector[column](%id = 18446745896624462294)

(3)

x := LinearSolve(A, b)

Vector[column](%id = 18446745896652349678)

(4)

P1 := x+3*y

P2 := x+4*y

P3 := -2*x-7*y

plot3d([P1, P2, P3], x = -8 .. 8, y = -20 .. 20, plotlist = true, color = [blue, red, green])

Error, (in plot3d) unexpected options: [(Vector(3, {(1) = -4*_t[3], (2) = 3*_t[3], (3) = _t[3]})) = -8 .. 8, y = -20 .. 20]

 

``


 

Download problem.mw

Here's how to break Maple's 'D' function:

~$ cmaple mapleBug.mpl
    |\^/|     Maple 2018 (X86 64 WINDOWS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2018
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> D[1]((x, y) ->x^2-y^2);
                                 (x, y) -> 2 x

> D[2]((x, y) ->x^2-y^2);
                                 (x, y) -> -2 y

> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');
> D[1]((x, y) ->x^2-y^2);
                                  (x, y) -> 0

> D[2]((x, y) ->x^2-y^2);
                                  (x, y) -> 0

> quit
memory used=2.4MB, alloc=8.3MB, time=0.06

~$

What if a person needs to have these lines:

> with(VectorCalculus):
> assume(x, 'real');
> assume(y, 'real');

and then he wants to take partial derivatives? Not possible? Once you load VectorCalculus and declare x and y real, Maple stops doing partial derivatives? Why.

Sorry,

I have been away from Maple for a year.
Then, when I used op command, I am puzzed to notice the results were different from those I know.

>op((x+5)^2*(x+y));
      _EXPSEQ((x+5)^2, x+y)

Result I know is 

        (x+5)^2, x+y

Has a modifire such as _EXPSEQ   automatically come to be attatched?
Or, can I have maple express it  in the form I know:  (x+5)^2, x+y?

Thank you in advance.

taro

 

 

 

 

 


 

A mathematical friend wrote to me recently with the following problem:

a + b + c = 1

a² + b² + c² = 2

a³ + b³ + c³ = 3

Find the values of  a^4 + b^4 + c^4 and a^5 + b^5 + c^5.

Note the question doesn’t ask for the values of a, b and c, but can you find them?

Hi all, I would be most grateful if I could get some help with solving the tasks below using Maple.

Given the function: mx''(t)+cx'(t)+kx(t)= F_y(t)

  1. Rewrite the equation above to a system of 1. order differential equations, by defining the two variables x_1(t) = x(t) and x_2(t)=x'(t) (Hint what is x'(t)?) This gives the first differential equation in the system. What is x_2'(t)?
     
  2. Write the equations as a linear system when the outer force F_y(t) is the influence and the position x_1(t) is the answer, in other words give the system matrix A and the vectors b and r.
     
  3. I'm given the constants m = 5kg, c = 3Ns/m and k = 20 N/m and I'm trying to find the transfer function of the system.
     
  4. Give the systems transfer function H(s) and draw the graphs for the amplitude and phase characteristic.

Thank you!

 

 

I have triangle TAD. Now I want to take any point inside the triagle TAD. How can I take it? I tried
 

restart; 
with(Student:-MultivariateCalculus); 
A := [1, 2, 3]; 
DD := [-2, 1, 0]; 
T := [1/2, 1/2, 3/2]; 
P := Plane(T, A, DD); 
GetRepresentation(P)

I got the quation of the plane TAD is
 

-3*x-3*y+4*z = 3

With the point P(x,y,z). What is the condition of x, y, z?

Given the following functions and respective intervals graph them and determine all values of in the interval (a,b) such that

f'(c) =f(b)-f(a)/b-a (apply the Mean Value Theorem) 

 Question 1: f(x)=x^3-2*x      [0,2]

 Question 2 : g(x)= cuberoot(x-3)^2     [-3,4]

 

Please HELP!!! 

Dear All

I wanted to use the ColorTools of Maple to study the conversions between color spaces and different color definitions, but I find the tool very limited and rather confusing.

My main issue is to understand really which "RGB" definition is used ?
I assume it's a "RGB" = sRGB from Adobe(r) that is then translate to CIE 1931 values XYZ, xyz, Lab and more recent Luv values, all based on D65 illumination ? This must be really better defined in the help !!!

This is really not clearly stated as today "RGB" means mostly Adobe 1998 RGB, the larger gamut color space from Adobe and not the older and more reduces sRGB.

Color Space and Color understanding is subtile and require really a clear differentiation about illumination, color mappings, input, and output devices, and more ...

This issue applies to the "HSV" and "CMYK" these are all HW associated devices, and at least the standard illumination considered here must be defined, from my undersanding (and within the CIE definitions there are at least half a dozen of illumination standards, the most common, for me, are the D50, & D65).

It would be great if the ColorTables allowed us to really study colors in a correct way and following more the appraoch of i.e. "Digital Color Management, ENCODING SOLUTIONS" by Edward J. Giorgianni and Thomas E. Madden, Wiley (2.Ed, 2008) or some of the other serious book on color management.

 

Thanks in advance for your replies

Sincerely

Ivar

 

 

how I can write a program code for newmark method.

in this method time has 3 order derivation

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