Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021

When trying to evaluate the following line with values where units are attached Maple chrashes.

(add(eval(F, {x = XY[n, 1], y = XY[n, 2]})^2, n = 1 .. 4), location)

Problem_units.mw

What is the problem here

Dear helpfull community. I stumbled over a problem which I cloud not sort out even after hours of trying to find the error I do. 
A simple IF statement does not work when I attach a unit to a value.

tt := 80*Unit('knot');
if tt < 100*Unit('knot') then
    lprint(got*it);
end if;

Surprisingly Maple can evalue the expression if a use a = instead of the <. File should be attached.

Please can anyone tell me what I did wrong.

NULL`~`[unassign](`<,>`(anames(user)))

with(LinearAlgebra); with(Optimization); Restart

NULLNULL

NULL

Problem 1 ( If Statement with units)

 

The if statement could not evealuated with the logical operator < or > when a unit is attached to the value

 

tt := 80*Unit('knot'); if tt < 100*Unit('knot') then lprint(got*it) end if

Error, cannot determine if this expression is true or false: 100*Units:-Unit(knot) < 80*Units:-Unit(knot)

 

 

 

But it works if the logical operator " = "

 

tt := 80*Unit('knot'); if tt = 80*Unit('knot') then lprint(got*it) end if

got*it

 

 

Anyone an idea why.

``

 

 

NULL

 

 

NULL

NULL

Download Problem_IF.mw

I have my code in mla. Using try/catch, I am able to capture an error that happend deep in some call chain. But it is hard to know the exact location where this error happened.

I use StringTools:-FormatMessage( lastexception[2..-1] inside the catch clause to print the exception. But this only prints the message. It does not tell me exactly which line/function/module this happened.

Is there a way to display these information?  Using debugger and stoperror all did not help at all. It does not stop at the line where the error happened. not sure why. I tried it many times. may be I am not using it correctly?

Is it possible to display may be the trace of the calls inside the catch of the try? To know the actual statement that generated the error? Now each time I get an exception, I have to step into the debugger line by line until  I get to the place where the error was which is time consuming. Here is a MWE

 

restart;
A:=module()  
  local B:=module()
     export foo:=proc(n)
         1/n;
     end proc;
  end module;

  export main:=proc()
    try
       B:-foo(0);
    catch:
      print("error happened", StringTools:-FormatMessage( lastexception[2..-1] ));
    end try;
  end proc;

end module;

And now

    A:-main()

                "error happened", "numeric exception: division by zero"

I'd like to get more information than the above as I said. Line number/proc name/module name or stacktrace showing the calls made up to where the exception started (similar to output from where command in debugger).

The above was done in worksheet. My actual code in inside .mla build from lots of .mpl files.

Maple 2021.2 on windows

Here is short description of the problem with code MWE below.

Short version of the question

I want to change

parent:=module()
  local foo:=proc()
     NULL;
  end proc;

  local child:=module()    
     export boo:=proc()
        foo(); #call works as is
     end proc;
  end module;

end module;

To

parent:=module()
  local foo:=proc()
     NULL;
  end proc;

  local child:=module()    
     export boo:=proc()

         #now call no longer works. Maple wants foo exported
         #I want to add parent:- to the call to remind me where foo((
         #lives but do not want to make foo() in parent exported

         parent:-foo();

     end proc;
  end module;
end module;

Longer version of the question

I have a parent module with one child local module inside it. In the child module, there is a proc which wants to call parent's local proc named foo().

As is, the child module can just call the parent's local proc foo() by typing foo() without the need to do parent:-foo() this is because child module has access to parent local proc's and maple knows which foo() by searching the scope from bottom up.

The problem comes when I added a proc also called foo() (by mistake) in the child module without noticing there is one with same name in the parent's.

Now the call foo() will end up calling the child's module foo() and not the parent's foo() becuase that is the "closest" one with this name in the scope. All of this makes sense so far.

The problem comes when the child module wants to really call the parent's foo().

One solution is to change the call to parent:-foo() to explicitly says which foo() to call.

This however now fail, since the parent foo() is local ! And Maple when it sees call to parent:-foo() it now insist it be exported proc (even though the call is being made from inside, i.e. from the child).

I do not want to make the parent's foo() exported just so the child can call it.  I want to keep parent's foo() local, as it is meant to be used only inside the parent and by its children.

