Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

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

 

 

 

 

 


 

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!!! 

 

how I can write a program code for newmark method.

in this method time has 3 order derivation

 We know the following facts: 

The SequenceGraph command returns a graph with the specified degree sequence given as input, if such a graph exists. It raises an exception otherwise. 
 But  If I  want to get more graphs  that satisfy this condition of degree sequence ? (If graphs are not many ,I want get all graphs better)
what should I do.?
For example: DrawGraph(SequenceGraph([3, 2, 2, 1, 1, 1]));  It returns the first graph below, but it is obvious that the second graph also fits the condition.

squenceGraph.mw

Hello Dear,

I have the following equation

 This equation is satisfied if the coefficients are zero.

So I need an order in Maple to write that

 

 

Good morning everyone, 

I have a problem, when I try to evaluate the definite integral below, Maple can not provide a result. What can I do so that the Maple can calculate this integral?

This is the Maple code with the result:

 

 

restart

with(VectorCalculus):

with(LinearAlgebra):

with(CodeGeneration):

N := 1:

M := 2:

``

for i to N do rpv1 || i := 0; rpv2 || i := 0; rpv3 || i := 0; for j to M do rpv1 || i := VectorCalculus:-`+`(rpv1 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), Phi || i || j)); rpv2 || i := VectorCalculus:-`+`(rpv2 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), `&varphi;` || i || j)); rpv3 || i := VectorCalculus:-`+`(rpv3 || i, Typesetting:-delayDotProduct(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), gamma || i || j)) end do; rp || i := Matrix([[rpv1 || i], [rpv2 || i], [rpv3 || i]]) end do:

``

for i to N do rppv1 || i := 0; rppv2 || i := 0; rppv3 || i := 0; for j to M do rppv1 || i := VectorCalculus:-`+`(rppv1 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), Phi || i || j)); rppv2 || i := VectorCalculus:-`+`(rppv2 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), `&varphi;` || i || j)); rppv3 || i := VectorCalculus:-`+`(rppv3 || i, Typesetting:-delayDotProduct(diff(diff(VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^j, s), s), gamma || i || j)) end do; rpp || i := Matrix([[rppv1 || i], [rppv2 || i], [rppv3 || i]]) end do:

``

``

for i to N do for j from 0 to 0 do U || i || j := 0 end do end do:

for i to N do for j from 0 to 0 do V || i || j := 0 end do end do:

for i to N do for j from 0 to 0 do W || i || j := 0 end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do U || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(U || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do V || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(V || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do for j from 0 to VectorCalculus:-`+`(M, -2) do W || i || (VectorCalculus:-`+`(j, 1)) := VectorCalculus:-`+`(W || i || j, VectorCalculus:-`*`(VectorCalculus:-`+`(s, VectorCalculus:-`-`(xi || i)), 1/L || i)^VectorCalculus:-`+`(j, 1)) end do end do:

for i to N do f || i := VectorCalculus:-`+`(Typesetting:-delayDotProduct(VectorCalculus:-`*`(Typesetting:-delayDotProduct(E, A), 1/mu), VectorCalculus:-`+`(VectorCalculus:-`+`(rpp || i, VectorCalculus:-`-`(VectorCalculus:-`*`(rpp || i, 1/evalc(norm(Re(rp || i), 2))))), VectorCalculus:-`*`(Typesetting:-delayDotProduct(rp || i, Typesetting:-delayDotProduct(rp || i^%T, rpp || i)), 1/evalc(norm(Re(rp || i), 2))^3))), Typesetting:-delayDotProduct(g, e3)) end do:

for i to N do for j to VectorCalculus:-`+`(M, -1) do fun || i || j := int(VectorCalculus:-`*`(U || i || j, Row(f || i, 1)), s = xi || i .. L || i) end do end do;

