Maple Questions and Posts

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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

I have made a table and did a programme to do calculations inside.

While converting into a pdf, i found that the table cells being continuous overlaps on pages. I now want to trim the table or split the table to convenient size. Any suggestion.

How do I convert a 7 x 3 table into a 4 x 3 and 3x3 table? Reducing font size does not alter the row and cell size. Is there a way to alter the columnwidth and row height in maple?

Thanks for suggestion.

Why does this happen

interface(Typesetting)
                                         

interface(Typesetting=standard)
                                                      

interface(Typesetting)
                                            

a2

          

 

 

I've looked up previous answers to this but __ double underscore only works in math input, and ctrl + shift + ^ or ctrl + shift + _ does not seem to work. I'm using Maple 18, windows computer.

I'm using a maple doc to do a homework assignment that is mostly text with only a few equations and math sections. I need to draw a table of material properties in, and when I create a table all the cells default to math inputs. Because of this if I try to evaluate the entire document I get tons of blue evaluation numbers in the table that I don't want, since all the mateial properties show up as math. I can set each cell to text one by one but there are like 30 cells and it's tedious. How do I set the entire table so that each cell is a text cell?

Hi!

Let F(z) (with z complex) a given function. I want to compute F^n(z0), i.e. the composition of F with itself n-times, where z0 is a given point (complex).

Is correct the following procedure to compute F^k(z0)?

App := proc (k, z0) local z1, z2, j; z1 := z0; z2 := NULL; for j to k do z2 := F(z1); z1 := z2 end do; return z2 end proc

 

Many thanks in advance for your comments.

Hi

Consider the piecewise function

f:=x->piecewise(x≤0,−3,0<x≤1,x^2,1<x,-x)

can Maple solve the inequation  in R:   f(x)> a

where "a" is a given number in R

Of course the results depend on parameter a

 

 

Many thanks for your help

 

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