## How to tweak physics notation?...

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

## In seq function "division by zero"...

Hello everybody.

I have a function:

f(x,y)=GAMMA(y, -ln(x))/GAMMA(y)

seq(sum(f(x, y), y = 0 .. 1), x = 0 .. 5)

and I got a error message:

Error, (in ln) numeric exception: division by zero ??
This is normal behavior in seq function or Bug?

but  when I'm first calculate the sum sol := sum(f(x, y), y = 0 .. 1) -> x,

and evalf([seq(sol, x = 0 .. 5)]) ->[0., 1., 2., 3., 4., 5.] works fine.

Seq-division_by_zero.mw

Mariusz Iwaniuk

My old harddisk recently died and I am currently using a new one. I still have the license code for Maple 2016. Is it still possible for me to install Maple 2016 or 1 license = 1 installation?

## Problem with maplet ...

Maplet file failed to open by double click in windows 7 x64 file browser

There is no response when double click a Maple file

But it runs correctly by using command line

Anyone knows why?

## Geometric Proof...

I attempted to show that two lines are parallel.  I started with a problem in Geometry for which I do not have the solution.

I tried several ways with Maple to show this to be true.  Most of the time, I ended when maple could not determine if a-b = c-d, etc.

brg_proof.txt contains a statement of the problem and my latest maple code.

Question: How should I approach the proof, by the compass and straight edge method?  Is this possible in maple?

## Geometry Intersection Fails...

intersection in the geometry package does not seem to recognize assume.

restart: with(geometry):

assume(p[1]<>0, p[2]<>0, p[3]<>0);
assume(q[1]<>0, q[2]<>0, q[3]<>0);
point(T,[p[1],q[1]]);
point(U,[p[2],q[2]]);
point(V,[p[3],q[3]]);
point(Op,[0,0]);

line(OT,[Op,T]);
line(OU,[Op,U]);
line(OV,[Op,V]);

point(B,2*q[2],solve(subs(x=2*q[2],Equation(OU)),y));
coordinates(B);
IsOnLine(B,OU);

eval(x,sol);
point(A,eval(x,sol),eval(y,sol));  ## the intersection exists

## Extracting View from Several Plots...

I have several plots generated with geometry objects:

plt1 := draw(...); plt2 := draw(...)

I want to display all them with a reasonable window.  I have been looping and and using a rather dumb proc to find the window size. I use the view=[...] option with the values calculated to set the plot view.

I wanted to post the proc, but, really messed that up!  I will try the proc later.

Some of the plots I am working with have views like

> for itm in [relBrgLinePlot,relTgtPositPlot,relTgtLinePlot] do
op(-1,itm);
end do;
VIEW(0. .. 95., -61.58179461 .. 16.)
VIEW(5.48225506 .. 95., -61.58179461 .. 16.)
VIEW(5.48225506 .. 95., -61.58179461 .. 16.)

> for itm in [geoSensPositPlot,geoSensLinePlot,\
geoBrgLinePlot,geoTgtPositPlot,geoTgtLinePLot] do
op(-1,itm);
end do;
VIEW(0. .. 35.35331852, 0. .. 87.13244438)
VIEW(0. .. 35.35331852, 0. .. 87.13244438)
VIEW(0. .. 95., 0. .. 87.13244438)
VIEW(40.83557358 .. 95., 16. .. 25.55064977)
VIEW(40.83557358 .. 95., 16. .. 25.55064977)

Is there an easier way to do this?

## Grid Lines on X11 Device...

Linux.  I want to put grid lines on an x11 device.

The x11 device is better for plotting because if the window is resized, the plot resizes with it.

restart;
plotsetup(x11);plot(sin(x),x=-1..1,gridlines = true); ## no gridlines

restart;
plotsetup(maplet);
plot(sin(x),x=-1..1,gridlines = true); ## have gridlines

Any way to get gridlines on x11 device?

Tom Dean

## Place numerator after denominator?...

I have a Maple result presented in the first (top) formula which I would like to format as in the second (bottom) formula:

Can this be done? This is Maple 2016.1

## Maple does not save some variables?...

Hello

I have experienced that maple does not save all of the varibles. But some it does.

I calculate with units, could that be the reason?

I have allso been thinking that it has something to do with saving the document online in onenote. But that works like the file is saved on the Pc's harddrive.

Are there anybody else that has experienced this?

I calculate with units, but as the varible does not appear in the calculation with units, I make one varible with the same result, to get the next calculation to work.

