In practice, I need calculate the (principal) squareroot of some suitable large matrix exactly (so the desired result should not involve floating-point numbers, otherwise the decomposition will be of no theoretical value as a certificate …). But I find it difficult to do so in Maple. (What about the Efficient Computations - Maple Help (maplesoft.com)?)
Below are some matrices: (They are not contrived academic examples.) 

M__4 := <1,0,-2,0,1,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0|0,3,0,-6,0,3,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,-3,0,0,0,0,0,0,0,0,6,0,0,0,0,-3,0|-2,0,7,0,-8,0,3,0,0,0,0,0,0,0,0,1,0,-7,0,2,0,0,0,0,0,0,4,0,3,0,0,0,0,-3,0,0|0,-6,0,13,0,-8,0,1,0,0,0,0,0,0,0,0,6,0,-4,0,4,0,0,0,0,0,0,-1,0,-11,0,0,0,0,6,0|1,0,-8,0,13,0,-6,0,0,0,0,0,0,0,0,4,0,8,0,-1,0,0,0,0,0,0,-11,0,-6,0,0,0,0,6,0,0|0,3,0,-8,0,7,0,-2,0,0,0,0,0,0,0,0,-3,0,-1,0,1,0,0,0,0,0,0,2,0,4,0,0,0,0,-3,0|0,0,3,0,-6,0,3,0,0,0,0,0,0,0,0,-3,0,-3,0,0,0,0,0,0,0,0,6,0,3,0,0,0,0,-3,0,0|0,0,0,1,0,-2,0,1,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0|0,0,0,0,0,0,0,0,3,0,0,0,3,0,-3,0,0,0,0,0,0,-6,0,-3,0,6,0,0,0,0,3,0,-3,0,0,0|0,0,0,0,0,0,0,0,0,4,0,0,0,-2,0,0,0,0,0,0,0,0,-6,0,6,0,0,0,0,0,0,-2,0,0,0,0|0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,-2,0,-1,0,0,0,0,2,0,2,0,0,-1|0,0,0,0,0,0,0,0,0,0,0,12,0,-6,0,0,0,0,0,0,0,0,-6,0,-6,0,0,0,0,0,0,6,0,0,0,0|0,0,0,0,0,0,0,0,3,0,0,0,3,0,-3,0,0,0,0,0,0,-6,0,-3,0,6,0,0,0,0,3,0,-3,0,0,0|0,0,0,0,0,0,0,0,0,-2,0,-6,0,4,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,-2,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,0,0,-3,0,3,0,0,0,0,0,0,6,0,3,0,-6,0,0,0,0,-3,0,3,0,0,0|-2,0,1,0,4,0,-3,0,0,0,0,0,0,0,0,7,0,-1,0,2,0,0,0,0,0,0,-8,0,-3,0,0,0,0,3,0,0|0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,0,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,-6,0,0,0,0,3,0|2,0,-7,0,8,0,-3,0,0,0,0,0,0,0,0,-1,0,7,0,-2,0,0,0,0,0,0,-4,0,-3,0,0,0,0,3,0,0|0,3,0,-4,0,-1,0,2,0,0,0,0,0,0,0,0,-3,0,7,0,-7,0,0,0,0,0,0,-2,0,8,0,0,0,0,-3,0|-1,0,2,0,-1,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0|0,-3,0,4,0,1,0,-2,0,0,0,0,0,0,0,0,3,0,-7,0,7,0,0,0,0,0,0,2,0,-8,0,0,0,0,3,0|0,0,0,0,0,0,0,0,-6,0,-1,0,-6,0,6,0,0,0,0,0,0,13,0,8,0,-11,0,0,0,0,-8,0,4,0,0,1|0,0,0,0,0,0,0,0,0,-6,0,-6,0,6,0,0,0,0,0,0,0,0,12,0,-6,0,0,0,0,0,0,0,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,-2,0,-3,0,3,0,0,0,0,0,0,8,0,7,0,-4,0,0,0,0,-7,0,-1,0,0,2|0,0,0,0,0,0,0,0,0,6,0,-6,0,0,0,0,0,0,0,0,0,0,-6,0,12,0,0,0,0,0,0,-6,0,0,0,0|0,0,0,0,0,0,0,0,6,0,-1,0,6,0,-6,0,0,0,0,0,0,-11,0,-4,0,13,0,0,0,0,4,0,-8,0,0,1|1,0,4,0,-11,0,6,0,0,0,0,0,0,0,0,-8,0,-4,0,-1,0,0,0,0,0,0,13,0,6,0,0,0,0,-6,0,0|0,0,0,-1,0,2,0,-1,0,0,0,0,0,0,0,0,0,0,-2,0,2,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0|0,0,3,0,-6,0,3,0,0,0,0,0,0,0,0,-3,0,-3,0,0,0,0,0,0,0,0,6,0,3,0,0,0,0,-3,0,0|0,6,0,-11,0,4,0,1,0,0,0,0,0,0,0,0,-6,0,8,0,-8,0,0,0,0,0,0,-1,0,13,0,0,0,0,-6,0|0,0,0,0,0,0,0,0,3,0,2,0,3,0,-3,0,0,0,0,0,0,-8,0,-7,0,4,0,0,0,0,7,0,1,0,0,-2|0,0,0,0,0,0,0,0,0,-2,0,6,0,-2,0,0,0,0,0,0,0,0,0,0,-6,0,0,0,0,0,0,4,0,0,0,0|0,0,0,0,0,0,0,0,-3,0,2,0,-3,0,3,0,0,0,0,0,0,4,0,-1,0,-8,0,0,0,0,1,0,7,0,0,-2|0,0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,3,0,3,0,0,0,0,0,0,0,0,-6,0,-3,0,0,0,0,3,0,0|0,-3,0,6,0,-3,0,0,0,0,0,0,0,0,0,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,-6,0,0,0,0,3,0|0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,2,0,1,0,0,0,0,-2,0,-2,0,0,1>:
M__3 := 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Unexpectedly, LinearAlgebra[MatrixPower] does not work well. For instance: 
 