You might ask, why not then change the name of the child's foo() to some other name so it does not clash with the parent's local proc name. Yes, I can do this. But for large modules in different files with many procs(), there is a always a chance  a local proc can be added by mistake with happend to be the same name as one in the parent and having to manually keep checking names does not look like the right solution.

My question is: How can a child module call parent's local proc() explicitly, but without making the parent proc exported?  Is there is different syntax to use?

Here is a MWE

 

restart;
parent:=module()

  export main:=proc()
     child:-boo();
  end proc;

  local foo:=proc()
     print("in parent:-foo() proc");
  end proc;

  local child:=module()     
     export boo:=proc()
        print("in child:-boo() proc");
        foo(); #this works. It called parent's local foo()
     end proc;
  end module;

end module;

Now doing parent:-main() works as expected. Notice parent's foo is local to parent module.

Now I changed the child module and did this

parent:=module()

  export main:=proc()
     child:-boo();
  end proc;

  local foo:=proc()
     print("in parent:-foo() proc");
  end proc;

  local child:=module()
     local foo:=proc() #added this using same name by mistake
        print("in child:-boo()");
     end proc;

     export boo:=proc()
        print("in child:-boo() proc");
        foo(); #now this calls the child's foo() ofcourse. But it was meant to call the parents's
     end proc;
  end module;

end module;

The fix is to change the call from the child to becomes    parent:-foo() but now Maple will give an error saying parent does not export foo().

Since the child have access to parent's local proc's, is there a different way to tell Maple I want to call parent's foo() and not my own foo() without making parent's foo() exported? 

For example , in Python one call call parent's method expliclity using super().foo() 

Maple 2021.2

how to transform this program using LinearAlgebra instead of linalg  ?

restart;
with(plots);
unprotect(gamma, D);
interface(rtablesize = 10): _EnvHorizontalName := 'x': _EnvVerticalName := 'y':
f := (x, y) -> 4*x^2 + 4*y*x + y^2 - 8*x + 16*y - 17: (for instance)
NULL;
Fg := proc(P::polynom, v::set, V::list, N::list) 
local C, M, i, j; 
C := coeffs(f(x, y), v, M); seq(`if`(member(op(i, [M]), N, 'j'), op(j, V) = op(i, [C]), NULL), i = 1 .. nops([M])); end proc:
Fg(f(x, y), {x, y}, [A, B, C, D, E, F], [x^2, y*x, y^2, x, y, 1]):
assign(%);
Delta := -4*A*C + B^2:
var := [x, y]:
with(linalg):
AA := matrix([seq([seq(diff(f(x, y), var[i], var[j])/2, j = 1 .. 2)], i = 1 .. 2)]):
vp := sort([eigenvals(AA)]):
print(`Valeur propres de AA ` = vp):
DD := jordan(AA, 'P11'):
print(`Matrice diagonale semblable à AA:   DD` = evalm(DD)):
G := map(normalize, GramSchmidt([col(P11, 1 .. 2)])):
PP := map(simplify, concat(op(G))):
print(`Matrice de passage orthogonale:   PP` = evalm(PP)):
print(`Directions principales de la conique:`):
print(`I1 ` = col(PP, 1), ` J ` = col(PP, 2)):
alpha := 1/2*arctan(B/(A - C)):
print('alpha' = evalf(%)):                 

M1 := matrix(1, 2, [X, Y]):
M2 := matrix(2, 1, [X, Y]):
multiply(M1, AA, M2):
N := matrix(1, 2, [D, E]):
multiply(M1, AA, M2) + multiply(N, M2):
multiply(M1, transpose(PP), AA, PP, M2) + multiply(N, PP, M2):

NULL;
The parabola in the new base is Y`^2 =X*(8*sqrt(5))/5 , <sqrt(5), -2*sqrt(5)>, <sqrt(5), 2*sqrt(5)>

I am using GenerateMatrix to construct a matrix out of a set of 6 equations with 6 variables.  The output of Generate Matrix is not sorted correctly.  Where am I going wrong? Is this a bug?

restart

NULL``

with(LinearAlgebra)

NULL

NULL

The command GenerateMatrix is not sorting my set of equations properly.