Regards

Heide

## Why won't this procedure compile?...

Why won't this procedure Compile? All I get is a cryptic and ungrammatical error message.

step:= proc(
n::integer[4],
XYZ::Matrix(datatype= float[8]),
E::Vector(datatype=integer[4]), F::Vector(datatype=integer[4]),
W::Matrix(datatype= float[8]), #3x2 scratch matrix
mu::integer[4]
)
option autocompile;
local
i::integer[4], j::integer[4],
ed::float[8],
fd::float[8],
p::float[8], t::float[8]
;
to mu do
for i to n do
ed:= 0;  fd:= 0;
for j to 3 do
p:= XYZ[i,j];
t:= XYZ[E[i],j] - p;
ed:= ed+t^2;
W[j,1]:= t;
t:= XYZ[F[i],j] - p;
fd:= fd+t^2;
W[j,2]:= t
od;
ed:= sqrt(ed) + .01;  fd:= sqrt(fd) + .01;
for j to 3 do
XYZ[i,j]:= 0.995*XYZ[i,j] - 0.01*W[j,1]/ed + 0.02*W[j,2]/fd
od
od
od
end proc;
Compiler:-Compile(step);

Error, (in Compiler:-Compile1) In memory compilation failed

## A strange result from dsolve...

Hello guys,

I was just playing around with differential equations, when I noticed that symbolic solution is  different from the numerical.What is the reason for this strange behavior?

ODE := (diff(y(x), x))*(ln(y(x))+x) = 1

sol := dsolve({ODE, y(1) = 1}, y(x))

a := plot(op(2, sol), x = .75 .. 2, color = "Red");
sol2 := dsolve([ODE, y(1) = 1], numeric, range = .75 .. 2);

with(plots);
b := odeplot(sol2, .75 .. 2, thickness = 4);
display({a, b});

Mariusz Iwaniuk

## Problem with KelvinBei function...

Hello,

I need to crate a function to be evaluated in a range of values, and this function i would to use in other expression, example:

cel1      "seq(i,i=0.001..2,0.001)"

cel2      "A:=&1";cel1

cel3      "f:=x->diff(KelvinBei(0,x),x)"

cel4      ""B:=map(x->f(x),[A])"

This is ok with a lot of function but with diff(KelvinBei(0,x),x) in cel4 show this error "Error,(in f) invalid input:.1e-2, which is not valid for its 2nd argument.

Why??? How can I do??

## Why difference in speed?...

The first example is very slow compared to the second.  The difference is in the definition of f().

restart;
y := int(1/(-0.4016e-1*m^(2/3)-0.211e-3*m^(5/3)), m);
f:= unapply(abs(y), m):
n := 500: ## sample size
M := <seq(2*idx/n,idx=1..n)>; ## m
Y := f~(M)+~Statistics:-Sample(Normal(0,3), n)^+; ## signal + noise

restart;
y := int(1/(-0.4016e-1*m^(2/3)-0.211e-3*m^(5/3)), m);
f:= (x) -> abs(subs(m=x,y));
n := 500: ## sample size
M := <seq(2*idx/n,idx=1..n)>; ## m
Y := f~(M)+~Statistics:-Sample(Normal(0,3), n)^+; ## signal + noise

## How to project a fixed object illuminated by a mov...

The code below projects a torus illuminated by a point light source located at the origin onto an ellipsoid as the torus's centre moves along the x axis from [-0.8,0,0] to [0.8,0,0].

Ellipsoid := (1/32)*x^2+(1/18)*y^2+(1/12)*z^2 = 1:
EllipsoidTitle := Typesetting:-Typeset((1/32)*x^2+(1/18)*y^2+(1/12)*z^2 = 1):
DispEllipsoid := implicitplot3d(Ellipsoid, x = -10 .. 10, y = -10 .. 10, z = 1.25 .. 5, style = surface, color = yellow, grid = [30, 30, 30]):
TorusVorig := Vector([(1+.25*cos(v))*cos(u), (1+.25*cos(v))*sin(u), .6+.25*sin(v)]):

i := 0;

for x from -.8 by .1 to .81 do

i := i+1;

TorusV := `<,>`(x, 0, 0)+TorusVorig:

DispTorusV := plot3d(TorusV, u = 0 .. 2*Pi, v = 0 .. 2*Pi, shading = xyz):

NormTorusV := Normalize(TorusV, Euclidean):

Vadj := solve((1/32)*w^2*NormTorusV[1]^2+(1/18)*w^2*NormTorusV[2]^2+(1/12)*w^2*NormTorusV[3]^2 = 1, w):

if evalf(eval(Vadj[1]*NormTorusV[3], [u = Pi, v = Pi])) > 0 then

DispTorusVproj := plot3d(Vadj[1]*NormTorusV, u = 0 .. 2*Pi, v = 0 .. 2*Pi):

else

DispTorusVproj := plot3d(Vadj[2]*NormTorusV, u = 0 .. 2*Pi, v = 0 .. 2*Pi):

end if:

Disp[i] := display(DispTorusV, DispEllipsoid, DispTorusVproj, view = [-10 .. 10, -10 .. 10, 0 .. 5], scaling = constrained, Plot3Daxes, title = typeset("Project %1 onto %2 from a light at the origin", TorusV, EllipsoidTitle), titlefont = [Courier, bold, 14]):

end do:

display(seq(Disp[j], j = 1 .. i), insequence = true);

How can I plot the unmoving torus centred on the z axis projected onto the ellipsoid illuminated by a point light source moving on the x axis from [-0.8,0,0] to [0.8,0,0]?

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