## Finding complex roots and the asymptotes...

I was able to fix the problem. But I wanna use if statements to differentiate between complex and real roots in the attached file below:SOLVING_SYS.mw.

## finding the solution as f approaches to zero...

I am trying to find the solution (\Psi) as approaches zero. However, after applying the limit the solution becomes zero. See the attached .mw file.limit.mw

## Francis QR algorithm...

I have tried a code in python for Francis QR algorithm but didn't desire the result. I don't know if it is possible to code in maple.

Given that A^0 = [[3.0, 1.0, 4.0], [1.0, 2.0, 2.0], [0., 13.0, 2]].

1. Write a little program that computes 1 step of Francis QR and test your program by starting from

A^0 = [[3.0, 1.0, 4.0], [1.0, 2.0, 2.0], [0., 13.0, 2]]  and compute A^1, A^2 ...A^6.

I expected to get:

A^0 = [[3.0, 1.0, 4.0], [1.0, 2.0, 2.0], [0., 13.0, 2]],

A^1 = [[3.5,  -4.264, 0.2688], [-9.206, 1.577, 9.197], [0., -1.41, 1.923]],

... A^6 = [[8.056,  1.596, 8.584], [0.3596, -2.01, -7.86], [0., 2.576*10^(-16), 0.9542]].

But didn't get the same results.

Here is my python code:

# Import packages
import numpy as np
from numpy.linalg import qr # QR from Linear Algebra Library
import scipy.linalg   # SciPy Linear Algebra Library

A = np.array([[3.0, 1.0, 4.0], [1.0, 2.0, 2.0], [0., 13.0, 2]])
p = [1, 2, 3, 4, 5, 6]
for i in range(30):
q, r = qr(A)
a = np.dot(r, q)
if i+1 in p:
print("Iteration {i+1}")
print(A)

I would really appreciate your help.

Thank you.

## How use maple to find all roots...

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

## How i do find a real roots for equation system dim...

hallo every body

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

roots.mw

## Why square roots are not simplifying in a fraction...

Please see the attached file; I'm attempting to do some calculations with the 'PDETools' package; notice the first term in equation (4), where sqrt(x2+y2) is not canceling in the fraction, despite using the 'simplify' command; why is this happening, and how can I achieve complete simplification?

Ques_Mapleprime.mw

 >
 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >

## Plot RowSpace of a 2-by-3 Matrix in 3D...

Consider matrices A and B below; how one can plot basis vectors of column space in 2d, and plane or line spanned by basis of row space in 3D?

with(LinearAlgebra):
A := Matrix([[2, 3, 5], [1, 2, 7]]);

ColumnSpace(A);
RowSpace(A);

B := Matrix([[6, 4, 2], [3, 2, 1]]);

ColumnSpace(B);
RowSpace(B);

## How to extract the values of D(h)(0) for two diffe...

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convODEPlot.mwODEPlot.mwert/ODEPlot.mw .

## avoid jumps in log() of complex-valued function...

Hey everyone!

I have a complex function stored in a file (Comp-func.txt). The function is continues everywhere on the real axis (X-axis.txt). However, its log shows a jump somewhere close to x=-1.5. I would like to understand how Maple interprets this "jump" and how to avoid such numerical artifact.

thank you.

Jump-Log-Func.mw

X-axis.txt

## Problem with solving an integral...

Hi guys,

I can not solve this integral with maple ! I really appreciate if someone can help me! Mathematical gives a solution in terms of hypergeometric function!

p^2 , m, \epsilon, D > 0 and i is imaginary number

Thanks 111.mw

## Error during integration...

I was computing an integral (Running Maple 18 on Windows 10):

The classic lenght of arc Integral of sqrt(1+(dy/dx)^2) dx

In this case, the function was a cartesian circle (x-R)^2+y^2=R^2 isolated as y=sqrt(R^2-(x-R)^2)

When I do the integration, the result of the integral is not correct.
But if I change R for a, the result is correct. Why? This does not make any sense.

R wasn't assigned to any variable. The code was:

Good Integral

[>y:=expand(sqrt(a^2-(x-a)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

Wrong Integral

[>y:=expand(sqrt(R^2-(x-R)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

In fact, any UPPERCASE letter used as the radius gives me the wrong answer whereas any LOWERCASE letter gives me the proper result. Why is this?

Thanks and have a nice day

## Why are symbols and indexed names handled differen...

Input:

a := x^2;
whattype(x);
b := x[1]^2;
whattype(x[1]);
CodeGeneration[C](a);
CodeGeneration[C](b);

Output:

Do you know why cg0 =/= x[0]*x[0]?