NULL

NULL

Define a set of 6 equations.

equation_set := [5964.000000-770.0000000*T__1+750.0000000*T__2 = 0, 20*T[1]-770.0000000*T[2]+750.0000000*T[3]+100.0000000 = 0, 20*T[2]-770.0000000*T[3]+750.0000000*T[4]+100.0000000 = 0, 20*T[3]-770.0000000*T[4]+750.0000000*T[5]+100.0000000 = 0, 20*T[4]-770.0000000*T[5]+750.0000000*T[6]+100.0000000 = 0, 5900.787944-770.0000000*T[6]+750.0000000*T[5] = 0]

[5964.000000-770.0000000*T__1+750.0000000*T__2 = 0, 20*T[1]-770.0000000*T[2]+750.0000000*T[3]+100.0000000 = 0, 20*T[2]-770.0000000*T[3]+750.0000000*T[4]+100.0000000 = 0, 20*T[3]-770.0000000*T[4]+750.0000000*T[5]+100.0000000 = 0, 20*T[4]-770.0000000*T[5]+750.0000000*T[6]+100.0000000 = 0, 5900.787944-770.0000000*T[6]+750.0000000*T[5] = 0]

(1)

NULL

NULL

NULL

This is what each one looks like individually.

equation_set[1]

5964.000000-770.0000000*T__1+750.0000000*T__2 = 0

(2)

equation_set[2]

20*T[1]-770.0000000*T[2]+750.0000000*T[3]+100.0000000 = 0

(3)

equation_set[3]

20*T[2]-770.0000000*T[3]+750.0000000*T[4]+100.0000000 = 0

(4)

equation_set[4]

20*T[3]-770.0000000*T[4]+750.0000000*T[5]+100.0000000 = 0

(5)

equation_set[5]

20*T[4]-770.0000000*T[5]+750.0000000*T[6]+100.0000000 = 0

(6)

equation_set[6]

5900.787944-770.0000000*T[6]+750.0000000*T[5] = 0

(7)

NULL

The variables used in the above set of equations.

variables_set := [T[1], T[2], T[3], T[4], T[5], T[6]]

[T[1], T[2], T[3], T[4], T[5], T[6]]

(8)

variables_set[1]

T[1]

(9)

A, b := GenerateMatrix(equation_set, variables_set)

Matrix(%id = 36893490238808803916), Vector[column](%id = 36893490238808803796)

(10)

This output seems wrong because a row of zeros appears in A``.  The first entry of the column vector contains the full equation. Thus, it seems GenerateMatrix didn't sort the set of equation properly.  I tried re-writing the  offending equation  as 5964.000000-770.0000000*T__1+750.0000000*T__2 = 0,but maple just changes it back on evaluation.NULL


 I think the output should look like:


A, b := Matrix(6, 6, {(1, 1) = -770.0000000, (1, 2) = 750.0000000, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = 20, (2, 2) = -770.0000000, (2, 3) = 750.0000000, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = 0, (3, 2) = 20, (3, 3) = -770.0000000, (3, 4) = 750.0000000, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 20, (4, 4) = -770.0000000, (4, 5) = 750.0000000, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 20, (5, 5) = -770.0000000, (5, 6) = 750.0000000, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 750.0000000, (6, 6) = -770.0000000}), Vector(6, {(1) = -5964.000000, (2) = -100.0000000, (3) = -100.0000000, (4) = -100.0000000, (5) = -100.0000000, (6) = -5900.787944})

NULL

I rename the matrix and column vector and use LinearSolve to find a solution for T.

AA := Matrix(6, 6, {(1, 1) = -770.0000000, (1, 2) = 750.0000000, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = 20, (2, 2) = -770.0000000, (2, 3) = 750.0000000, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = 0, (3, 2) = 20, (3, 3) = -770.0000000, (3, 4) = 750.0000000, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 20, (4, 4) = -770.0000000, (4, 5) = 750.0000000, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 20, (5, 5) = -770.0000000, (5, 6) = 750.0000000, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 750.0000000, (6, 6) = -770.0000000})

Matrix(%id = 36893490238866723772)

(11)

``

bb := Vector(6, {(1) = -5964.000000, (2) = -100.0000000, (3) = -100.0000000, (4) = -100.0000000, (5) = -100.0000000, (6) = -5900.787944})

Vector[column](%id = 36893490238885708252)

(12)

NULL

NULL

T := LinearSolve(AA, bb)

Vector[column](%id = 36893490238857651132)

(13)

