Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

 

ODE for electrical circuit (right click on Documentblock, unselect show command does not work. Command still visble)u(t) = T*(diff(`ϕ`(t), t))+L*(diff(i(t), t))+i(t)*R

u(t) = T*(diff(varphi(t), t))+L*(diff(i(t), t))+i(t)*R

(1)

 

ODE for motor (toggle Documentblock, unselect show command is only effective on equations  3 and 4)i(t)*T = J*(diff(`ϕ`(t), t, t))

i(t)*T = J*(diff(diff(varphi(t), t), t))

(2)

Isolate i(t) and taking the derivative

i(t) = J*(diff(diff(varphi(t), t), t))/T

(3)

``

diff(i(t), t) = J*(diff(diff(diff(varphi(t), t), t), t))/T

(4)

``

Download Document_Block_hide_command.mw

Hi MaplePrimes,

I've updated to the 2023 version of Maple. After the update I chose to remove older version folders in Windows.

Since then I cant't use my tasks any longer. I've re created the tasks and the are also shown in the Task Palette, but clicking on a task results in nothing. I can though create a new Task and after the creation all my tasks can then be used again.

Its like Maple doesn't recognize the correct Help Database from the beginning. I've reinstalled Maple 2023 two or three times to try to reset the whole installation to something from scratch. Nothing that I do seems to produce the desired result. Does anybody out there have a solution or suggestion to a probable solution?

I don't know of any file that I could attach to exemplify my problem. It's not a math/maple problem relating directly to the maple code language. My tasks themselves work fine once inserted in a document. It's the insertion itself that's the problem.

Thanks.

Q1: In the above, why can I only convert radians to radians. Or: Why does the menu "Chose unit" not offer arcdeg?

Q2: In the above, why is nothing happening when I enter arcdeg in the field "Enter Unit"?

Q3: How to change the displayed symbol for arcdeg to ° (in the attachment are failed attempts)?

arcdeg.mw

First issue I see in Maple 2023 integrate

Example 1

restart;
int( (e*x+d)^(3/2)*(c*x^2+a)^(3/2),x)

Example 2

restart;
int((1+x)^(3/2)*(x^2-x+1)^(3/2),x);

Example 3

restart;
int((c*x^4+b*x^2)^(3/2)/x^(3/2),x)

 

Worksheet below for 2023 and also for 2022.2 showing this did not have this problem in 2022.2. Internally for me, this cause other problem when post-processing this, that is why I found it. Any one knows what caused it?  Maple 2022.2 result is much longer, but it does have this "undefined" issue in the result.


 

interface(version);

`Standard Worksheet Interface, Maple 2023.0, Windows 10, March 6 2023 Build ID 1689885`

restart;

int( (e*x+d)^(3/2)*(c*x^2+a)^(3/2),x)

(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*undefined*x*(3*c*e*x^3+4*c*d*x^2+6*a*e*x+12*a*d)/(c*e*x^3+c*d*x^2+a*e*x+a*d)^(1/2)

restart;

int((1+x)^(3/2)*(x^2-x+1)^(3/2),x);

(1+x)^(1/2)*(x^2-x+1)^(1/2)*undefined*x*(x^3+4)/(x^3+1)^(1/2)

restart;

int((c*x^4+b*x^2)^(3/2)/x^(3/2),x)

undefined*(c*x^2+2*b)*(c*x^4+b*x^2)^(3/2)/(x^(1/2)*(c*x^2+b)*(x*(c*x^2+b))^(1/2))

 


 

Download bug_3_maple_2023_int_march_10_2023.mw

 

interface(version);

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

restart;

int( (e*x+d)^(3/2)*(c*x^2+a)^(3/2),x)

