jakubi

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These are replies submitted by jakubi

If you want to keep the float condition and allow your procedure to use also ScientificErrorAnalysis:- Quantity objects, one possibility is adding the function type as in:

dWdt:=proc (t::{float,function}) ...

I have not looked at point 1 yet.

If you want to keep the float condition and allow your procedure to use also ScientificErrorAnalysis:- Quantity objects, one possibility is adding the function type as in:

dWdt:=proc (t::{float,function}) ...

I have not looked at point 1 yet.

For examples as described above, i.e. when using int or dsolve, I have the impression that the most frequent case is probably not well described as a race (which algorithm succeeds first) but as a selection (which algorithm ever succeeds, if anyone does).

I wonder how far, for these computations the "correct order" (or even which algorithm could succeed) is something that can be assessed a priori for a given input, or it is an open question.

I do not find that the available documentation of these commands provide useful information justifying the choice of the default order, or describe when alternative orders would be better.

Talking about eventualities, if the library routines are so hard to parallelize so that it becomes a target for the far future,. but anyway running these alternative algorithms in parallel is deemed beneficial in the forthcoming O(10) core era, what about executing each algorithm in a separate independent kernel?

 

Some computations like the symbolic evaluation of a definite integral or solving an ordinary differential equation proceed, in general, I think, by trying a sequence of  independent methods until someone is succesful.  So, at least naively, it sounds to me like these sequential computations could be parallelized.

Does it make sense?

 

I mean adding this property for exclusive use in the symbolic domain, i.e. for symbolic manipulations, and not for numeric computations.

 

An "atomic identifier" or "literal name" is a kind of name to be used for typesetting purposes in Standard GUI. See ?worksheet,documenting,2DMathDetails#identifiers.

You may input them by clicking on menus and palettes, which is clumsy for me; or by typing their MathML like syntax at the (1D or 2D) input, which is also clumsy. For instance you get omega with subindex 0 by:

`#msub(mi("omega"),mn("0"));`;

An "atomic identifier" or "literal name" is a kind of name to be used for typesetting purposes in Standard GUI. See ?worksheet,documenting,2DMathDetails#identifiers.

You may input them by clicking on menus and palettes, which is clumsy for me; or by typing their MathML like syntax at the (1D or 2D) input, which is also clumsy. For instance you get omega with subindex 0 by:

`#msub(mi("omega"),mn("0"));`;

Yes, you could to add tracing commands to your program. See e.g. ?infolevel, ?trace, ?printlevel .

 

Yes, you could to add tracing commands to your program. See e.g. ?infolevel, ?trace, ?printlevel .

 

Certainly, infinity has multiple meanings. It should go as symbol like here:

is(I*infinity,OrProp(real,identical(-infinity),identical(infinity)));
                   false

For instance:

ss1:=-F[0]*(-sin(omega*t)*omega_0^2+sqrt(omega^2*(1+omega^2))*
cos(omega*t-arctan(omega^2, omega)))/
(omega^2+omega_0^4-2*omega_0^2*omega^2+omega^4):

expand(ss1):
collect(%,[sin,cos],factor):
convert(%,phaseamp,t): 
simplify(%) assuming omega^2+omega_0^4-2*omega_0^2*omega^2+
omega^4>0,F[0]>0;
                                        2          2
        F[0] cos(omega t - arctan(-omega  + omega_0 , -omega))
        ------------------------------------------------------
               2          4            2      2        4 1/2
         (omega  + omega_0  - 2 omega_0  omega  + omega )

 

For instance:

ss1:=-F[0]*(-sin(omega*t)*omega_0^2+sqrt(omega^2*(1+omega^2))*
cos(omega*t-arctan(omega^2, omega)))/
(omega^2+omega_0^4-2*omega_0^2*omega^2+omega^4):

expand(ss1):
collect(%,[sin,cos],factor):
convert(%,phaseamp,t): 
simplify(%) assuming omega^2+omega_0^4-2*omega_0^2*omega^2+
omega^4>0,F[0]>0;
                                        2          2
        F[0] cos(omega t - arctan(-omega  + omega_0 , -omega))
        ------------------------------------------------------
               2          4            2      2        4 1/2
         (omega  + omega_0  - 2 omega_0  omega  + omega )

 

This is the six pages Maple V Release 5 product brochure. It has been split into individual files, one for each page, because of the 800KB upload limit:

Page 1
Page 2
Page 3
Page 4
Page 5
Page 6

Yes, I have a pdf brochure of Maple V Release 5 (and a review of R4 in the journal PERSONAL ENGINEERING, August 1996).

 

Yes, I have a pdf brochure of Maple V Release 5 (and a review of R4 in the journal PERSONAL ENGINEERING, August 1996).

 

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