Download performance_of_`sqrtm`.mw

The last six numerical experiments all fail to compute the square root. (Accordingly, here it is impossible to convert each numeric element to one of the "simplest" algebraic numbers that approximates it well.) As you can see, if I execute them directly (i.e., without converting each entry to the nearest floating-point value), the elapsed time required to run the procedure is still unacceptable! (Note that they can be evaluated symbolically in fact.) Is this a bug of Maple? And how do I get the desired results in Maple efficiently?

Hi,

I want to illustrate the intersection between The ellipsoid   "x^2/4 + y^2/9 + z^2/16 = 1"and the plane  "z = 3"

Normally, I should obtain an ellipse G1, but its graph does not match the graph obtained ? Thanks for your ideas
 

G2Exercice1.mw

How to solve this RLC Electric Circuit  with this initial conditions,I couldn't plot this equation.Help me to do this problem.

EC-2.mw

Let y＞1. It can be proved (maybe by hand) that the following four expressions are mathematically equivalent: 

assume(y > 1); # Assumption!
expr := [0, 0, 0, 0]: # Preallocation.
expr[1] := exp(y*LambertW(ln(y))):
expr[2] := (ln(y)/LambertW(ln(y)))^y:
expr[3] := eval(x^(x^x), x = exp(LambertW(ln(y)))):
expr[4] := eval(x^(x^x), x = ln(y)/LambertW(ln(y))):

But unfortunately, when I tried to simplify expr_i - expr_j (symbolically), I just got: 

seq(seq(ifelse(j <> i, [i, j, verify(expr[j], expr[i], equal)], NULL), j = 1 .. numelems(expr)), i = 1 .. numelems(expr)); # is(expr[j] = expr[i]) does not work as well.
 = 
   [1, 2, FAIL], [1, 3, FAIL], [1, 4, FAIL], [2, 1, FAIL], 

     [2, 3, FAIL], [2, 4, FAIL], [3, 1, FAIL], [3, 2, FAIL], 

     [3, 4, true], [4, 1, FAIL], [4, 2, FAIL], [4, 3, true]

In other words, Maple can only determine that expr[3] = expr[4].
One may check that, for example, 

MmaTranslator:-Mma:-Chop([seq](seq(evalhf(subs(y = log10(rand()), expr[i] - expr[j])), j = 1 .. numelems(expr)), i = 1 .. numelems(expr)), 2^(-26));
 = 
        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

However, the desired approach is simplifying them symbolically. Is there a way to do so in Maple?

Hi, I'm trying to add the display of graphs G1, G2, and G3 (representing the intersections -AnimCompl file-) to my three animations (G5Ex2-file). I've tried using the background option and the display command, but without success. Thank you for your help.