(2/1155)*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(372*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticF((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*c*a^3*d*e^6+245*x^6*c^4*d*e^6+300*x^5*a*c^3*e^7+145*x^5*c^4*d^2*e^5-x^4*c^4*d^3*e^4+255*x^3*a^2*c^2*e^7+2*x^3*c^4*d^4*e^3+8*x^2*c^4*d^5*e^2+60*x*a^3*c*e^7+360*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticF((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*c^2*a^2*d^3*e^4-12*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticF((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*c^3*a*d^5*e^2-16*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticF((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*(-c*a)^(1/2)*c^3*d^6*e-432*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticE((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*c*a^3*d*e^6-336*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticE((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*c^2*a^2*d^3*e^4+112*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticE((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*c^3*a*d^5*e^2+766*x^4*a*c^3*d*e^6+16*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticE((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*c^4*d^7+60*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticF((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*(-c*a)^(1/2)*a^3*e^7+518*x^3*a*c^3*d^2*e^5+581*x^2*a^2*c^2*d*e^6+46*x^2*a*c^3*d^3*e^4+373*x*a^2*c^2*d^2*e^5+2*x*a*c^3*d^4*e^3+60*a^3*c*d*e^6+47*a^2*c^2*d^3*e^4+8*a*c^3*d^5*e^2+105*x^7*c^4*e^7-24*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticF((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*(-c*a)^(1/2)*a^2*c*d^2*e^5-100*(-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2)*((-x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e+d*c))^(1/2)*((x*c+(-c*a)^(1/2))*e/((-c*a)^(1/2)*e-d*c))^(1/2)*EllipticF((-(e*x+d)*c/((-c*a)^(1/2)*e-d*c))^(1/2), (-((-c*a)^(1/2)*e-d*c)/((-c*a)^(1/2)*e+d*c))^(1/2))*(-c*a)^(1/2)*a*c^2*d^4*e^3)/(c^2*e^5*(c*e*x^3+c*d*x^2+a*e*x+a*d))

restart;

int((1+x)^(3/2)*(x^2-x+1)^(3/2),x);

-(1/55)*(1+x)^(1/2)*(x^2-x+1)^(1/2)*(-10*x^7+(27*I)*3^(1/2)*(-2*(1+x)/(-3+I*3^(1/2)))^(1/2)*((I*3^(1/2)-2*x+1)/(I*3^(1/2)+3))^(1/2)*((I*3^(1/2)+2*x-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(1+x)/(-3+I*3^(1/2)))^(1/2), (-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-81*(-2*(1+x)/(-3+I*3^(1/2)))^(1/2)*((I*3^(1/2)-2*x+1)/(I*3^(1/2)+3))^(1/2)*((I*3^(1/2)+2*x-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(1+x)/(-3+I*3^(1/2)))^(1/2), (-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-38*x^4-28*x)/(x^3+1)

 


 

Download maple_2022_int_march_10_2023.mw

When will the PDF Maple User Manual be released for Maple 2023. Also I hope the Programming guide is updated too as it is still at 2020.

I know that this is not really a question regarding core Maple package, but I am running into problems during the installation process.

After having upgraded Maple networktools as mentioned, I am unable to run the activation program due to an error.

"Java Virtual Machine Launcher: Error: Could not create the Java Virtual Machine."

I've never had that problem before in previous versions. There was no Java installed on the (virtual) server, so I installed the latest OpenJDK to check if that solved the problem.

Unfortunately it didn't.

Any hints would be appreciated.

Windows Server 2012R2

My main question is: How to change the font used in worksheet by Maple for 1D input from Courier to another font say times new roman? Is there a setting for this so it applies all the time?

ps. I found Can-I-Change-the-Default-Fonts-or-Style-for-Maple-Worksheets-and-Documents?language=en_US  (very hard to follow and confusing, but it seems that is only way to fix this problem now is to change the default font).

-----------------------------------------------------------------------------------------------------------------

I noticed strange font problem using Maple 2023 on windows 10. This problem does not show on Maple 2022.2 (at least I do not think I've seen it or noticed it before). 

Variables with _ between the names, will have the underscore not display sometimes as I move the cursor around (movie at end).

When scrolling back up, the underscores no longer become visible. 

But as I move the cursor over the variable name which containes the underscore, they will now show up.

