AmirHosein Sadeghimanesh

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4 years, 8 days

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Finished Ph.D. in Applied Algebraic Geometry in Biology and now postdoc in Mathematics of Chemical Reaction Networks, University of Copenhagen. Main interests; Applied and Computational Algebraic Geometry, Mathematical Biology. I'm also a language lover!

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These are questions asked by AmirHosein Sadeghimanesh

Assume we have an expression in several variables, x,y,z,..., where all of them are function of one parameter, t, for an example consider the following simple expression;

f := 2*y(t)*(diff(x(t), t))^2+3*(diff(x(t), t$3))-3*x(t)*(diff(y(t), t));

Is there any command or a way to ask Maple to give the highest order of derivation of x or y with respect to t in the expression? For example in the above example, the answer for x is 3 and for y is 1. If we remove the second term, then the answer for x should be 1.

I'm using Maple on a compute server (via Putty from my computer which has windows system). It is an only-text mode server so it is a black screen and text and no menu bar to choose file and then save by clicking etc. You only can write commands and press Enter.

The IT section suggested to use writeto("filename.txt"), but I can't see any file on my drive, I used writeto("\drvename\filename.txt"), but still nothing.

Thanks to @acer@Joe Riel and the IT section. The problem now is solved. It was about the way that I was writing the directory path. I had to add something before the "drivename" in my case. Plus that it is a Unix path, so I should use / not \.

Here I put two functions defined by piece-wise command and then using int(...,numeric) to take their integration but Maple computes only one while for the other one just gives the expression back. The integration domain is bounded, the function is bounded too so I don't think the reason is being divergent in the one that Maple is not computing it.

Is there any prepared command or package for Maple which computes the integrals like this or is better than just int(...,numeric)? Or I have to write an algorithm an force Maple to compute my integral using an algorithm given by myself?
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The codes in plain text:
 

int(piecewise(0 < -k5*x1*x2+k1*x1 < 1, 1, -k5*x1*x2+k1*x1 <= 0 and 1 <= -k5*x1*x2+k1*x1, 0)*piecewise(0 < -k5*x1*x2+k2*x2 < 1, 1, -k5*x1*x2+k2*x2 <= 0 and 1 <= -k5*x1*x2+k2*x2, 0), k1 = 0 .. 1, k2 = 0 .. 1, k5 = 0 .. 1, x1 = 0 .. 1, x2 = 0 .. 1, numeric);
int(piecewise(0 < x+y < 1, 1, x+y <= 0 and 1 <= x+y, 0)*piecewise(0 < y*x^2 < 1, 1, y*x^2 <= 0 and 1 <= y*x^2, 0), x = 0 .. 1, y = 0 .. 1, numeric);

 

We know that Grid:-Map(x->f(x),[x1..xn]) is for parallel computing f(xi)'s but when some xi's are equal I think Maple copies one result for the others. But maybe my function f has some random sampling inside and so will have different output for same inputs. So I need to do parallel computations for same inputs without cheating of copying the result of one for the rest. For a very simple case that Maple copies while it is wrong to copy, see the following.

I will be happy if someone tells me how to solve this issue. Thanks.

More surprising to me is that if I try to use different xi's and then typing same xi's, I will see some new patterns of copying. 

For example in output (3) and (4), first random point of one parallel computation is the second random point of another computation. Or in output (6) only the two last computations are copy of each other!

 

I may need to add that I did this computations on a computer with 4 core processor. Is Maple producing random numbers using something like processor's time? Or something like this?
I can't report Maple computations if they don't really produce random points independently in seperate parallel computations.

If I type pi, Maple just show what I typed, but if I insert the Greek letter pi, then it works. Are there other things that I should take care of them when I'm using "floor" command in my programming?

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