## Error with dsolve...

Dear all,

I'm using Maple to calculate the geodesics of the Poincare' Half Plane:

restart:
with(LinearAlgebra): with(DifferentialGeometry): with(Tensor): with(Tools): with(plots):
DGsetup([x,y],M1)
g1 := evalDG(1/y^2*(dx &t dx+dy &t dy))
R1 := CurvatureTensor(g1)
K := SectionalCurvature(g1,R1,D_x,D_y)
Gamma := Christoffel(g1)
C := [x(t), y(t)]
V := GeodesicEquations(C, Gamma, t)
DE := Tools:-DGinfo(V, "CoefficientSet")

simplify(dsolve(DE, explicit))

Error, (in simplify/siderels:-simplify/siderels) specified variables must be names or functions

How can I fix this error?

Thanks, Nicola

## Print function values in the animation...

Hello,

I would like to print the current values of both displayed functions for x=1 in each frame of the animation. My example code is below:

```plot1 := animate(plot, [a*x^2, x = -1 .. 1, color = "Green", thickness = 3], a = 0.2 .. 1.2);
plot2 := animate(plot, [a*x^2 + 0.3, x = -1 .. 1, color = "Red", thickness = 3], a = 0.2 .. 1.2);
display([plot1, plot2]);```

I would be grateful for any tips.

Thank you,

Iza

## Why doesn't ImportGraph provide an "output=Array...

ImportGraph reads one or more graphs from a file. For a file containing multiple graphs, the supported formats are digraph6, graph6, and sparse6. I notice that one option is "output = graph or list, or iterator". However, in my programming with Maple, I was reminded several times that list is only good for a small amount of data.

Although I can convert the list to an array using the convert function, the time spent in the conversion process needs to be considered.

```restart:
with(GraphTheory):
L:=ImportGraph("C:/Users/eul10c.g6", graph6, output=list):#31026 connected eulerian graphs on 10 vertices graphs and Change to your path here.
convert(L,Array)
```

So does it make more sense to provide an "output=Array" as an output option?

eul10c.txt

## Problem with using solve and summation...

I am trying to use "solve" to solve a set of 2 equations defined by using summation function "sum". But I got an error saying "Error, (in sum) summation variable previously assigned, second argument evaluates to 3 = 1 .. 2".

The Maple code is listed here

restart;
N := 2:
var:= seq(alpha[n], n = 1 .. N):
v(x):=sum(alpha[n]*phi[n](x), n = 1 .. N):
R(x):=diff(v(x), x \$ 4) - p/EI:
eqs := seq('int'('R(x)'*phi[n](x), x = 0 .. L) = 0, n = 1 .. N):
for n to N do
phi[n](x):= sin((2*n - 1)*Pi*x/L):
end do:
solve({eqs}, {var});
Error, (in sum) summation variable previously assigned, second argument evaluates to 3 = 1 .. 2

## How can I create a Vector using symbolic name for ...

I have the following example.

> A:= Vector(3,symbol=v)

A:=

>v[1]:= 5

v[1]:=5

> A

Is there any way such that v[1] is actually referring to the first element in the vector? In other words, changing v[1] actually modifies the vector A.

If the question does not make sense, then here is the actual scenario that I faced.

I need to solve a system of equations in the form of

2 = c[2] + a[1],
2 = 2*c[3] + a[2],
-2 = -3*c[1] + a[3],
-1 = -2*c[2] + a[1],
-1 = -c[3] + a[2],
1 = a[3]

where a[i], c[i] refers to the entries in the vector.

`solve` returns the following:

[[a[1] = 1, a[2] = 0, a[3] = 1, c[1] = 1, c[2] = 1, c[3] = 1]]

I then did an `assign(%)`. However, the entries in A and C are not changed. I want the answer returned by solve to be properly applied to the entries of the vectors.

## How can I store a result directly to a function in...

a := x -> x + 1;
b := x -> a(x) + x^2;
a := x -> x + 5;
b(x);
2
x  + x + 5

However, I wish my b(x) to be x^2 + x + 1. How could I do it?

## Using an package modifies the behaviour of functio...

I have the following code snippet.

f := x^11 + 2*x^9 + 2*x^8 + x^6 + x^5 + 2*x^3 + 2*x^2 + 1;
g := 2*x^10 + x^7 + 2*x^4 + x;

Gcd(f, g) mod 3;
9      6    3
x  + 2 x  + x  + 2
with(Algebraic);
Gcd(f, g) mod 3;
6
x  + 1

It is surprising to me that using a package actually changes the behaviour of functions not in the package!

Is this a bug or a feature that I am not aware of?

## Determinants, Gauss and Cramer

Maple 2021

Applications to develop exercises on systems of equations using the technique of determinants, Gauss and Crammer. For science and engineering students. In spanish.

Determinantes_Gauss_Crammer.mw

Lenin Araujo

## Locally flat coordinates with arbitrary metric Gen...

I have just started using the GR functions available in Maple and have struggled to implement locally flat coordinates whilst using an arbitrary metric. I would like Maple to know that the first partial of g_ is 0 but that the second may not be. This knowledge would help simplify down some of the bulky expressions for the Riemann tensor in terms of g_. Any suggestions would be great as I have very little background knowledge with the submodule.

Thanks!

For_mapleprimes.mw

## Why does solve give me 2 wrong answers?...

Why do I get 2 wrong answers here?

I see that they are all false but the last answer is close enough for my purposes

 =    =  =  =  =

## How to quickly find the spectral radius of a matr...

The spectral radius  is maximum of the absolute values of the eigenvalues of the matrix A.  We can use the function SpectralRadius in Student package. But we noticed a sentence in the help document:

The output from this procedure will be as symbolic as computationally feasible. If the exact spectral radius of A is too time-consuming to compute, it may be computed numerically.

This means that SpectralRadius will evaluate the exact value when it can. Anyway, the internal evaluation process will take time. So for the sake of efficiency, we just want the numerical results of the spectral radius of a matrix.

I tried to write the following function, but I feel that it is not very efficient, especially for solving characteristic polynomials and their roots.  I even feel that there is a way to find the spectral radius without taking the absolute value of all the eigenvalues and ordering them.

