## Verifying more complex trig identities...

Asked by:

Maple evaluates:

but when I ask:

Maple will verify sin(u)/cos(u)=tan(u) but beyond that it does not seem to work too well. I suspect this has something to do with verify being a "semi-boolean" function but searching the docs for what that mean returns no results. It may mean "I am unable to decidee". But how should I know? :-(

This is Maple 2016.1 on Windows. There is a post on verifying very simple identities.

Edit As usual some very helpful answers for which many thanks. It is poor that Maple does not document the meaning of FAIL.It seems that for trig identities the expandverfier is the best.

Edit Maple documents FAIL under ? FAIL. I am not sure how I got a blank page when I searched.

## Spam titles with http...

Asked by:

Couldn't any question with title beginning with http be removed automatically? There has been quite a few containing nothing but spam.

## Elapsed days to date and vice versa...

Asked by:

Dear Community,

Is there an easy way to convert elapsed days since January 1 1900 to date, i.e. to year, month, day in Maple? E.g. 23021 days should convert to 1963.01.10. Also what is the opposite, i.e. from date to elapsed days?

tx in advance,

best regards

Andras

## Integrating an expression...

Asked by:

Hello Everyone

I have an expression which I would like to integrate from x=0 to x=L. The expression is

x1:=(sin(beta*x)*cos(m*Pi*x/L))/(1+alpha*x)

Here, beta, m, alpha are constant. However I want the result in terms of these quantities.

I will be grateful if you could help mw in this regard.

Thanks a lot.

## Consecutive odd numbers summed up to 3375...

Asked by:

Ex: Give: Sum = 16;

Result: [1,3,5,7]

## Newton iteration is not converging...

Asked by:

Dear All,

I am going to solve the following systems of ODEs but get the error: Newton iteration is not converging.
Could you please share your idea with me. In the case of AA=-0.2,0,0.2,0.4,...; I could get the solution.
Thank you in advance.

restart;
with(plots);
Pr := 2; Le := 2; nn := 2; Nb := .1; Nt := .1; QQ := .1; SS := .1; BB := .1; CC := .1; Ec := .1; MM := .2;AA:=-0.4;

Eq1 := diff(f(eta), `\$`(eta, 3))+f(eta).(diff(f(eta), `\$`(eta, 2)))-2.*nn/(nn+1).((diff(f(eta), eta))^2)-MM.(diff(f(eta), eta)) = 0; Eq2 := 1/Pr.(diff(theta(eta), `\$`(eta, 2)))+f(eta).(diff(theta(eta), eta))-4.*nn/(nn+1).(diff(f(eta), eta)).theta(eta)+Nb.(diff(theta(eta), eta)).(diff(h(eta), eta))+Nt.((diff(theta(eta), eta))^2)+Ec.((diff(f(eta), `\$`(eta, 2)))^2)-QQ.theta(eta) = 0;
Eq3 := diff(h(eta), `\$`(eta, 2))+Le.f(eta).(diff(h(eta), eta))+Nt/Nb.(diff(theta(eta), `\$`(eta, 2))) = 0;

bcs := f(0) = SS, (D(f))(0) = 1+AA.((D@@2)(f))(0), theta(0) = 1+BB.(D(theta))(0), phi(0) = 1+CC.(D(phi))(0), (D(f))(etainf) = 0, theta(etainf) = 0, phi(etainf) = 0

Error, (in dsolve/numeric/ComputeSolution) Newton iteration is not converging

## From Python into Maple...

Asked by:

