DarkMath

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@ecterrab Thank you. It worked.

I see that vectors in Physics[Vectors] are defined as vector fields, is that correct?

If you are working topology, group theory, graph theory,etc.; then SageMath should be your number one choice. The developers of SageMath are matematicans from these fields. So, my recommendation would be that instead of choosing Maple to be your primary platform and tyring to link SageMath to Maple, go with SageMath and link Maple to it for this particular project of yours. Hence you will get the best of both.

@Carl Love Thanks. This is what I have been looking for. And also the code is very instructive.

@nm In SageMath you can.  So, generalizing "..there is no such thing, and there will never be such thing in CAS." is a very unfortunate statement.

You can input a 1st order differential equation as 

ode=-(x^2+x*y(x))*diff(x)+1*diff(y(x))==0

and it is a very valid statement. For me, It really doesn't matter how internally a CAS represents this. SageMath represents it as the following before it is sent to desolve

-x^2-x*y(x)+diff(y(x),x)==0

The bottom line is I shouldn't have to be forced to enter a differential equation in the derivative form. The differential form of a 1st order differential equation is a very common form one can see in any text book and I don't see why it shouldn't be in any CAS let alone Maple. 

 

@acer I don't actually need to use Pi/6 but just that Maple gave me that error somehow shattered my understanding of the way Maple handles vectors. But what I see is that this is a problem with Maple. Is it considered a bug?

@tomleslie No problem :)

@tomleslie I re-read it again and I still think that my question is not answered there.

The dot product of a free vector (cartesian) with a rooted vector (spherical): no error is given when theta=pi/4, but throws an error when theta=pi/6. If this behaviour is explained, could you please kindly point me to where it is written exactly then?

@tomleslie This question is actually inspired from an expample on that page. I thought during the dot product, it converts the free vector into rooted vector using the rooted vectors root, but apparently, it doesn't and I am confused. 

@vv @Carl Love Thanks a lot. I really like this way of solving. Much better than writing a for loop 

@Carl Love Makes sense. I hope Maplesoft integrates this in the next version

@Carl Love In @Axel Vogt 's example above. It shouldn't be related to (explicit,allsolutions), though. Since there is only one root, but still the integral is left unevaluated. Don't you think so?

@Carl Love Are those ineffective epecially against differential equations? or ineffective in general?

@Axel Vogt Could this be a bug? or something else going on?

@acer I was just about to ask how to get all the solutions for a given interval. 

Thanks for the example. It is weird that I didn't see those keywords under solve's documentation. Did I miss something?

I tried this 

solve({sin(x)},x,real,explicit,allsolutions) assuming -3/2*Pi<=x<=3/2*Pi

But this gives 

{x=Pi_Z14~}

I take Z14 is just an arbitrary constant here, but this means that it didn't take the assumption into acount. 

So, using assume like this is not allowed in solve?

@nm This is exactly what I initially did to verify the result 3. I was expecting Maple to handle this easily, though. 

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