acer

8 years, 335 days


These are answers submitted by acer

multiplication intended?

9 hours ago acer 10101
3 0

If you intend that expression as a multiplication (and not as a compound function application) then insert an explicit multiplication sign (ie. the * on you keyboard) between the two bracketed terms.

(x-4)*(x-4);

                                   2
                            (x - 4) 


(x-4)(x-4);

                          x(x - 4) - 4

Otherwise your input would can get parsed as the function application x(x-a) - a(x-a). That is, the compound operator (x-a) applied to the argument x-a.

Note that 4 applied to x-4 (or pretty much anything) produces a result of 4.

There are some situations, including your example, where an extra blank space between the two bracketed terms would also get interpreted implicitly as a multiplication, if you used 2D Math input mode. In 1D Notation that would produce a parsing error. It can get more confusing still. I suggest getting in the habit of always using an explicit multiplication symbol, to avoid ambiguous situations with implicit multiplication.

acer

cat

9 hours ago acer 10101
1 0

One way is to make your absolutely qualified filenames be a concatenation of a base location and some relative paths.

# Uncomment the line you want, and comment out the line you don't want.
#base:="C:/officeplace/location 1/":
#base:="C:/homecomputer/location 2/":

datafileA:=cat(base,"fileA.txt");
datafileB:=cat(base,"../../folderQ/fileB.txt");

readdata(..., datafileA, ...);
...
readdata(..., datafileA, ...);
...

Another way could be to use the currentdir command to set the current working directory.

acer

14.01 or 14.00?

August 28 2014 acer 10101
1 1

I see white grid line artefacts using f=1 for that densityplot in Maple 14.00, but they do not appear for me in Maple 14.01.

I am using 64bit Linux.

You might have to contact Maplesoft Tech Support in order to get the point-release update to 14.01, as it's no longer available here I believe.

[edited] You might be able to get the 14.01 update from here.

acer

block diagonal

August 27 2014 acer 10101
2 1

If I understand what you want then here are two ways to form the block diagonal Matrix result, using repeats of the Matrix Q as the blocks.

restart:                 
Q:=Matrix([[1,2],[3,4]]):
N:=3:                    

LinearAlgebra:-DiagonalMatrix([Q$N]);

                         [1    2    0    0    0    0]
                         [                          ]
                         [3    4    0    0    0    0]
                         [                          ]
                         [0    0    1    2    0    0]
                         [                          ]
                         [0    0    3    4    0    0]
                         [                          ]
                         [0    0    0    0    1    2]
                         [                          ]
                         [0    0    0    0    3    4]

Matrix([Q$N],scan=diagonal);

                         [1    2    0    0    0    0]
                         [                          ]
                         [3    4    0    0    0    0]
                         [                          ]
                         [0    0    1    2    0    0]
                         [                          ]
                         [0    0    3    4    0    0]
                         [                          ]
                         [0    0    0    0    1    2]
                         [                          ]
                         [0    0    0    0    3    4]

acer

format for printf/sprintf

August 26 2014 acer 10101
2 0

There are formatting options for sprintf (and friends) which support this directly. It is fast and lean on memory use. The code below also works in Maple 12.

> M:=Matrix(3,[[1,2,3],[4,5,6],[7,8,9]]);           

                                   [1    2    3]
                                   [           ]
                              M := [4    5    6]
                                   [           ]
                                   [7    8    9]

> parse(sprintf("%{ns}ld\n",M));                     

                                   123456789

See the help-page on topic rtable_printf for details. Within the {} brackets the qualifier `n` suppresses new lines between rows, and the qualifier `s` suppresses any space between entries.

acer

Matrix

August 22 2014 acer 10101
2 2

You were close, with your third attempt. Another level of square bracketing specify that things are stacking vertically.