fun11

(int((s-xi1)*(E*A*(2*Phi12/L1^2-2*Phi12/(sqrt((gamma11/L1+2*gamma12*s/L1^2-2*gamma12*xi1/L1^2)^2+(`&varphi;11`/L1+2*`&varphi;12`*s/L1^2-2*`&varphi;12`*xi1/L1^2)^2+(Phi11/L1+2*Phi12*s/L1^2-2*Phi12*xi1/L1^2)^2)*L1^2)+(Phi11/L1+(2*(s-xi1))*Phi12/L1^2)*((2*(Phi11/L1+(2*(s-xi1))*Phi12/L1^2))*Phi12/L1^2+(2*(`&varphi;11`/L1+(2*(s-xi1))*`&varphi;12`/L1^2))*`&varphi;12`/L1^2+(2*(gamma11/L1+(2*(s-xi1))*gamma12/L1^2))*gamma12/L1^2)/((gamma11/L1+2*gamma12*s/L1^2-2*gamma12*xi1/L1^2)^2+(`&varphi;11`/L1+2*`&varphi;12`*s/L1^2-2*`&varphi;12`*xi1/L1^2)^2+(Phi11/L1+2*Phi12*s/L1^2-2*Phi12*xi1/L1^2)^2)^(3/2))/mu+g*e3)/L1, s = xi1 .. L1))*e[x]

(1.1)

``

NULL

``


 

Download integral.mw

 

Thank you !

Hello,

What is the minimum period of the following equation.


 

d := evalf(expand((100+100*cos(6*t)+200*cos(12*sqrt(2)*t))^2))

40000.-2580480000.*cos(t)^2*cos(1.414213562*t)^6+604800000.*cos(t)^2*cos(1.414213562*t)^4-51840000.*cos(t)^2*cos(1.414213562*t)^2+2621440000.*cos(t)^6*cos(1.414213562*t)^12-7864320000.*cos(t)^6*cos(1.414213562*t)^10+8847360000.*cos(t)^6*cos(1.414213562*t)^8-4587520000.*cos(t)^6*cos(1.414213562*t)^6+1075200000.*cos(t)^6*cos(1.414213562*t)^4-92160000.*cos(t)^6*cos(1.414213562*t)^2-3932160000.*cos(t)^4*cos(1.414213562*t)^12+0.1179648000e11*cos(t)^4*cos(1.414213562*t)^10-0.1327104000e11*cos(t)^4*cos(1.414213562*t)^8+6881280000.*cos(t)^4*cos(1.414213562*t)^6-1612800000.*cos(t)^4*cos(1.414213562*t)^4+138240000.*cos(t)^4*cos(1.414213562*t)^2+1474560000.*cos(t)^2*cos(1.414213562*t)^12-4423680000.*cos(t)^2*cos(1.414213562*t)^10+4976640000.*cos(t)^2*cos(1.414213562*t)^8+720000.*cos(t)^2+274560000.*cos(1.414213562*t)^4-5125120000.*cos(1.414213562*t)^6+0.4942080000e11*cos(1.414213562*t)^8-0.2811494400e12*cos(1.414213562*t)^10+0.1013841920e13*cos(1.414213562*t)^12+0.1677721600e12*cos(1.414213562*t)^24-0.1006632960e13*cos(1.414213562*t)^22+0.2642411520e13*cos(1.414213562*t)^20-0.3984588800e13*cos(1.414213562*t)^18+0.3810263040e13*cos(1.414213562*t)^16-0.2406481920e13*cos(1.414213562*t)^14-5760000.*cos(1.414213562*t)^2+10240000.*cos(t)^12-30720000.*cos(t)^10+34560000.*cos(t)^8+1320000.*cos(t)^4-16000000.*cos(t)^6

(1)

``


 

Download period

 

 

  I want list all  diameter-2  Nonisomorphismgraphs  of order n . I use the following code, but its running speed  is slow with  order of graph gradually increasing . (for example,n=10)
 Are there other ways to Improve it? 
restart:
with(GraphTheory):
Graphs_data:=[NonIsomorphicGraphs(4,restrictto =[connected], output = graphs, outputform =graph)]:
Diameter_select:=select[flatten](t->Diameter(t)=2,Graphs_data):
DrawGraph(Diameter_select,size=[50,50]);

  By the way,  Why doesn't size=[50,50] work ?