I am sure this is a font issue. The zoom is set at 100%. I made no changes at all other than making the input 1D math as I normally do and set the default to worksheet. Some of my setting are below.

This could be a DPI issue settings of some sort. My monitor is standard monitor (not a 4K one) and again, I have not changed any settings on my PC after I installed Maple 2023 and did not change any hardware.

 

 

 

 

Here is some system information also

 

 

Here is the movie showing the problem

 

 

As I play more with it, I notice a common theme. This happens when I hit the UP ARROW to go to the line above. Then suddenly the underscroes no longer visible. Once I hit the LEFT arrow (now I am at the above line), they show up again.

Here is another movie which more clearly shows this.

This makes it very hard to work with the code in the worksheet. But I am sure this can be fixed as it looks like just a font configuration issue with Maple on windows. But I do not know what it is and how to fix it.

 

I found something new. When setting the ZOOM at 125% instead of 100% as above, I notice the underscores do not completely disappear but become THINNER but one can still see them. This affects only the underscores. When the ZOOM at 150%, they do not change at all.  Here is a movie. first part at 125%. Notice how they become little thinner when doing the same thing as above. But at 150% they remain visible because they do not change thinkness. When going back to 100% zoom, they  no longer show.

So the problem is that they are there all the time, but depending on the ZOOM level, they beome thinner and thinner until they become invisible to the eye.

 

I found some related issue on windows 10 with some application where this problem shows up.

some-characters-missing-or-cut-off-when-displayed-on-screen

 "When you view your document in Microsoft Word, some characters may be missing, or the top (or bottom) of some characters may be cut off.

This problem may affect the following types of characters:

Underscore"

The above is about WORD, but it could as well apply to Maple?

I also found  underscore not rendering with courier

"Underscore characters are not rendered in new Google Docs in the Courier
New 11pt or 12pt fonts."

My question is: How to change the font used in worksheet by Maple? Now it is using Courier. May be if I change the font, this problem will go away?

 

Update: Found a workaround!  It is the font used!  I changed from Courier to Times New Roman and now the underscore do not change thinkness!  I just need a way to make this permenant for all 1D Maple input.   Here is a new movie showing it is fixed. You can see the underscores remain visible, all at 100% ZOOM level. Once I change to Courier, the problem show up again. 

I am not sure if this is a Maple issue or windows.

 

 

 

The new command ArrayTools[GeneralOuterProduct] (introduced in Maple 2021) computes the generalized outer product of two rtables, and again, there exists a similar function Outer in Mma (cf. the end of this question). But in practice, it appears that this Maple command is not so fast as Mma's one. To begin with, we need to generate four lists: w, x, y, and z. Our goal is forming all possible combinations of the lowest‐level elements in a nested structure (rather than a flat structure). Now let us start the test.

In Mathematica (the real time is about ): 

And in Maple (the real time is about ): 
 

restart;

w := [`$`](0 .. 1e4):
x := [`$`](0 .. 2e3):
y := [`$`](0 .. 3e2):
z := [`$`](0 .. 4e1):

"time[real]((p1:=MmaTranslator:-Mma:-ReplaceRepeated(convert(ArrayTools:-GeneralOuterProduct(convert([w,x],Array,fill=NULL),()->`if`(nargs=2,`[]`(args),NULL),convert([y,z],Array,fill=NULL)),listlist),[]=NULL)))"

199.880

(1)

"time[real]((p2:=(s4->(s3->(s2->(s1->`[]`(s3,s1))~(s2))~([y,z]))~(s4))~([w,x])))"

7.699

(2)

p3 := parse(StringTools:-CharacterMap("{}", "[]", FileTools:-Text:-ReadFile("E:/data.txt")))

evalb(p1 = p2 and p2 = p3) = trueNULL


 

Download Outer.mw

As you can see, Maple and Mathematica returns identical results (∵p1p3); nevertheless, Maple consumes too much time: the ratio is 199.880/0.784176 ≈ 254.892. (What a wide gap between them!) 
So, is there any possibility of speeding up Maple's ArrayTools:-GeneralOuterProduct? Or any ideas of obtaining the same results in Maple efficiently?

