Suppose that we have something like

plots:-animate(F,[theta],theta=0..2*Pi,background=plot([cos(t)-2,sin(t),t=0..2*Pi]),
scaling=constrained,axes=none);

I want to change the range of the parameter theta to something like theta=L[i],i=1..20.
Here, L is a list of numbers. Can I?
Thank you.

mapleatha

I can't figure what is going on here. I have an expression, where when I run the program, I see inside the debugger that the result of evalb(simplify(tmp_1)) where tmp_1 is the expression, gives false

When I copy the same tmp_1 expression to new worksheet and do evalb(simplify(tmp_1)) it gives true.

I added print statements in the code to print tmp_1 and print result of simplify(tmp_1) and for some reason, it gives false when I run the program, but it gives true when I do the same thing in a work sheet, by copying tmp_1 and trying it there.

Never seen anything like this, as expression is all numbers. Here is the print out when I run the program

Here is the same thing in worksheet

restart;
tmp_1 :=-(2*ln(-2))/7 - ln(-1)/7 = ln(1) - (2*ln(-2))/7 - ln(-1)/7;
simplify(tmp_1);
evalb(simplify(tmp_1));

                      true

and if you think I made mistake somewhere, here is also screen shot from the debugger window itself

again, same thing gives true in separate worksheet, copying same exact expression from above

There seem to be something loaded when I run my program that causes this difference, but I have no idea now what it is.  This has nothing to do with the debugger loaded btw, I am just using the debugger to show the details. When I run the program, without the debugger, I get false for the above, and I was trying to find why.

Any suggestions what to try and what to check for and what could cause this? Should it not give true when I run the program also? Could it be some Digits setting changed when the program run? I do not change any system defaults of any sort when running the program. 

Maple 2020.1

edit june 12, 2021

Here is another manifestation of the same problem I just found. There is something seriously wrong for it to behave this way.

This is an expression called tmp_1 in a local variable in a proc inside a module. There are not even any local symbols in it. When I run the program, all the attempts to show it is true fail. Some give FAIL and some give false when the result should be true

When I simply copy the expression from the debugger window to an open worksheet, I get true

Here is the screen shot

Only when I did is(expand(tmp_1)) did it give true

But when I copy the expression to the worksheet, it gives true using all the other attempts:

restart;
tmp_1:=1 = 5/4*exp(0)+1/4*piecewise(0 <= 1,-1,1 < 0,exp(-2)):
is(tmp_1);
is(simplify(tmp_1));
is((rhs-lhs)(tmp_1)=0);
is(simplify((rhs-lhs)(tmp_1)=0));
evalb(simplify((rhs-lhs)(tmp_1)=0));
is(expand(tmp_1))

I can't make a MWE so far, since these problems only show up with I run my large program. I think Maple internal memory get messed up or something else is loaded that causes these stranges problems.

For now, I added expand() to the things I should try. My current code now looks like

if is(tmp_1) or is(simplify(tmp_1)) or is((rhs-lhs)(tmp_1)=0)
               or is(simplify((rhs-lhs)(tmp_1)=0)) or evalb(simplify((rhs-lhs)(tmp_1)=0))
               or is(expand(tmp_1)) then    
   ....

Maple 2021.1

... and two suggestions to the development team

POINT 1
In ?DiscreteValueMap (package Statistics) it's given an example concerning rhe Geometric distribution along with this comment:
"The Geometric distribution is discrete but it necessarily assumes integer values, so (bold font is mine) it also does not have a DiscreteValueMap"

This sentence seems to indicate that "because a distribution is discrete over the set of integers, it cannot have a DiscreteValueMap", some sort of logical implication...

But my feeling is that the Geometric distribution (or any other discrete distribution) does not have a DiscreteValueMap because this attribute has just not been specified when defining the distribution.

restart:
with(Statistics):

GeomRV := RandomVariable(Geometric(1/2)):
f := unapply(ProbabilityFunction(GeomRV, n), n):

AnotherGeomRV := Distribution(
      'ProbabilityFunction'=f,
      'Support'=0..infinity,
      'DiscreteValueMap'=(n->n),
      'Type'=discrete
):
DiscreteValueMap(AnotherGeomRV , n);

Thus having the set of natural numbers as support doesn't imply that DiscreteValueMap cannot exist.