 
                       
                   
               
               
           
           
               
                   
                 

  Hello: 
    As a first step to my question, let  G be  a graph and  I'd like to know  whether it contains a C4 (cycle of 4) as its subgraph.
     For example: .   it contains C4.  So  program may be return true.  
    I'm most concerned about the following thing ( it is important problem for me, since in graphtheory, we usually consider some class graphs contain no sepecific graph ) :
   1 Further , I want to  get all connected graphs of order less than 6  which  contains no C4 .
   2 More generally, I want  to konw  a graph  whether contains some graph as its subgraph.For example : does it contain K4CompleteGraph(4)K32  CompleteGraph(3, 2)  and so on ?
    I read the  function subgaph.  But  It didn't solve my problem. Many thanks for your help or advise.
   # I  just know there is a function  IsTriangleFree which test if graph is triangle-free ( graph comtains no C3 in Maple 2019. I think my question and how to program may be  meaningful.

Hi, 

Versions concerned:  [ Maple 2015 ... Maple 2018 ]

I use DocumentTools:-Tabulate to display a matrix of numbers while coloring them according to some condition.
(line DocumentTools:-Tabulate(M, color=((M,i,j)->`if`(M[i,j]>3,....) below ... please note the output is not loaded for some unknown reason).
The fact is that the matrix appears with black characters meaning 'color' doesn't work.

In a second attempt I convert matrix M into a matrix of strings and use now
DocumentTools:-Tabulate(S, color=((S,i,j)->`if`(parse(S[i,j])>3,...)
I get now the desired result with some blue and red numbers.

So converting to strings could be a workaround.
But think to matrices where elements would be algebraic expressions, for instance 
M := Matrix(2, 2, (i,j)->exp(x^i)+cos(x*j))
and that we use the coloring scheme is color=((M,i,j)->`if`(i+j>3, "Red", "Blue")
Converting M to a string matrix will display the element [2, 2] in red and the others in blue, but what you get then is a no longer a 2D pretty output but, literally, things like exp(x^2)+cos(x*2) 

The "convert to string" workaround is thus far from perfect.
Is the fact that 'color' only acts on strings a "normal and known" behaviour?
Is it possible to change the color of the font for non "string type matrices" ?
 

restart:

M :=Matrix(2, 2, (i,j)->i+j)

M := Matrix(2, 2, {(1, 1) = 2, (1, 2) = 3, (2, 1) = 3, (2, 2) = 4})

(1)

DocumentTools:-Tabulate(M, color=((M,i,j)->`if`(M[i,j]>3, "Red", "Blue")), width=30)

S :=convert~(M, string):
DocumentTools:-Tabulate(S, color=((S,i,j)->`if`(parse(S[i,j])>3, "Red", "Blue")), width=30)

 


 

Download Tabulate_Color.mw

Dear friends~

Recently I wanted to create some funny gif with Maple based on other interesting pictures but I met some problems:(1)I read many commands in ImageTools but few can aid me.(2)If I use “plot(,background=file_address)”,then the whole background will be filled with pictures but I just want it to be a part of my gif.I finally noticed that “plot3d(,image=file_address)”can realize my idea to some extents if I adjust orientation’s value  suitably.

However,I still think my operations can be improved(for example,my code consumes a fair amount of  memory) and there maybe one better approach to be good too. Hence I upload my code and sincerely look forward your suggestions and help~

#Janesefor do it in 2019/4/15 13:20 with Maple2018~
with(plots):
# smile.jpg's address
image_file:="C:/Users/ysl-pc/Desktop/":
str:="有","朋","自","远","方","来","不","亦","乐","乎","?":
location_func,dy,dz:=3*sin(2*3.14/10*y),.75,.75:

display(seq(display(textplot3d([0,1,4.5,cat(str[1..ha])],align='right'),textplot3d([0,3.5,-4.5,"By Janesefor ~"],align='right'),plot3d([0,s,t],subs(y=ha-1,[s=y-dy..y+dy,t=location_func-dz..location_func+dz])[],image=cat(image_file,"smile.jpg"),axes=none,scaling=constrained,orientation=[180,90,-180],view=[default,0..10,-5..5],glossiness=0,lightmodel=light4)),ha=[`$`(1..nops([str]))]),insequence=true);
Export(cat(image_file,"smile.gif"),%)


smile.mw

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