Is it possible to show using maple if a given line in 3d space intersects a 2d plane with given co-ordinal vertices?

Ive been given a task to write a fuction that will print true/false to if a given line will intersect a triangle given the co-ordinates of the vertices. 
I have a general idea on what needs to be done mathmaticly, but i have poor maple skills and the syntax is killing me.
I would appreciate some help in this regard.

Thanks.

Warning: I am newbie in Maplem so if I am missing something obvious, please do not scream at me.

I noticed something strange here. I was trying to simplify this expression to sinh(x). The first step is to convert it to exp() form. Then the next step should have been just another convert to sinh since the resulting exp() expression from the first step was clearly a sinh(). Yet, I find that expand() and also simplify() in order for Maple to see this.

So my question is, what are the rules of the game here? Does one really have to baby step the simplification process like this to the extent of telling Maple that

is the same as

by using simplify(), before getting the result needed?

Here is the code: (the goal again is to obtain sinh(x) as final simplification)

%------ this works --------------
s:=(1/2)*exp((1/2)*x)*(cosh((1/2)*x)-cosh((3/2)*x)+sinh((1/2)*x)+sinh((3/2)*x));
convert(s,exp);
expand(%);
simplify(%);   %-----> without this, will not work
convert(%,sinh);
%--------------------------

but

%---- this does not ----------------
s:=(1/2)*exp((1/2)*x)*(cosh((1/2)*x)-cosh((3/2)*x)+sinh((1/2)*x)+sinh((3/2)*x));
convert(s,exp);
expand(%); 
convert(%,sinh);  % is simplify really needed BEFORE this step?
simplify(%);  % 
----------------------------

Fyi, in Mathematica, I only needed to convert to exp() and back again to Trig to get the answer:

Or using Simplify

I've been on this question a week now and still no conclusive answer! What I need is a function that produces the inequalities that determine a triangle given the 3 points and then using a 4th point, prints true if the 4th point satisfies 2 or 3 or the inequalities and prints false if it only satisfies 1 or none of the inequalities. I need to have this solved by tonight so any quick help would be greatly appreciated!

Consider the curve defined by f(x, y) = 3+2x+y+2x^2+2xy+3y^2 = 0.Locally on the curve we can view y as a function of x, i.e. y = y(x).Compute formulas for the first and second derivative of y with resoect to x.

2. Give the Maple command(s) to compute \frac{\partial^8 f}{\partial^5 x \partial^3 y} for f(x, y) = e^{2x+ cos(y)}.

Ok so my problem is that I need to write a function which produces the three inequalities defining a triangle given the 3 points that form its vertices, then with the 4th point supplied to the function I need the function to print false if the 4th point satisfies less than 2 of these inequalities and true if it satisfies more than 2 of these inequalities. Can anybody help me with this? On a previous post I obtained part of the function that produces the triangle, but the 2 inequalities part was not solved.

Thanks for your time

How to show the code in file with extension .lib and edit it?

Hi,

I'm new to these forums. I'm using Maple 17. What am I missing about the odd behaviour exhibited below? (the code can be copy pasted into Maple)

Suppose I define m,n,p,q as integers and x as real, then define the function h(x,m,n,p,q) below.

assume(m::integer, n::integer, p::integer, q::integer, x::real);
h:=(x,m,n,p,q)->-(1/8*I)*(exp((2*I)*Pi*x)-1)^2*(exp(-(2*I)*Pi*x*(n-q+2))-exp(-(2*I)*Pi*x*(n-q+1)))/(Pi^3*x*(m-x)*(p-x));

If I do:

int(h(x, m, n, p, q), x = -infinity .. infinity)

It says it's 0, but that's not true. The integral is not always 0 but depends on m,n,p,q ... and even Maple acknowledges this. If I do:

int(h(x, 1, 1, 1, 1), x = -infinity .. infinity)

I get -(1/2*I)/Pi ... so clearly not 0.

Also, if I do:

int(h(x, m, n, m, n), x = -infinity .. infinity)

I get -(1/2*I)/(m*Pi) ... again, not 0.

What am I missing? How can I correct this and obtain the analytic expression for int(h(x, m, n, p, q), x = -infinity .. infinity)?

Trying without the assume() causes Maple to run into issues not knowing anything about m,n,p,q.

[ Edit: I finally solved the integral on paper, see my post below if you're curious. The Maple inconsistency and wrong result explained above are still there though ]

Any help would be greatly appreciated.

Regards,

Alex.

I am not able to find way to do this very basic and common operation.

I use worksheet mode, and many times I'd like to split/divide a large execution group I've build of some code to 2 execution groups at some place. i.e. I'd like to point my mouse at a line and say divide here. Here is an example:

I see only the options Insert->Execution group-> After Cursor or Before cursor. Both of which do not do what I want. I want to divide it at that point.  So what I end up doing is to make a new execution group manually (using the Insert command), then go back and cut and paste the code I want in the new group.

I hope there is an option to do this. I do these sorts of things all the time when using Mathematica, which has Divide cell, Merge cells and other options. A cell in Mathematica is similar to execution group in Maple. Are there other options to maniuplate execution groups other insert before/after cursor that I might have missed? I am using 17.02 on windows 7.

Please note, I only use worksheet mode.

I am stuck with an IVP which is

eq1:=diff(y(x),x$2)+2/x*(diff(y(x),x))+y^M=0;

ic:=y(0)=a,D(y)(0)=0;

its quite easy to find the series solution of the ode 

dsolve({eq1, ic}, y(x), series);

y(x)=a-(1/6)*exp(M*ln(a))*x^2+(1/120)*(exp(M*ln(a)))^2*M*x^4/a;

But I am facing problem when I try to solve it numerically,

dsolve(subs(a=1,M=3,{eq1,ic}),numeric);

THanks

Hello

Am trying to convert a vector projection to matrix type output.

Attached is a sample worksheet.

Transformation_matri.mw 

Consider:

> restart:
> int(exp(I*x)/x,x=-infinity..infinity,CauchyPrincipalValue)
                                                                                                   Pi I

> int(exp(I*3*x)/x,x=-infinity..infinity,CauchyPrincipalValue)
                                                                                                   Pi I

> int(exp(I*k*x)/x,x=-infinity..infinity,CauchyPrincipalValue) assuming k::positive;
                                                                                                  2 I Pi

I would expect the last line to also give me Pi I

Mathematica gives a Pi I via:

FullSimplify[Integrate[Exp[I k x]/x, {x, -\[Infinity], \[Infinity]}, PrincipalValue->True, Assumptions->{k>0}],  Assumptions->{k>0}]

Any idea what this could be?

thanks.

intEq:= 2*cosh(x)-sinh(x)-(2-x)= 1 + int( (2-x+t)* phi(t),t=0..x):
intsolve(intEq,phi(x));

I'd like to extract the (1/2) out, so that it shows as (1/2)*exp(x/2) *  (cosh(x/2) - etc....)

Any recommended way to do it? My attempts did not work well. I am newbie in Maple. Thanks.

I need to make a graph that has dates 1/14/2000 on the x axis and intrest rates on the y axis but when i import my spread sheet from excell the dates keep getting converted into lager numbers like 37000 for some reason and i cannot figure out how to stop this odd conversion. Has anyone encountered this?? i tried looking up dates in maple hepl but cant find much on this topic. Hope i explained what is happening well enough. Graph_One_b.mwGraph_One_b.mw