The runtime redistributables of some MKL v11.x exist in Maple 18.01 for 64 bit Linux and OSX. I have obtained some performance results for the cited Matrix float[8] Rank test using Maple 18.02 that are pretty much identical to those of Mathematica 9 and 10, on those two platforms. I tried up until about size 2500x2500. (See also this post and comment.)

The version of MKL used in Maple 18.x on 32 and 64bit Windows appears to be some v10.x, which series dates from about 2008-2009. And on the 64bit Windows platform (which is what Nasser used in the first link you've cited) there is still a discrepancy. A quoted timing of 0.35 sec for computing all the singular values of a 1000x1000 float[8] Matrix is pretty fast, but not as fast as the quoted timing for Mathematica as 0.16 sec.

The author of the pages in the first link you gave posted in the Wolfram Community forum a while back. He encountered new out-of-memory problems when running his test at larger sizes in Mathematica 10. He apparently resolved that by setting a preference to disable the new multi-undo feature.

acer

One way is to use a customized system. Eg, compare the before and after.

restart:

Unit(m^2*kg/(s^4*A));

simplify( Unit(m^2*kg) / Unit(s^4*A) );

simplify( 1/Unit(s) );

with(Units):
AddSystem( MySI, GetSystem(SI), volt/microsecond, hertz );
UseSystem( MySI );

Unit(m^2*kg/(s^4*A));

simplify( Unit(m^2*kg) / Unit(s^4*A) );

simplify( 1/Unit(s) );

This should also work with Units[Standard] functionality, combine(..,units), etc.

Note that other poswers of these dimensions are not necessarily affected. To get 1/second^2 to come out as Hz^2 you'd need to also include hertz^2 in the additional arguments, when defining the new system. Etc.

Another way is to just compute with some stock system like SI, and then convert final results. Eg,

restart:
convert( 55*Unit(mm^2*g/(ms^4*A)), units, volt/microsecond );

acer

add(x, x in A);

or,

convert(A,`+`);

or, (essentialy like the last one),

`+`(A[]);

acer

If you are not using high precision (ie, Digits > evalhf(Digits) ) then you may as well just use method=LU. And that is the default method for such float data.

Below, I set the infolevel so that some additional details about the computation are shown.

restart;
with(LinearAlgebra):

infolevel[LinearAlgebra]:=2:

A:=Matrix([[1,3],[2,5]],datatype=float):
b:=Vector([1,1],datatype=float):
LinearSolve(A,b);

LinearSolve: using method LU
LinearSolve: calling external function
LinearSolve: NAG hw_f07adf
LinearSolve: NAG hw_f07aef
                                    [-2.]
                                    [   ]
                                    [ 1.]

acer

The display command is part of the plots package. So either load that package first, by issuing,

with(plots):

or call it by its long-form names plots:-display or plots[display].

I edited your code a bit. As a general rule, don't try and use a non-indexed name such as x alongside its indexed form such as x[i]. Check that I didn't mess it up.

restart:

h := .1;
x[0] := 0;
y[0] := 1;
xf := 3;
n := floor(xf/h);
f:= (x,y)->1/(3*y-x-2);

for i from 0 to n do
k1 := f(x[i], y[i]);
k2 := f(x[i]+(1/2)*h, y[i]+(1/2)*h*k1);
k3 := f(x[i]+(1/2)*h, y[i]+(1/2)*h*k2);
k4 := f(x[i]+h, h*k3+y[i]);
k := (k1+2*k2+2*k3+k4)*(1/6);
y[i+1] := h*k+y[i];
x[i+1] := x[i]+h
end do:

data := [seq([x[n], y[n]], n = 0 .. 30)]:

p[2] := plot(data, style = point, color = blue):
p[3] := plot(data, style = line, color = blue):

exact := dsolve( { diff(Y(X),X)=1/(3*Y(X)-X-2), D(Y)(0)=1 } ):

Pexact := plot( eval(Y(X), exact), X=0..3, style=point,
                symbol=cross, symbolsize=20,
                adaptive=false, numpoints=20 ):

plots:-display(seq(p[n], n = 2 .. 3), Pexact);

acer

What you see at the end of the AiryBiZeros procedure is an unevaluated return. Notice the single right-quotes in that function call, which will be a return value.

It just means that, when argument n is something for which the procedure cannot compute a result then the procedure returns an unevaluated function call to itself.

acer

In your example eq is of type `=` and lhs(eq) is of type `+`.