Explanatory notes. Here is an illustrative animation: 

That is to say, a generalized map
E.g., here is a nested list: 

nl := [[[[s, t]], [u, [v, w]]], [[x, [y, z]]]]:

We can use map to apply the mapped function F to "each operand" (i.e., the first‐level parts) of : 

:-map(F, nl);
 = 
         [F([[[s, t]], [u, [v, w]]]), F([[x, [y, z]]])]

But in Mathematica, we can make further explorations: 

In[1]:= nl = {{{{s, t}}, {u, {v, w}}}, {{x, {y, z}}}}; 

In[2]:= Map[F, nl, {1}] (*Maple's result*)

Out[2]= {F[{{{s, t}}, {u, {v, w}}}], F[{{x, {y, z}}}]}

In[3]:= Map[F, nl, {2, -2}]

Out[3]= {{F[{F[{s, t}]}], F[{u, F[{v, w}]}]}, {F[{x, F[{y, z}]}]}}

In[4]:= Map[F, nl, {-3, 3}]

Out[4]= {{F[{F[{s, t}]}], F[{F[u], F[{v, w}]}]}, {F[{F[x], F[{y, z}]}]}}

In[5]:= Map[F, nl, {0, \[Infinity]}, Heads -> \[Not] True]

Out[5]= F[{F[{F[{F[{F[s], F[t]}]}], F[{F[u], F[{F[v], F[w]}]}]}], F[{F[{F[x], F[{F[y], F[z]}]}]}]}]

Note that the last case has been implemented in Maple as MmaTranslator[Mma][MapAll]:  

MmaTranslator:-Mma:-MapAll(F,nl);
 = 
   F([F([F([F([F(s), F(t)])]), F([F(u), F([F(v), F(w)])])]), 

     F([F([F(x), F([F(y), F(z)])])])])

Naturally, how to reproduce the other two results in Maple programmatically? (The output may not be easy to read or understand; I have added an addendum below.)

Addendum. It is also possible to display in "tree" structure (like dismantle) manually: 

`[]`
(
    `[]`
    (
        `[]`
        (
            `[]`
            (
                s
            ,
                t
            )
        )
    ,
        `[]`
        (
            u
        ,
            `[]`
            (
                v
            ,
                w
            )
        )
    )
,
    `[]`
    (
        `[]`
        (
            x
        ,
            `[]`
            (
                y
            ,
                z
            )
        )
    )
)

As you can see, the "depth" of  is five (0, 1, 2, 3, and 4), while the classical map just maps at the first "level". (Moreover, such descriptions may lead to a confusion.)

Supplement. Unfortunately, there remains a bug in the MmaTranslator[Mma][Level]. Compare: 

MmaTranslator:-Mma:-Level(nl, [4]); (*Maple*)
                             [v, w]

MmaTranslator:-Mma:-Level(nl, [-1]); (*Maple*)
          [s, t, u, v, w, x, y, z, -1, x, c, r, y, 2]

In[6]:= Level[nl, {4}] (*Mathematica*)

Out[6]= {s, t, v, w, y, z}

In[7]:= Level[nl, {-1}] (*Mathematica*)

Out[7]= {s, t, u, v, w, x, y, z}

Hello there, 

Is there any chance to ask this one question?

The attached (following) worksheet shows the result of LieDerivative operation, which is not correct. 

The correct answer is given in the image in the middle of the worksheet. Is there any particular reason regarding Maple's way of conducting the operation in that way?

restart;

with(LinearAlgebra):

with(DifferentialGeometry):

with(LieAlgebras):

DGsetup([x1, x2], M, verbose);

`The following coordinates have been protected:`

 

[x1, x2]

 

`The following vector fields have been defined and protected:`

 

[_DG([["vector", M, []], [[[1], 1]]]), _DG([["vector", M, []], [[[2], 1]]])]

 

`The following differential 1-forms have been defined and protected:`

 

[_DG([["form", M, 1], [[[1], 1]]]), _DG([["form", M, 1], [[[2], 1]]])]