NULL

Download GenerateMatrix_Improper_Sorting.mw

intersection de deux droites l1 et l2 telles que l1 sous forme parametrique est [57/5 + 20*t, -21/5 - 40*t, 20*t] et de la meme façon

 l2 [249/100 - 120*t, 471/100 - 80*t, 200*t]. t est le parametre  . maple donne pour l'intersection de l1 et l2 le point P de coordonnes

 [249/100, 471/100, 0] que je ne trouve pas .expliquez moi ce resultat et merci beaucoup.

restart:
digits := 20;
unprotect(D);
G := 0.04361098108*x^2 + 0.4810001561*x*y + 1.326278064*y^2 - 0.7320831383*x - 2.656083763*y + 1 = 0
f := (x, y) -> lhs(G);
coeffs(f(x, y));
A, B, C, D, E, F := coeffs(f(x, y));
A := coeff(f(x, y), x, 2);
B := coeff(coeff(f(x, y), x), y);
C := coeff(f(x, y), y, 2);
D := coeff(coeff(f(x, y), x, 1), y, 0);
E := coeff(coeff(f(x, y), y, 1), x, 0);
F := tcoeff(f(x, y));
expand(B^2 - ((4*A) . C));
                          digits := 20

   f := proc (x, y) options operator, arrow; lhs(G) end proc

  1, -0.7320831383, 1.326278064, 0.04361098108, 0.4810001561, 

    -2.656083763


A, B, C, D, E, F := 1, -0.7320831383, 1.326278064, 0.04361098108, 

  0.4810001561, -2.656083763


                       A := 0.04361098108

                       B := 0.4810001561

                        C := 1.326278064

                       D := -0.7320831383

                       E := -2.656083763

                             F := 1

                               0.


with(geometry):
_EnvHorizontalName := 'x': _EnvVerticalName := 'y':
conic(co,f(x,y),[x,y]):
detail(co);
                 /                            
   GeometryDetail\["name of the object", co], 
   ["form of the object", ellipse2d], 
   ["center", [1.212351672 ^(10, 10), -2.198412833 ^(10, 9)]], 
   ["foci", [[2.424703344 ^(10, 10), -4.396825668 ^(10, 9)], 
   [0.1787052775, 0.9855002601]]], 
   ["length of the major axis", 2.464245740 ^(10, 10)], 
   ["length of the minor axis", 66579.62094], 
   [                                               2
   ["equation of the ellipse", 1. + 0.04361098108 x 
                                      2                 
    + 0.4810001561 x y + 1.326278064 y  - 0.7320831383 x
                       ]\ 
    - 2.656083763 y = 0]/;
   "_noterminate";

G is a parabola with B^2-4*A*C=0 or an ellipse ? A =1 or F=1 ? Thank you for youy answer. 

I have code which in module which does this

           DEtools:-kovacicsols(ode,func)

Where ode is some ode and func is y(x).  When I step in the debugger, I get exception at this. It says

       DBG> DEtools:-kovacicsols(ode,func)
       Error, `DEtools` does not evaluate to a module

Same exact code works OK from worksheet as expected.   SO for some reason, inside this module it does not see DEtools and I have no idea why.

Then I tried with :-  before DEtools, but this did not help. it gives

DBG> :-DEtools:-kovacicsols(ode,func)
Error, `table([(dperiodic_sols)=proc () `DEtools/init`() <> 0; `ODEtools/intfactor`(_passed); end etc...
` does not evaluate to a module

In a worksheet, it all works OK

ode:=diff(diff(y(x),x),x) = (-3/16/x^2-2/9/(x-1)^2+3/16/x/(x-1))*y(x);
func:=y(x);
DEtools:-kovacicsols(ode,func)

Gives the solution with no error.

Any suggestion what could be the cause and what to try next? I never seen anything like this. I am running this code using 

interface(warnlevel=4);
kernelopts('assertlevel'=2):

I am able to make a MWE. It seems this always happens in the debugger.  But if  I let it run, it works somehow. Only when I try to step into it, it gives error. Here is MWE

interface(warnlevel=4);
kernelopts('assertlevel'=2):
foo:=proc(ode,func)
   local result;
    DEBUG();   
    result:=DEtools:-kovacicsols(ode,func);
    return result;
  end proc;

And now

ode:=diff(diff(y(x),x),x) = (-3/16/x^2-2/9/(x-1)^2+3/16/x/(x-1))*y(x);
func:=y(x);
foo(ode,y(x))

Now in the debugger if I do DEtools:-kovacicsols(ode,func) or if I stepin the call, I get the error. But I hit the continue botton, I do not get the error and it gives solution. 