The op command allows you to pick off specific operands (addends of the sum), by position.

restart:

act := proc(eqn)
  if type(eqn,`=`) and type(lhs(eqn),`+`) then
    eqn - op(2, lhs(eqn));
  end if;
end proc:

act( a + b = 0 );

                             a = -b

act( a + b + c = 0 );

                           a + c = -b

acer

eq := (a*b+a)^n * a^(-n):

new := (b+1)^n:

eval( [eq, new], [a=-1, b=-2, n=1/2] );

                            [-I, I]

simplify(eq) assuming real, a>=0;

                                   n
                            (b + 1) 

simplify(eq) assuming n::integer;

                                   n
                            (b + 1) 

acer

Remove the inert=true option.

If you include that option then it returns an inert integral. If you don't then it tries to compute the integral.

acer

What all these do... is another question.

restart:
interface(warnlevel=0):
started := false:
T := 'T':
for i from 1 to 1000 do
  f := eval(parse(cat("proc() option builtin=",i,"; end proc")));
  p := (s->StringTools:-Take(s,StringTools:-Search(";",s)-1))(convert(eval(f),string)[26..]);
  if not type(parse(p),posint) then
    T[i] := p;
    started := true;
  else
    if started then i:=1000; next; end if;
  end if;
end do:
i;
[ entries(T,nolist) ];
nops(%);

acer

Try setting infolevel[`pdsolve/numeric`] before calling the solver.

For example,

infolevel[`pdsolve/numeric`]:=2:

At value 2 I am seeing a brief description, such as, "Deriving 3-point (space) theta scheme for input PDE". At value 3 I am seeing printout of what appear to be differencing procedure(s).

acer

One way to get that smoother is to use the `gridrefine` option of implicitplot. Eg,

plots:-implicitplot(-x^3+3*x+a = 0, a = -3 .. 3, x = -4.0 .. 4.0,
                         view = [-3 .. 3, -4 .. 4], gridrefine = 2);

acer

Try that as `Or`, rather than `OR`.

acer

Look at the help page with topic examples,Explore for the cobweb plot of the logistic map.

For the bifurcation diagram see this message threa on this site.

acer

How you go about it may depend on whether you want to be able to programmatically access any displayed values after manually updating them in the tabulated representation.

If you insert a DataTable Embedded Component from the palettes then you can associate that with a Matrix or Array. This includes the functionality that if you update the Matrix then the DataTable entry reflects that. And vice versa. Also, you can put customized row and column headers on the Component. There is no command at present to insert such a DataTable via a command. (I suspect that it might be done with some very low level XML manipulation, but it is not straightforward and the insertion may be buggy.)

If you only need to display the data and not to interact with it (as you've stated is the case) then there are some undocumented routines that can accomplish this. (These are evident by inspectng the Explore:-ModuleApply and ImageTools:-Embed library procedures.) Of course your success might be limited, with undocumented routines. For example, using Maple 18.01, with the purely numeric entries of data being represented as strings,

restart:

makegrid := proc(M::Matrix)
  uses DocumentTools:-Layout;
  local i,j,m,n,wks;
  m,n := op(1,M);
  wks := Worksheet(Table(alignment=center,width=20,
                         seq(Column(),j=1..n),
                         seq(Row(seq(Cell(Textfield(sprintf("%a",M[i,j]))),
                                     j=1..n)),i=1..m)));
  DocumentTools:-InsertContent(wks);
end proc:

f:=x->x^2:
g:=x->x^3:
data:=[seq([i,f(i),g(i)],i=0..5)]:

makegrid(<<'i'|'f(i)'|'g(i)'>,Matrix(data)>);

In Maple 17 the following seems possible. This makes a little effort at weighting the width of the columns according to string length. (That weighting will break down if the entries are long enough to line-wrap, I think.)

restart:

grid := proc(M::Matrix)
  uses DocumentTools:-Layout;
  local i,j,Ms,m,n,wks;
  m,n:=op(1,M);
  Ms:=map(convert,M,string);
  wks:=XMLTools:-ToString(
         _XML_Worksheet(Table(':-alignment'=':-center',':-width'=20,
           seq(Column(':-weight'=3+max(map(length,Ms[..,j]))),j=1..n),
           seq(Row(seq(Cell(`_XML_Text-field`("alignment"="centred",
                                              "style"="Text",Ms[i,j])),
               j=1..n)),i=1..m))));
  streamcall(INTERFACE_TASKTEMPLATE(':-insertdirect',':-content'=wks));
  NULL:
end proc:

f:=x->x^2:
g:=x->-x^13:
data:=[seq([i,f(i),f(i)/g(i)],i=1..5)]:

grid(<<'i'|'f(i)'|'f(i)/g(i)'>,Matrix(data)>);

The mechanism used above is not in Maple 16 or earlier, so this won't work there.

acer