 

`frame name: M`

(1)

 

M > 

f := evalDG((x2)*D_x1 + (c1 * (1 - x1^2) * x2 - c2 * x1)*D_x2);

_DG([["vector", M, []], [[[1], x2], [[2], -c1*x1^2*x2+c1*x2-c2*x1]]])

(2)
M > 

h := evalDG((x1)*D_x1 + (0)*D_x2);

_DG([["vector", M, []], [[[1], x1]]])

(3)
M > 

###### answer

M > 

M > 

LieDerivative(f, h);

_DG([["vector", M, []], [[[1], x2], [[2], x1*(2*c1*x1*x2+c2)]]])

(4)
M > 

 

Download Q20230307.mw

In graph theory, the lexicographic product  or graph composition G ∙ H of graphs G and H is a graph such that

 - the vertex set of G ∙ H is the cartesian product V(G) × V(H); 
 - and any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent with x in G or u = x and v is adjacent with y in H.

 

Given two graphs, it is easy to obtain their lexicographic product. However the inverse process does not look so easy. 

Recognition problem: Given a graph G, can we guess whether there exist graphs G_1,...,G_k such that G=G_1 ∙ ⋯ ∙G_k ?

 

I read the book "Handbook of product graphs" and wiki, that say that the recognition complexity of lexicographic products is polynomially equivalent to the graph isomorphism problem

 

For the lexicographic product, I know that there is some algorithm without codes to implement the decomposition of the lexicographic products of a graph.

  • Feigenbaum, J.; Schäffer, A. A. (1986), "Recognizing composite graphs is equivalent to testing graph isomorphism", SIAM Journal on Computing, 15 (2): 619–627, doi:10.1137/0215045 (https://www.cs.yale.edu/homes/jf/FS-SICOMP86.pdf)

However, I did not understand the algorithm process mentioned in the article, nor did I see the program implementation of this algorithm. About 5 months ago, I asked similar questions on multiple platforms, but did not receive any feedback.

The potential algorithm can help us discover some theorems, so I am very interested in the implementation of the algorithm in the above article.

 

PS:We also know that there are already polynomial algorithms for the decomposition of the cartesian product of a graph. A polynomial time algorithm for finding the prime factors of Cartesian-product graphs", Discrete Applied Mathematics, 12 (2): 123–138, doi:10.1016/0166-218X(85)90066-6, MR 0808453 and we can find the java codes for implementation of finding the prime factors of Cartesian-product graphs.

I teach high school math where we use Maple. Some times some students who use Maple 2022 on Mac computers both older and new version of the OS, experience that the document won't react to simple things like plot, solve of loading packages with the "with" command. 

Any idea could be causing this? Because the error goes away if we load a new document within Maple or restart the program.

Let a, b be arbitrary real parameters. I intend to compute something like: (with exact piecewise output) 

Optimization:-Maximize(8*x + 7*y, {5*y <= 6 - 9*b, -6*x - 4*y <= 8 - 5*a - 7*b, -4*x + 7*y <= -1 - 2*a - 7*b, -x + y <= 6 + 4*a - 5*b, 7*x + 5*y <= a + 4*b}, variables = {x, y}): # Error
Optimization:-Minimize((x - 1)^2 + (2*y - 1)^2, {x - 2*y <= 2*a - b + 1, x + 2*y <= a + b, 2*x - y <= a - b + 1}, variables = {x, y}): # Error

Unfortunately, these Maple codes are virtually invalid, and the relevant commands minimize, maximize, extrema, and Student[MultivariateCalculus][LagrangeMultipliers] do not support general inequality constraints. Is it possible to tackle these small-scale constrained parametric problems in Maple?

Quite often, Maple freezes, and the file cannot be saved, and Maple cannot be closed.

Did you get the problem ?

Can someone give me an example for using

linear regressor function from deep learning package

By passing one dependent variable say Y

And a set of independent variables say X

As a matrix say 

Can we be able to split data into train and test and use this linear regressor command on train and do validation

As I am not able to see some examples on the implementations using command kind help 

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