A:=< <1|2|3>,<4|5|6>,<7|8|9>>;

                                    [1  2  3]
                                    [       ]
                               A := [4  5  6]
                                    [       ]
                                    [7  8  9]

Matrix([ [A[1..2,..]], [Vector[row]([91,92,92])], [A[3,..]] ]);

                                [ 1   2   3]
                                [          ]
                                [ 4   5   6]
                                [          ]
                                [91  92  92]
                                [          ]
                                [ 7   8   9]

Note that you forgot square brackets around entries in your Vector call.

acer

Palette?

August 21 2014 acer 10101
2 2

You could use a color palette. Eg,

c:=ColorTools:-GetPalette("Niagara"):
plots:-display(seq(plots[odeplot](sol[i],t=0..10,color=c[i]),i=1..nops([sol])));

See also the pre-made palettes listed by the ColorTools[PaletteNames] command.

One thing I like about a color palette such as `c` is that its membership widens on demand. When you reference c[i] for higher value of `i` then a new shade is generated which matches the tonal "feel" of the previous colors while trying to stay well spaced w.r.t. the previous colors. (The color computation sometimes gets sluggish, but values are remembered.) You can also create your own palette, and install one for automatic use by `plot`, etc.

acer

both?

August 21 2014 acer 10101
1 7

Focusing on your package usage question, and leaving aside that this particular example might be done directly under assumptions on z, could you both load the (table-based) inttrans package and call its member laplace with the longer, qualified syntax so as to have a visual cue as to what is being called by your code source? Granted, that does not give a cue as to what the call in the output may be. So much for table-based packages...

restart;

with(inttrans):

f:=t->piecewise(t<0,0,t>=0 and t<z,t,t>z,z):
r:=convert(f(t),Heaviside):
r:=inttrans[laplace](r,t,s);

                                                                                 z
    r := laplace(t Heaviside(z - t), t, s) - z laplace(Heaviside(z - t), t, s) + -
                                                                                 s
eval(r,z=0.5);

                0.5000000000 (2. - 1. exp(-0.5000000000 s) (s + 2.))
                ----------------------------------------------------
                                         2.                         
                                        s                           

                                                   1.      
                 0.5 (1. - 1. exp(-0.5000000000 s))     0.5
               - ------------------------------------ + ---
                                  1.                     s 
                                 s                         

You might even try loading only a subset of members of such a table-based package. For example, replacing with(inttrans) above with with(inttrans,laplace). That might help if you also wish to keep your global namespace less altered.

Not directly related to your example but somewhat on-topic is the following. In some circumstances it is simpler to call module-based package members with the P:-m syntax, rather than the safer form of the indexed syntax such as P[':-m']. Perhaps see the final examples for the table-based student package, on the colondash help-page.

acer

Table

August 20 2014 acer 10101
2 2

Like your previous Question, this is about Array plots, GUI Tables and plot sizing. Please see my Answer there.

BodePlot happens to return an Array plot (a _PLOTARRAY structure). But the issues relate to all Array plots, and not just to BodePlot per se.

In this example you have forced one part of the size to 300, but then complain that the aspect ratio is not right.

You might instead try something like these. The first forces one dimenstion only. The second forces the percentage of GUI width (assuming Table properties match). And the third forces only the aspect ratio.

DS:-BodePlot(sys,range=0.1..100,size=[default,300]);

DS:-BodePlot(sys,range=0.1..100,size=[0.4,300]);

DS:-BodePlot(sys,range=0.1..100,size=[default,0.7]);

You haven't said what aspect ratio you're hoping for.

acer

Table

August 20 2014 acer 10101
2 1

That framed "window" is a GUI Table. If you right-click inside it you should see an item "Table" in the second section of the pop-up context-menu. Under "Table" look for menu item "Properties...". Select that choice. This brings up a pop-up in which you can toggle off the display of the exterior and interior borders of the Table.

You can also resize the Table by dragging the exterior or interior borders with the mouse. You might wish to experiment with that alongside, say,

DS:-BodePlot(sys,output=horizontalplot,size=[300,300]);

or

DS:-BodePlot(sys,output=horizontalplot,size=[0.3,300]);

The choice for "Table Size Mode" in the popup for context-menu item Table->Properties affects how the Table and its plot entries re-size (or not) to match any manual resizing of the full Maple GUI. You can experiment with that too, perhaps with the second code example above.