Suggestion 1: modify the ?DiscreteValueMap help page so that it no longer suggests that some discrete distributions cannot have a .DiscreteValueMap 

______________________________________________________________________________________

POINT 2
I think there exists a true problem with the definition of discrete distributions in Maple: the ProbabilityFunction of a (discrete) random variable) takes non zero values outside their definition set.
For instance

ProbabilityFunction(GeomRV, Pi);  # something non null

To ivercome this problem I defined a new Geometric distribution this way (not entirely satisfying):

restart:
with(Statistics):

GeomRV := RandomVariable(Geometric(1/2)):
f := unapply(ProbabilityFunction(GeomRV, n), n):
g := n -> (1-ceil(n-floor(n)))*f(n)    # (1-ceil(n-floor(n))) = 1 if n in Z, 0 otherwise

AnotherGeomRV := Distribution(
      'ProbabilityFunction'=g,
      'Support'=0..infinity,
      'DiscreteValueMap'=(n->n),  # is wanted
      'Type'=discrete
):
ProbabilityFunction(AnotherGeomRV, 2);
                 1/8
ProbabilityFunction(AnotherGeomRV, Pi);
                  0

PS: None of the statistics based upon the  ProbabilityFunction (Mean, Variance, ... ) is correctly computed with the previous construction. This could be easily overcome by completing this definition, just as its done in Maple, for all the requires statistics, for instance 

AnotherGeomRV := Distribution(
      ....
      'Mean'=1   # or more generally (1-p)/p form Geometric(p)
):

Suggestion 2: modify the way discrete distributions are defined in Maple in order to avoid ProbabilityFunction to return wrong values.

Given finite points on a plane, how to calculate the Newton polygon, i.e. the lower bound of its convex hull?

The convex hull can be obtained by ConvexHull command from ComputationalGeometry package, but I don't know how to get its lower bound easily. Besides that, theoretically the Newton polygon does not depend on the full structure of convex hull, so maybe there is a more effective way to do that?

P.S. There is a method DEplot_polygon in DETools that can "generate the plot of the Newton polygon of a linear differential operator at a point“, but I not sure how it can be used to calculate the Newton polygon for general cases.

I came across this example from Maple's Online Help:

F := proc(t)
plottools[line]([-2,0], [cos(t)-2, sin(t)], color=blue),
plottools[line]([cos(t)-2, sin(t)], [t, sin(t)], color=blue),
plot(sin(x), x=0..t, view=[-3..7, -5..5]);
end proc:

animate(F,[theta],theta=0..2*Pi,background=plot([cos(t)-2,sin(t),t=0..2*Pi]),
scaling=constrained,axes=none);

Why is it not working?

Thank you!

mapleatha

Hi, I have a problem with tensor calculus. Please guide me.

I have two Tensors B[mu, nu] and A[~mu, ~nu].

Furthermore, I have two mixed tensors as U[~1, mu, nu] and U[~2,mu,nu]

rho, mu, and nu can run from 1 to 2. Hence, A, B, and both Us are 2*2 matrices.

Note that there was only one U, but since it is a mixed tensor, hence I have separated it into two tensors for making it easy.

Now I want to compute the following summation:

U[~rho,mu,nu] U[~alpha,beta,gamma] B[rho,alpha] A[~mu,~beta] A[~nu,~gamma].

Maple must give a number for rho, mu, nu, alpha, beta, and gamma (which can take 1 and 2) and compute "all" possible summations. Since the result will be just "a number", hence I could not use TensorArray.

How can I do it and get a result?

The forms of all tensors are in the attached maple file:
question.mw

Download question.mw

I need to change any occurance of   anything*sqrt(anything)  to say Z in any large expression.  (later, I can add the correct replacement once I know how to do it for Z).

I can change   sqrt(anything) with the help of the answers in Substitution-Of-Sub-Expressions-Is  but not  anything*sqrt(anything)

Here is an example to make it clear. Given

expr:=(-x + sqrt(9*x^2*exp(2*c) + 8)*exp(-c)+99)/(4*x)+ (a*sqrt(z)-99+sin(c*sqrt(r+4)+20))/3+10+1/(c+exp(-x)*sqrt(exp(x)))+sqrt(h)

Need to all some transformation on  those subexpressions circled above. For now, lets say I wanted to replace them with Z so it should becomes this

I can do this

subsindets(expr,anything^({1/2,-1/2}),ee->Z)

But I need to have the term (if any) that multiplies the sqrt as well included.

And that is the problem. Can't figure how to do it. When I try

subsindets(expr,anything*anything^({1/2,-1/2}),ee->Z)

Maple says Error, testing against an invalid type Ok. So anything*anything^({1/2,-1/2}) is not a type. What to do then?  Tried also subsindets(expr,t::anything*anything^({1/2,-1/2}),ee->Z) same error

And 

applyrule(t1::anything*sqrt(t0::anything)=Z, expr);

gives  Z which is wrong.

How to make this work in Maple using subsindets? Can one use pattern with subsindets? How to make a type for

               anything*sqrt(anything) 

Maple 2021.1

I 'd like to extract all items that contain "a" in an expression except "ab". What I can think of is to use the two functions select and remove to do it, but I feel a little less automated. Is there a better way?

 s := [a c, a]

Hi,

I'm a student learning calculus I

Would someone explain what the synax in the steps means? I don't understand what is going on with the section that has _X0 in it.

