## miscalculation with complex...

z1 := a1+I*b1; z2 := a2+I*b2; abs(z1) = 1; abs(z2) = 1; argument(z1) = alpha; argument(z2) = beta; On considère dans ℂ les complexes z1 et z2 de module 1 et d'argument α et β Show that (z1+z2)^2/(z1+z2) est un réel positf ou nul. Dans quel cas est-il nul ? is((z1^2+2*z1*z2+z2^2)/(z1+z2) = z1/z2+z2/z1+2);#wrong answer z1/z2 = exp(I*(alpha-beta)); z2/z1 = exp(I*(beta-alpha)); is(z1/z2+z2/z1+2 = 2*(1+cos(alpha-beta)));#wong answer Miscalculations. Thank you for your help.

## How to numericaly solve a system of differential e...

I'm trying to obtain the dynamical response of a simply-supported beam with a cantilever extension, coupled to a spring-mass system. In mathematical terms, this system is ruled by three PDEs (relative to each bare part of the main structure) and one ODE (relative to the spring-mass system). I think my mathemical model is finely formulated, but Maple keeps telling me this:

Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector

I believe it is because my PDEs depend on "x" and "t", while the ODE depends solely on "t". I have tried to transform my ODE into a "PDE", making it also dependent of "x", but without imposing any boundary conditions relative to "x". However, after this Maple points a new error message:

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

Could someone help me finding a solution? My algorythm in shown in the attached file below.

Worksheet.mw

## Why does the exception indexing function prevent m...

Here's a very simple example, working as intended:

Now, if I try to use the exception indexing function:

We can notice that b[1] isn't using exception anymore (as if the fourth input overwrote the second one) and that b[1][2] isn't linked to the value "two". However, if I define the tables first, I get the expected result:

Why does the exception indexing function prevent me from getting an existing table entry in the second case?

## decomposition of a square in sum of 2 squares...

Let E all triplets as X=(p,q,r) such as p^2+q^2=r^2. We define the application f of E dans C complex as X in E f(X)=(p+Iq)/r=Z. Calculate abs(Z). Show that in E the law noted * defined by
X1*X2=(p1*p2-q1*q2,p2*q1+p1*q2,r1*r2) is an internal law. Calculate f(X1*X2). Then if X0=(3,4,5), find
X0*X0, X0*(X0*X0).Thank you for the help.

## help me for solve the error ...

help me for solve the error of plot

p1.mw

## Output during loop processing...

I'm using Maple to solve academic problems.
At a certain stage, I need a loop to perform numerical calculations, from where I extract a graph. However, each step takes a long time and therefore, I would like to evaluate the performance of the result at each step of time.
To simulate my calculation, I created a test code:

restart:                                                                  # Restart
a := 2*((ceil(rand()/10^10)-50)*(1/10)):                # Random Value
b := 2*(ceil(rand()/10^10)-50):                             # Random Value
c := 2*ceil(rand()/10^10)-100:                             # Random Value
f := proc (x) options operator, arrow; a*x^2+b*x+c end proc;                  # Generic function that i'm ploting.
np := 10:                                                              # Number of Points i'm ploting
vmax := 10:                                                         # Maximum funcxtion value
VAR1 := Matrix(np+1, 2, proc (m, n) options operator, arrow; if n = 1 then (m-1)*vmax/np else 0 end if end proc):       # Declaring VAR1 as a "null" matrix

for i to np+1 do                                                  # Loop Start
VAR1[i, 2] := f((i-1)*vmax/np):                           # VAR1 value update
print(plot([VAR1], x = 0 .. vmax,  gridlines)):                           # Ploting VAR1
Sleep(.25):                                                         # Simulating longer processing time
od;

However, all graphs are displayed simultaneously after the last step of the for loop.
I would like to print the result (output) after each time step, plotting a new graph for each time an iteration ends.
Would anyone know how to do this?

## Fractional Reduced Differential Transform Method...

Can anyone help me to frame the equations in Fractional Reduced Differential Transform Method

system of nonlinear ordinary diﬀerential equations
ds/ dt = b−γ s(t)− (δ s(t)(i(t) + βa(t)) /N − ε s(t) m(t)
de/ dt = δ (s(t)(i(t) + βa(t))/ N + ε s(t) m(t) − (1−ϑ) θ e(t) − ϑ α e(t) − γ e(t)
di/ dt = (1−ϑ) θ e(t) − (ρ + γ) i(t)
da/ dt = ϑ α e(t) − (σ + γ) a(t)
dr /dt = ρ i(t) + σ a(t) − γ r(t)
dm /dt = τ i(t) + κ a(t) − ω m(t)

## How can I select 2 variables from 3 to obtain a co...

Good day to all.

