Please, how can I find all the roots  of: (H/(Hc))^2 -(4*q^2)/Pi^2*((tan(q)- q/(1-alpha))/(tan(q)-q)) with q=(i-1)*Pi+Pi/2..i*Pi+Pi/2 for n=20.

See my attempt below:

restart:with(RootFinding):
a[1] := .1093; k[3] := 7.5*10^(-12); k[2] := 3.8*10^(-12); d := 0.2e-3; eta[1] := 0.240e-1; alpha[2] := -.1104; alpha[3] := -0.1104e-2; eta[2] := .1361; xi := 1.219*10^(-6); alpha := 1-alpha[3]^2/(a[1]*eta[1]); theta[0] := 0.5e-1;
Hc := (Pi/d)*sqrt(k[2]/xi):

H := 5.5*Hc;
lambda := a[1]/(xi*H^2);

RootFinding:-NextZero(proc (q) options operator, arrow; (H/(Hc))^2 -(4*q^2)/Pi^2*((tan(q)- q/(1-alpha))/(tan(q)-q)) end proc, 0);

for j to 9 do RootFinding:-NextZero(proc (q) options operator, arrow; H^2/Hc^2-4*q^2*(tan(q)-q/(1-alpha))/(Pi^2*(tan(q)-q)) end proc, %) end do;

Error, invalid input: RootFinding:-NextZero expects its 2nd argument, zz, to be of type numeric, but received FAIL

Hi

I wanted to know how to search a list of permutations given criteria: print the permutation(s) If the 4th element of each perm was equal to [C,Z} and the seventh was equal to [B,Y]

perm.mw

Hello, 

I have an equation in the form:

x(t)=2*a+b*t+2*t;

where a and b are the unknowns that I have to find. 

my initial conditions are x(0)=1 and x(1)=1. How can I solve this equation in maple?

Thank you very much for your help!

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.
 

Is it possible to read and/or convert Mapleflow sheets to Maple?

This is the first time I see such an error installing Maple on windows.

Right after the MS VS run-time installation completed (which is started by Maple installer) I got an error message saying it could not install fonts and to install them "manually".

Are there detailed instructions how is one supposed to do this? And what does this actually affect? As Maple starts ok and so far I see no issue with fonts but I have not done much with it yet other than open a worksheet and type few commands.

Looking at the folder in question, I see no instructions. Only font files. It will be good if Maplesoft could provide instructions for users on how to do that.  I do not want to do something that could end breaking the Maple installation or make things worst.

Does anyone know how to make a command for Leibniz formula for pi?

I would preferably like to use: 1-1/3+1/5-1/7+1/9..=pi/4

I don't want to sit and write everything out, but would like to make it a command, and decide myself how many calculations I would like. I have no clue how though. Anyone have an idea for that?

restart;
with(LinearAlgebra):
a := .1093;
b[3] := -0.1104e-2;
k[1] := 3.8*10^(-12);
d := 0.2e-3;
xi := -1;
theta0 := 0.1e-3;
eta[1] := 0.240e-1;
alpha := 1-b[3]^2/(a*eta[1]);
c := b[3]*xi*alpha/(eta[1]*(4*k[1]*q^2/d^2-b[3]*xi/eta[1]));

f:= q-(1-alpha)*tan(q)- c*tan(q) ;
plot(f,q=0..4*Pi,view=[DEFAULT,-1..10]):

   
n:=3: 
q[1]:=fsolve(f,q=(0..Pi/2)): 
for i from 2 to n do
q[i]:=fsolve(f,q=(2*i-3)*Pi/2..(2*i-1)*Pi/2): ##q[n]
od:

printlevel := 2;
for i from 2 to n+1 do for j from i+1 to n do b[i, j] := int((cos(q[i]-2*q[i]*z/d)-cos(q[i]))*(cos(q[j]-2*q[j]*z/d)-cos(q[j])), z = 0 .. d); b[j, i] := b[i, j] end do end do;

for i from 2 to n do a[i, i] := int((cos(q[i]-2*q[i]*z/d)-cos(q[i]))*(cos(q[i]-2*q[i]*z/d)-cos(q[i])), z = 0 .. d) end do;

for i from 2 to n do f[i] := theta0*(int(cos(q[i]-2*q[i]*z/d)-cos(q[i]), z = 0 .. d)) end do;

## I have generated a matrix using the a[i,i] above
A := Matrix([seq([seq(a[i, j], i = 2 .. n)], j = 2 .. n)]);

b := Vector([seq(f[i], i = 2 .. n)]);
     

#Please, how do I generate an upper triangular matrix using b[i,j] above?        