how to translate python code which use scipy, numpy to maple code

```import numpy as np
from scipy.sparse.linalg import svds
from functools import partial

def emsvd(Y, k=None, tol=1E-3, maxiter=None):
"""
Approximate SVD on data with missing values via expectation-maximization

Inputs:
-----------
Y:          (nobs, ndim) data matrix, missing values denoted by NaN/Inf
k:          number of singular values/vectors to find (default: k=ndim)
tol:        convergence tolerance on change in trace norm
maxiter:    maximum number of EM steps to perform (default: no limit)

Returns:
-----------
Y_hat:      (nobs, ndim) reconstructed data matrix
mu_hat:     (ndim,) estimated column means for reconstructed data
U, s, Vt:   singular values and vectors (see np.linalg.svd and
scipy.sparse.linalg.svds for details)
"""

if k is None:
svdmethod = partial(np.linalg.svd, full_matrices=False)
else:
svdmethod = partial(svds, k=k)
if maxiter is None:
maxiter = np.inf

# initialize the missing values to their respective column means
mu_hat = np.nanmean(Y, axis=0, keepdims=1)
valid = np.isfinite(Y)
Y_hat = np.where(valid, Y, mu_hat)

halt = False
ii = 1
v_prev = 0

while not halt:

# SVD on filled-in data
U, s, Vt = svdmethod(Y_hat - mu_hat)

# impute missing values
Y_hat[~valid] = (U.dot(np.diag(s)).dot(Vt) + mu_hat)[~valid]

# update bias parameter
mu_hat = Y_hat.mean(axis=0, keepdims=1)

# test convergence using relative change in trace norm
v = s.sum()
if ii >= maxiter or ((v - v_prev) / v_prev) < tol:
halt = True
ii += 1
v_prev = v

return Y_hat, mu_hat, U, s, Vt```

## From RootOf to explicit form...

Asked by:

hi.how convert root of to explicit form.

w is a imaginary..

thanks

123.mw

 (1)

 (2)

Download 123.mw

## List of random colors...

Asked by:

Dear Community,

How could I specify a list of random colors using some kind of an RGB function, which then could be used in another command for coloring? I think of something like this:

myColors := [ seq( RGB ( [rint(0,255) , rint(0,255) , rint(0,255)] ) , j = 1 .. 20 ) ] :

which does not work of course :-)  This should produce me a list of 20 random colors.  What would be the right RGB color function?

Tx for the kind help in advance

best regards

Andras

## Problem with pointplot ...

Asked by:

Dear Community,

I generate two vectors and try to plot them one vs. the other ( ZPLOT vs. PREDS )  with the pointplot command. Unfortunately I get the message "points are not in the correct format" ... Probably a minor error, but it is unclear what format Maple expects here? What do I do wrong?

Tx. for the kind help in advance,

best regards

Andras

P.S. Maple file attached

Z_DAK_PROC.mw

## Real solution x of equation y=x^3...

Asked by:

Hello people in mapleprimes,

I tried to solve y=x^3 for x, expecting of getting a result of x^(1/3),

through using restart;assume(x::real,y::real);
b:=y=x^3;
solve(b,x);

But, the result was:

Warning, solve may be ignoring assumptions on the input variables.
(1/3)    1  (1/3)   1    (1/2)  (1/3)
y     , - - y      + - I 3      y     ,
2          2

1  (1/3)   1    (1/2)  (1/3)
- - y      - - I 3      y
2          2

.

It means that solve couldn't use the assumption of x and y being real.

On the other hand, reading RealDomain package, y^(1/3) is returned properly:

with(RealDomain):
solve(b,x);
(1/3)
y

What I want to ask you is

Aren't there ways other than using the RealDomain package, to obtain the solution of y^(1/3)?

I will be very glad if you give me answers.

Best wishes.

taro

## How to tweak physics notation?...

Asked by:

Hi,

I'm new to the physics package - wondering if i can tweak it a bit to look like things i'm used to:

is there a way to make Christoffel symbols print as upper case gamma, instead of  'G'?

KroneckerDelta print as lower case delta, instead of 'd'?

can i make the Schwarzschild metric look like it does in Hartle, Carroll, and others:

-(1 - 2M/r)dt^2 + (1-2M/r)^-1 + r^2(dtheta^2 + sin(theta)^2 dphi^2)

i know about setting the signature in Setup.

i have tried the 'Coordinates' command, but when i give it X=[t,r,theta,phi] i always seem to get back

[t,r,q,f]

i am running maple 2016

many thanks,

larry

## Symbolic Solution of Polynomial System...

Asked by:

Hello everyone,
I would like to get a symbolic result of each variable x,y and z for the following 3 nonlinear equations. Maple does not respond to the following code at all. (Not even an error report.)

restart;

eq1 := x^2+y^2+z^2-134*x+800*y-360*z+31489, 2;
eq2 := x^2+y^2+z^2-934*x+900*y-370*z+321789, 2;
eq3 := x^2+y^2+z^2-614*x+1350*y-1110*z+70048, 97;
solve({eq1, eq2, eq3}, {x, y, z});

Thanks in advance.

P.S: Afterwards my intention is to solve these equaitons numerically for different variable values, and transfer to MatLab in order to plot animations and graphs.

## ODE boundary value problem ...

Asked by:

It is known that ODE boundary value problem is similar to the problem of solving systems of nonlinear equations. Equations are the boundary conditions, and the variables are the values of the initial data.
For example:

y '' = f (x, y, y '), 0 <= x <= 1,

y (0) = Y0, y (1) = Y1;

Where y (1) = Y1 is the equation, and Z0 is variable, (y '(0) = Z0).

solve () and fsolve () are not directly suitable for such tasks. Directly should work the package of optimization in relation to a system of nonlinear equations. (Perhaps it has already been implemented in Maple.)
Personally, I am very small and unprofessional know Maple and cannot do it. Maybe there is someone who would be interested, and it will try to implement this approach to solving ODE boundary value problems?

## Request for ONEOptimal package...

Asked by:

I am trying to find a download for the ONEOptimal package for Maple (http://iopscience.iop.org/article/10.1088/0253-6102/61/2/03). I read the article but there is no download link to the file. Does anyone know where I can download the package?

 First 802 803 804 805 806 807 808 Last Page 804 of 2122
﻿