I have a function, z(x,y), that I am interested in exploring. The contour plot returns the z-contours on the x-y grid (see attached).

Can anyone suggest a way in which I can now assign z to the vertical axis (instead of y), x to the horizontal axis, and plot the contours for various y-values?

Contour_Plot_MaplePrimes.mw

## numerical solutions of PDE-integral equation...

Dear experts

I am interested to solve the following equation numerically by Maple. I would appreciate it if you let me how I can do and what the boundary conditions and initial values are needed

eq:= diff(2*diff(eta(x,y,t),t)+3*eta(x,y,t)*diff(eta(x,y,t),x)+(1/3-1/epsilon/B)*diff(eta(x,y,t),x,x,x),x)+diff(eta(x,y,t),y,y)-1/sqrt(Pi*R)*int(diff(eta(x+zeta,y,t),x,x)/sqrt(zeta),zeta=0..t/epsilon)=0;
where

1) epsilon, B and r are constant

2) 1/epsilon/B is not equal to 1/3 at all

## how to show which region of the plan points belong...

how to show which region of the plan belongs to the argument points between 0 and Pi/2 and the module points between 0 and 2 ?

## Special Integral...

f(x) = tanh(x)/sqrt(x^2+1)

limits x_initial =1, x_final =100

Thanks

## Ppossible Issue with Seq...

I am trying to work through an example in a textbook, but its a few years old and uses maple 2015. I am currently using the 2018 edition of maple. The code is an example of how to generate the points on an elliptic curve given a specific input.
Here is the example code from the textbook:

epoints := proc(ec, x, ub, p)
local ecurve, z, pct, k, i;
pct := 0;
for k from 0 to p-1 while pct <= ub do
z := subs(x=k, ec) mod p;
if z = 0 then
pct := pct+1;
ecurve[pct] := [k,z];
fi:
if z &^ ((p-1)/2) mod p = 1 then
z := z &^ ((p+1)/4) mod p;
ecurve[pct+1] := [k,z];
ecurve[pct+2] := [k, -z mod p];
pct := pct+2;
fi:
od:
if pct > ub then
pct := ub:
fi:
seq(ecurve[i], i=1..pct):
end:

Here is my code, written to work with Maple 2018:

ecpoints := proc (ec, x, ub, p) local ecurve, z, pct, k, i;
pct := 0; for k from 0 to p-1 while pct <= ub
do z := `mod`(subs(x = k, ec), p);
if z = 0 then pct := pct+1;
ecurve[pct] := [k, z] end if;
if `mod`(z^((1/2)*p-1/2), p) = 1 then
z := `mod`(z^((1/4)*p+1/4), p) = 1;
ecurve[pct+1] := [k, z];
ecurve[pct+2] := [k, `mod`(-z, p)];
pct := pct+2 end if
end do;
if ub < pct then pct := ub end if;

seq(ecurve[i], i = 1 .. pct)
end proc

The problem is with the output. The output should be [0, 5], [0, 14], [2, 4], [2, 15], [3, 6], [3, 13], [4, 6], [4, 13], [6, 0], [10, 16], [10, 3], [12, 6], [12, 13], [14, 16], [14, 3], [18, 17], [18, 2].
What I get is [0, 5 = 1], [0, 14 = 18], [2, 4 = 1], [2, 15 = 18], [3, 6 = 1], [3, 13 = 18], [4, 6 = 1], [4, 13 = 18], [6, 0], [10, 16 = 1], [10, 3 = 18], [12, 6 = 1], [12, 13 = 18], [14, 16 = 1], [14, 3 = 18], [18, 17 = 1], [18, 2 = 18].
Any hints on what I could be doing wrong here or what is going on?

## Ordinary differential equation with singularity...

Dear All,

I am trying to solve the following differential equation, which is a kind of Spherical Harmonics. Can anyone please help me out how to solve this?

((D@@2)(y))(r)+(D(y))(r)/r-sin(y(r))*cos(y(r))/r^2+sin(y(r))^2/r-sin(y(r))-sin(2*y(r)) = 0

Thanks

## Cant plot my procedure...

Dear all

I use Maple 2018 and have following problem:

I define following procedure and want to plot it. However Maple displays the coordinate system but does not plot anything nor gives and error message. Hope you can help.

Thanks

b:=proc(n)
local b,i:
for i from 0 to n do
if i=0 then
b[0]:=0:
elif i=1 then
b[1]:=1:
else
b[i]:=(b[i-1]+b[i-2])/2:
end if:
end do:

return b[n]

end proc:

plot(b,0..10)