I want to plot a 2D graph without labels. The labes=["",""] option does half of the job—it prints the empty string for labels (that's good) but it reserves room for them (that's bad).  In the following code I use a large size labelfont in order to exaggerate the effect:

restart;
plots:-setoptions(labelfont=[TIMES,64]);  # large labelfont selected on purpose
p1 := plot([[0,0],[1,1]], labels=["", ""]);

Note the large blank space at the bottom reserved for the the non-existent label.

I know one way to eliminate the label altogether:

p2 := subs(AXESLABELS=NULL, p1);

This does the right job but is there a more orthodox way of doing that?

Afterthought:  It would be good if the labels option to the plot command  accepted none as argument, as in labels=[none, none].

Why Maple likes to extract exp() outside the sqrt when its argument has minus sign vs. not?  Compare the following

restart;
eq2 := ln(2*u^2 + u - 1) = -c - 2*ln(x);
sol:=[solve(eq2,u)]:
simplify(sol[1])

and

eq2 := ln(2*u^2 + u - 1) = c - 2*ln(x);
sol:=[solve(eq2,u)]:
simplify(sol[1])

I like the above much better than the first one. Mathematica keeps both same form (i.e. keeps the exp() inside):

Maple's answers are correct ofcourse, I just do not understand the logic why when there is a minus sign on c it likes to format it differently as shown.

Is there a way to make not do that?

I am trying to get Maple to recognize that

diff(x^n,x) does not equal n*x^(n-1), but rather 0 if n=0, or n*x^(n-1) otherwise.

This comes up when differentiating an infinite sum (power series). The constant term gets transformed into n/x instead of becoming zero. Maybe this is really a bug/lack of feature in how sum/Sum works.

For example: diff(Sum(x^n, n = 0 .. infinity), x) yields

Does anybody have a fix to get the differentiation right (other than expanding some terms of the series before taking the derivative)? 

(edited) Please note I am not trying to get an answer to this specific question. It is just illustrates a simplified example of behavior that leads to other bizarre results. Please see the attached worksheet for more weirdness: Problems_with_summation_Mapleprimes.mw

how can i remove, zero after dot from my result

restart;
V := 4;
K := 16.56;

H := 0.5;

q1 := evalf(diff(y[1](x), x) = V*y[2](x)/H - K*y[1](x)/H);
 

Hello

Consider

alias(x=x(t),y=y(t),phi1=phi1(x(t),y(t)));

phi:=[x,ph1];

I need to calculate the Jacobian of phi in relation to x and y (and finally to t)  but using VectorCalculus[Jacobian] does not work. I guess it is because of the time dependence.   What am I missing?  

Can the Physics package be used?

Many thanks.

Hello,
I want to update Alphabets in my ‘for loop’ instead of numbers. Please look at the code below:

for Tl from 263 by 5 to 313 do
   for Ql from 25 by 25 to 300 do
        myvel:= my_porous(Ql, Tl, ratiol);
        Export(<myvel>, "HPporousmodel.xlsx", 1, my_alph[vcount]);
        vcount := vcount+1;

   end do

end do
 

Here, my_alph is a manually created alphabets corresponding to excel columns as below:

my_alph:=[ "A1", "B1", "C1", "D1", "E1", "F1", "G1", "H1", "I1", "J1", "K1", "L1", "M1", "N1", "O1", "P1", "Q1", "R1", "S1", "T1", "U1", "V1", "W1", "X1", "Y1", "Z1", "AA1", "AB1", "AC1", "AD1", "AE1", "AF1", "AG1", "AH1", "AI1", "AJ1", "AK1", "AL1", "AM1", "AN1", "AO1", "AP1", "AQ1", "AR1", "AS1", "AT1", "AU1", "AV1", "AW1", "AX1", "AY1", "AZ1", "BA1", "BB1", "BC1", "BD1", "BE1", "BF1", "BG1", "BH1", "BI1", "BJ1", "BK1", "BL1", "BM1", "BN1", "BO1", "BP1", "BQ1", "BR1", "BS1", "BT1", "BU1", "BV1", "BW1", "BX1", "BY1", "BZ1"]:

The idea is to export the velocity vector that I get from proc (my_porous(Ql, Tl, ratiol)) in to an excel sheet (HPporousmodel.xlsx)with the command (Export(<myvel>, "HPporousmodel.xlsx", 1, my_alph[vcount]);). I want to export the velocities into a new column for every iteration starting from A, B, C,….. and so on. However, since I don’t know how to do that I’ve used a manually created list my_alph. This has a big disadvantage of restricting the number of times I can loop. For this case, I can only loop (3*26=78 times). Anything more asks for manually increasing the entries of my my_alph list. I want to loop for 100's of times which is becoming a big problem with this method.

Can anyone please help me in automating this without any such constraints as we do with numbers (like we have done for vcount here)?
 

Thank you.