I would be interested if you felt that the above manual adjustments of the Table were simply too onerous -- if say you desperately needed a command that would just display exactly what you wanted, perhaps because you needed to do it many times. (The Table adjustments are clobbered if you re-execute the BodePlot call.)

 

acer

dsolve,numeric,bvp

July 29 2014 acer 10101
0 0

It is described in the second bullet point of the Description section of the help-page dsolve,numeric,bvp .

acer

3D

July 23 2014 acer 10101
0 1

Your T is an operator with only two parameters, which returns a list with only 2 entries. But the 3D plot has three components. So what do you expect the transformation to do?

Try a transformation that accepts three parameters and returns a list of three components. You'll have to figure out what you want it to actually do, of course. ("back-transform" doesn't mean anything special, to me...)

For example, this produces a transformed 3D plot. Whether it is the transformation you intend is for you to decide, naturally.

T3 := plottools[transform]((s, u, z) -> [piecewise(s <= a_1, 1000000*K*s,
                                                   1000000*a_0+1000000*g*(s-a_1)), u, z]):

plots:-display( T3(pic) );

acer

eliminate

July 23 2014 acer 10101
1 1

If you replace `solve` by `eliminate` and assign the result to `sols` then sols[1] will contain expressions for T and n in terms of del and p.

Unfortunately the results appear to be the roots of a polynomial which don't factor explicitly for unknown del and p (and not even for some explicit values of same). Note that the problem might be math, not Maple, as there are no general explicit formula for roots of polynomials higher than 5.

If you leave e,f,ep, and q all unassigned then it is actually easier for Maple to do and the result are an implicit RootOf of a 7th degree polynomial for both T and n. Similarly if you assign those float values to e,f,ep, and q but wrap the set of equations to be solved in a call to convert(...,rational). If you try to do it using the float values then the result seems to contain implicit RootOfs involving a 15th degree polynomial.

It may interest you that the 7th degree polynomial will have at least one real root pair T and n, for each purely real pair of inputs del and p. But I don't see how to get an explicit formula for that.

Perhaps this is an appropriate moment to ask what you intended on doing with an explicit pair of formulas for T and n, if you had them. Suppose that you had the explicit closed formulas in terms of dep and p, and they were each ten thousand pages long. What would you do with them that you could not do with a black-box procedure that -- given any numeric values as input for parameters del and p -- computed all real roots in terms of T and n?

acer

variables

July 22 2014 acer 10101
0 6

NLPSolve is having difficulty figuring out what are the variables over which to optimize.

Try is as,

NLPSolve(1/(n^3*(F0*F1-F1)), tau1 = 115 .. 201, tau2 = 237 .. 273, variables=[tau1,tau2]);

           [                       -8                            ]
           [-3.15130715961255079 10  , [tau1 = 158., tau2 = 255.]]

But that doesn't seem right, as a result, considering what the 3D plot looks like over that range.

Better seems,

Digits:=30:
NLPSolve(subs(int=Int,1/(n^3*(F0*F1-F1))), tau1 = 115 .. 201, tau2 = 237 .. 273, variables=[tau1,tau2]);

                 [                                   -8   
                 [-3.18004616322786483130789361569 10  , [

                   tau1 = 201.000000000000000000000000000, 

                                                          ]
                   tau2 = 273.000000000000000000000000000]]

acer

Tasks, Student:-Precalculus

July 21 2014 acer 10101
0 0

Have a look through the Tasks, such as those in the subsection for Algebra. See the Table of Contents (left side panel) of the Help system (in your installed Maple, or online here and here) and look for the section called Tasks. (If you need help on using and inserting content from those Tasks then also see here.)

Perhaps also have a look at the visualization commands in the Student:-Precalculus package.

If you're a student and new to Maple, you might also wish to look here.

There are also some Math Apps that cover a bit of what you mentioned. Perhaps see here, and here.

acer

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