```Spectralradius := proc(A::Matrix)
local Spectrum;
Spectrum := sort(abs~([fsolve(LinearAlgebra:-
CharacteristicPolynomial(A,x)=0,x )]),`>`);
Spectrum[1]
end proc:```

One example: In general, the matrices I encounter come from adjacency matrices of graphs, which are always real symmetric. So their eigenvalues are always real. But the Eigenvalues command very slow because it's always trying to get the exact value. So If we use Eigenvalues  to find all the eigenvalues and then sort them, it will be very slow.  Thus  I'm thinking about finding the numerical results.

 > with(LinearAlgebra): with(GraphTheory): G2:=Graph({{1,2},{2,3},{3,1},{3,4}}): A2:=AdjacencyMatrix(G2): Eigenvalues(A2);
 (1)
 > evalsN:=evalf(%);
 (2)
 (3)
 (4)
 >

Maybe I need a way to find all the numerical eigenvalues of a real symmetric matrix not using  CharacteristicPolynomial or Eigenvalues.

## Why does print to PDF put content without leftmost...

macOS 12.3 + Maple 2021.2

* --> Print
* --> Print to PDF

The created document essentially has no left border (margin). This has been a problem over at least the last three versions in Maple. I end up having to use an extra PDF cropping tool to reset the margins on the document.

What is the solution to this problem?

## Why does Copy as image not work?...

macOS 12.3 + Maple 2021.2

* select a region on a document
* context click
* --> Copy as image

Copy as image does not put an image on the clipboard.

What is solution?

## How to implement decomposition function respect ba...

I describe my problem accurately in mws file. I have a step function

 > First step. This is f(x) function
 >
 (1)
 > Next step. I try to approximate this function f(x) using wavelet transform, and  I  want to decomposite this function, choose wavelet Haar function and scaling functon  , choose basisn funtion from multiresolution analysis of the Lebesgue space  L^2(R). I choose  such wavelet fucntion  from space MRA V0 and scaling function from space MRA V0:
 >
 (2)
 >
 (3)
 > After I try approximate initial function f(x), decomposed using such contruction:
 >
 >
 > where coeff m shows, space MRA, to which the basis function belongs, and kk shows,basis function shift (x-k)
 > i.e. I try decompose function respective to basis function, where coeffs calculate the such way:
 >
 >
 > The approximation is considered satisfactory if the following condition is  true:
 >
 >
 > For example  calculate that such way:
 >
 > if the wavelet Haar functions:
 >
 (4)
 >
 > Then vector of Haar functions compute using the follow code:
 >
 >
 > Then integrals
 >
 >
 > where  is an d-square matrix called an operational matrix of integration
 >
 >
 > And now, it's not working, so I have troubles for calculate coeffs and writing and  plotting this result, so, I have some questions: 1) How to calculate coeffs and   for my fucntion f(x) and get value of coeffs? 2) How to implement integration and write the final sum (approximation of function f(x)? 3) How to calculate
 >
 >
 > and plot initial function f(x) and approximation sum at one plot?
 > Do I understand correctly that I need to calculate this integral for my function on each interval of my function?
 >
 >
 > How to implement this procedure?

Code for calculating procs a I try ude from this source: http://www.m-hikari.com/ams/ams-2012/ams-125-128-2012/sunmonuAMS125-128-2012.pdf

I would be very grateful for any help!

## Syntax for the seq function with units...

So all I'm trying to do is a simple sequence like seq(i^2, i=1..10, 1) but with units.  The seq function is part of the Units:-Standard and Units:-Simple packages.  I couldn't find any examples with units in the help system.  For my first attempt, I tried to create a simple sequence of values with units using what is, to me, a logical syntax.  I have included the Maple input below.  I bolded the input.

with(Units:-Standard);
[*, +, -, /, <, <=, <>, =, Im, Re, ^, abs, add, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin,

arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, cos, cosh, cot, coth, csc, csch, csgn, diff, eval,

evalc, evalr, exp, expand, factor, floor, frac, int, ln, log,  log10, log2, max, min, mul, normal, polar, root, round, sec,

sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan,   tanh, trunc, type, verify]

seq(ii, ii = 1.0*Unit('m') .. 10.0*Unit('m'), 1.0*Unit('m'));

Error, (in Units:-Standard:-seq) wrong number (or type) of parameters in function seq

Can anyone show me the correct syntax for this?  Is there something in the help?  I tried it in 2021 and 2022 with the same result.

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