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Are you solving the equations symbolically or purely numerically? And exactly, or approximately in floating point? (Do you use solve or fsolve?)

Is it even possible that you are lucky enough that an approximate solution step might be replaced by an exact solution which could be more quickly/efficiently evaluated at different numeric parameter values?

What are you doing with all the solutions? Are you making Maple hold on to them all at once? Perhaps you could write/save them to a file while also releasing/unassigning the names to which they were assigned, so as to allow Maple to do memory managment in the form of garbage collection.

Another tool for replacing some old with new is `eliminate`.

For example, using the equations given above

> eliminate({Eq1,Eq2},{OldVar1,OldVar2}):

> %[2][1]=0;

                           -OldVar6 OldVar5 + OldVar3 NewVar = 0

Another tool for replacing some old with new is `eliminate`.

For example, using the equations given above

> eliminate({Eq1,Eq2},{OldVar1,OldVar2}):

> %[2][1]=0;

                           -OldVar6 OldVar5 + OldVar3 NewVar = 0

@vie_charlie It's hard to say much more that could help without access to all the underlying code and routines. Are you at liberty to upload a worksheet (green arrow button) so that we could see/run it all?

@vie_charlie It's hard to say much more that could help without access to all the underlying code and routines. Are you at liberty to upload a worksheet (green arrow button) so that we could see/run it all?

@afeddersen I added this example, if it helps. Note the denominator.

MyExpectedValue(X,t->(1-exp(-phi*t))/t);

But it's since been pointed out that ExpectedValue does in fact support the application of a weighting function directly. Namely,

u := t->(1-exp(-phi*t)):
Statistics:-ExpectedValue(u(X));

So it is not necessary to go to the trouble of creating a new random variable with weighted PDF as I did above. But it does work.

@afeddersen I added this example, if it helps. Note the denominator.

MyExpectedValue(X,t->(1-exp(-phi*t))/t);

But it's since been pointed out that ExpectedValue does in fact support the application of a weighting function directly. Namely,

u := t->(1-exp(-phi*t)):
Statistics:-ExpectedValue(u(X));

So it is not necessary to go to the trouble of creating a new random variable with weighted PDF as I did above. But it does work.

I'd be really impressed if anyone could model the Jabulani's behaviour in Maple/MapleSim well enough to show the purported instability of that relatively lighter ball at higher speeds/altitude. (It may not be necessary to achieve fluid dynamics simulation for this, if the seam pattern's effect could be combined with oscillating wake driving forces. I don't know.)

Sorry, in my excitement I forgot what Maple was taking as the princpal branch.

But doesn't the example using the RealDomain package still pertain?

Sorry, in my excitement I forgot what Maple was taking as the princpal branch.

But doesn't the example using the RealDomain package still pertain?

@herclau Why not just use SingularValues(A,output=['U','S','Vt']) instead of the output=list in a separate call to get the S?

Maple computes the singular values anyway, internally, during the computation of the left and right singular vectors in U and Vt. So it's a waste of resources to have it go back and compute S separately. Also, if you compute them all together then they all get calculated using the same working precision (and by default that is external hardware double precision).

If you really want to round the results down to less digits, after computation, then that's one thing. But it's not a good idea to decrease the working precision of a computation just so that the final results are nicely rounded.

@herclau Why not just use SingularValues(A,output=['U','S','Vt']) instead of the output=list in a separate call to get the S?

Maple computes the singular values anyway, internally, during the computation of the left and right singular vectors in U and Vt. So it's a waste of resources to have it go back and compute S separately. Also, if you compute them all together then they all get calculated using the same working precision (and by default that is external hardware double precision).

If you really want to round the results down to less digits, after computation, then that's one thing. But it's not a good idea to decrease the working precision of a computation just so that the final results are nicely rounded.

You can extract operands in a few ways. One way is to use op (again, or repreatedly). Another way is to index into a partial result by postpending with [] or [1] where legitimate. Or you can mix your approaches, if a structure is more deeply nested.

 PiecewiseTools:-ToList is an undocumented routine, which would probably help you only as much as op and others.