AnimCompl.mw

G5Ex2.mw

I want to put one option of tetrahedron SABC with AB=c, BC=a, AC=b, SA=m, SB=n, SC=p. I tried
restart;
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [c, 0, 0];
C := [(-a^2 + b^2 + c^2)/(2*c), sqrt((a + b - c)*(a - b + c)*(-a + b + c)*(a + b + c))/(2*c), 0];
S := [x, y, z];
solve([distance(S, A) = m, distance(S, B) = n, distance(S, C) = p], [x, y, z]);

I got warning, solutions may have been lost. How can I solve that system of equations?

Just need some help using URL:-Get

Get("https://sdo.gsfc.nasa.gov/assets/img/browse/2023/05/05/20230505 _184918_512_0304.jpg")

I'm sure there are some tags to use but not sure how.  The site does show a script on best practices, but at the moment don't know how to apply them.  Can anyone offer some help?

Just installing Maple 2023 on my office machine (a mac); installed it on my travel computer (a Surface Pro running Windows) yesterday.

Configured Jupyter notebooks to use the 2023 Maple Kernel and it all went smoothly.  I was *delighted* to notice that plotting Lambert W in Jupyter with the command

plot( [W(x), W(-1,x)], x=-1..4, view=[-1..4, -3.5..1.5], colour=[red,blue], scaling=constrained, labels=[x,W(x)] );

produced a *better* plot near the branch point.  This is hard to do automatically!  It turns out this is a side effect of the better/faster/more memory efficient adaptive plotting software, which I gather from "What's New" was written for efficiency not for quality.  But the quality is better, too!  Nice!

I am working my. way through the "What's New" and I'm really pleased to learn about the new univariate polynomial rootfinder, *not least because it cites the paper describing the algorithm*.  Lots of other goodies too; the new methods of integration look like serious improvements.  Well done. (One thing there: "parallel Risch" is a term of art, and may lead people to believe that Maple is doing something with parallel computing there.  I don't think so.  Could a reference be supplied?)

The new colour schemes and plotting features in 3d and contour plotting look fabulous.

Direct Python language support from a code edit region is not at all what I expected to see---I wonder if it will work in a Jupyter notebook?  I'm going to have to try it...

I'm quite impressed.  The folks at Maplesoft have been working very hard indeed.  Congratulations on a fine release!

i want to plot form 15 to 0 and 5 to 1.....but my plot shows only increasing order..how can i change it?

Download plot.mw

Is there a way to suppress dependencies of a all functions appearing in a worksheet without having to do suppress([each function])?

I followed the code on the website https://de.maplesoft.com/support/help/maple/view.aspx?path=updates/Maple18/GraphTheory to convert a graph to LaTeX code. However, after compiling with pdflatex, I found that some edges of the graph are jagged.

restart:    
with(GraphTheory):
with(SpecialGraphs):
S:=SoccerBallGraph():
Latex(S,FileTools:-JoinPath([currentdir(), "soccer.tex"]),300,300,true)

soccer.pdf

I suspect it's because of the converted LaTeX code.

PS: The PDF conversion issue from last time still remains unsolved in Maple 2023; see

https://www.mapleprimes.com/questions/236142-How-To-Remove-The-Mosaic-Of-Vertices.

How to rectify this Error,in RK Method.Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 3, got 2.

I cound't plot p5,p6,p7.

If RK Method is suitable for this or not please tell the suitable numerical method code for this.Help me

IP-TEMP.mw

The example worksheet uses table to determine the covering relations in a POSET. This is old (Maple 11 and earlier code) that I have been trying to update into a package to explore calculations in an algebraic structure.  The example procedure seems to work well, but because of problems with similar procedures elsewhere, I have some concerns about the validity of using tables in this fashion. Specifically, this procedure initializes a table, then proceeds to modify the table entries, and then reformats the sequences into sets.  I have not been able to find documentation for modifying entries in tables after they have been defined. The documentation for tables only covers adding entries, removing entries, but not modifying entries.

Is modifying tables as my  procedure does an undocumented feature?

In addition, the documentation does not explain how to clear a table. It only describes how to clear a table entry. Older code sometimes purported to clear a table by assigning its name (with uneval quotes) to itself, but this does not seem to work.

exampletableoperations.mw

Hi to All! I have a big expression including 10 constant parameters (k_1, k_2, k_3, omega_1, omega_2, omega_3, a_3, b_2, c_0, c_2) to be solved for a_3, b_2, c_0, c_2. I wonder if there is any relation between the constants a_3, b_2, c_0, c_2 not depending on (k_1, k_2, k_3, omega_1, omega_2, omega_3) satisfying this big expression e.g. a_3=2, b_2=c_0/5, c_2 free. 

I also tried fsolve but I could not get an answer.

Thank you in advance.

Regards,

question1.mw