I am using Maple 2021.2 on Ubuntu Linux 20.04 LTS. Sometimes the Maple after start does not show Sig in part of top Maple desktop panel. So I need to restart Maple and 2nd or 3rd start is mostly OK. After that is the situation for some time good.

See attached snapshot... Any idea what is wrong?

hallo every body 

please how i do find a real roots for this equation system 

roots.mw

I set infolevel[dsolve]:=2; and first time I use it, it gives very long output. Next time I use it on same ode with same command it gives much shorter output.

Why is that and how to make it give the shorter output from first call?  This is very strange behavior.  One would expect the same output each time. The worksheet attached shows that first time it is used, the output is very long. At the end of the worksheet the call is made again with same infolevel, and now output is much smaller.

(getting error uploading worksheet. Will try again. Unable to do insert content keep getting error from this site. So I am just attaching it as link. May be due to large size of the worksheet)

infolevel_changes.mw

In a video (watch from 7 min onwards) I have seen the definition of solution types in custom components. Is this possible in newer versions of MapleSim using the custom component app? If yes, how?

The Dates are not ordered in a timeseries. The Dates are random variables coming from a dataFrame

How can I write a formula for odd numbers?
Such that :
Show each odd number from the sum of two numbers: even + odd, except for one

The IsSubgraphIsomorphic command accepts either two undirected graphs or two directed graphs as input.  It returns true if G1 is isomorphic to some subgraph of G2. The GraphTheory [IsSubgraphIsomorphic] command was introduced in Maple 2021.

If a graph T is isomorphic to some subgraph T' of  a graph G, IsSubgraphIsomorphic(T,G)  will  return true. But there is no option to return T'. That makes it hard to check manually.

I've seen  IsSubgraphIsomorphic behaving strangely lately. I want to check whether K₈-P₆ contains K₇-K₃ as its subgraph.

T:=DeleteEdge(CompleteGraph(7),{{1,2},{2,3},{3,1}},inplace= false): 
G:=DeleteEdge(CompleteGraph(8),{{1,2},{2,3},{3,4},{4,5},{5,6}},inplace= false): 
IsSubgraphIsomorphic(T,G)

true

I think theoretically, the result of IsSubgraphIsomorphic is not correct. I also tested it from Mathematica, and it worked as I expected.

h = EdgeDelete[ CompleteGraph[7], {1 <-> 2, 2 <-> 3, 3 <-> 1}]; 
g = EdgeDelete[ CompleteGraph[8], {1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 5, 5 <-> 6}]; 
IsomorphicSubgraphQ[h, g]

False

I wonder what went wrong.

PS: Subgraph isomorphism is a question I've asked before, and we can refer to the following links and code. https://www.mapleprimes.com/questions/226937-How-To--Test--A--Graph--Whether-Contains

with(GraphTheory):
with(combinat):
T:=DeleteEdge(CompleteGraph(7),{{1,2},{2,3},{3,1}},inplace= false): 
G:=DeleteEdge(CompleteGraph(8),{{1,2},{2,3},{3,4},{4,5},{5,6}},inplace=false): 
nE,nV := NumberOfEdges(T), NumberOfVertices(T):
# Produce all subgraphs of G which have the same number of edges and vertices as the "test" sub-graph T
U:=choose(Edges(G),nE): nops(%):
U1:=select(t -> (nops(`union`(t[]))=nV), U): nops(%):
gL:= Graph~(U1): nops(%):
ans:= [ seq
          ( `if`
            ( IsIsomorphic( T, gL[j] ),
              j,
              NULL
            ),
            j=1..numelems(gL)
          )
        ]:
if   numelems(ans)>0
then HighlightSubgraph( G, gL[ans[1]], edgestylesheet=[thickness=4, color="Red"]);
     DrawGraph(G, style=spring);
fi;

These codes are due to tomleslie  and  vv. According to above codes, it seems that there is something wrong with IsSubgraphIsomorphic too.