Why this happens?

Maple 2021.2 on windows 10

j'ai deux spheres concentriques s1 et s2  de centre O(-1,-1,-1) de rayon respectivement 3 et 2. mais maple donne que FindAngle(s1,s2)=arcos(31/12). comment expliquez ceçi et merci beaucoup.

PDETWOSTEPVARIAMETHOD.mwPDETWOSTEPVARIAMETHOD.mw

Pls i need help to correct this iteration code, I wrote but is not given the correct answer. find attached the worksheet

Hi!

I am fairly new to maple and needing to use it for my project this year. I have been advised to use it to help solve the following integral:

int(2/(1-x^p)^(1/p), x=0..1)

It will give me the answer I am looking for, however I cannot get it to explain the steps to get the answer. I have tried Student Calculus1 and ShowSolution but neither of them seem to be working.

Any help would be really appreiacted!

Hi,

I have a problem with maple. I used to work with maple until 2019. Now I installed Maple 2021 and I wanted to plot something, but it didn't worked anymore. I have problems to plot anything. When I try to plot something, maple only writes a very long list instead of a graphic. Here you can see, what I wrote in the worksheet:

restart;
with(LinearAlgebra):
with(plots):

plot(x^2,x=0..2);
INTERFACE_PLOT(CURVES(Matrix(200,2,{(2, 1) = HFloat(.105152100502512568e-1), (2
, 2) = HFloat(.110569642400905045e-3), (3, 1) = HFloat(.196644380904522631e-1),
(3, 2) = HFloat(.386690125413229849e-3), (4, 1) = HFloat(.299537019095477385e-1
), (4, 2) = HFloat(.897224258086043816e-3), (5, 1) = HFloat(.403111696482412116\
e-1), (5, 2) = HFloat(.162499039840928341e-2), (6, 1) = HFloat(.\
506194101507537672e-1), (6, 2) = HFloat(.256232468401023337e-2), (7, 1) =
HFloat(.601764686432160745e-1), (7, 2) = HFloat(.362120737836796758e-2), (8, 1)
= HFloat(.700722491457286406e-1), (8, 2) = HFloat(.491012010034106838e-2), (9,
1) = HFloat(.803064794974874402e-1), (9, 2) = HFloat(.644913064928037075e-2), (
10, 1) = HFloat(.905078885427135632e-1), (10, 2) = HFloat(.819167788846026160e-\
2), (11, 1) = HFloat(.101001291658291470), (11, 2) = HFloat(.102012609166432580\
e-1), (12, 1) = HFloat(.110243886834170857), (12, 2) = HFloat(.\
121537145843054698e-1), (13, 1) = HFloat(.120648859899497501), (13, 2) = HFloat
(.145561473950485756e-1), (14, 1) = HFloat(.131096556783919599), (14, 2) =
HFloat(.171863072005994551e-1), (15, 1) = HFloat(.141164848643216101), (15, 2)
= HFloat(.199275144924621096e-1), (16, 1) = HFloat(.150307822211055264), (16, 2
) = HFloat(.225924414178301988e-1), (17, 1) = HFloat(.161179702110552769), (17,
2) = HFloat(.259788963724465298e-1), (18, 1) = HFloat(.170389610452261309), (18
, 2) = HFloat(.290326193500733548e-1), (19, 1) = HFloat(.181102923316582926), (
19, 2) = HFloat(.327982688338121151e-1), (20, 1) = HFloat(.190586020502512554),
(20, 2) = HFloat(.363230312109841386e-1), (21, 1) = HFloat(.200990481105527641)
, (21, 2) = HFloat(.403971734950314618e-1), (22, 1) = HFloat(.21089798804020101\
8), (22, 2) = HFloat(.444779613594047732e-1), (23, 1) = HFloat(.221235432160804\
046), (23, 2) = HFloat(.489451164433777272e-1), (24, 1) = HFloat(.2307284328643\
21625), (24, 2) = HFloat(.532356097320257696e-1), (25, 1) = HFloat(.24096791658\
2914582), (25, 2) = HFloat(.580655368223104776e-1), (26, 1) = HFloat(.251603862\
412060286), (26, 2) = HFloat(.633045035806669570e-1), (27, 1) = HFloat(.2608624\
84522613070), (27, 2) = HFloat(.680492358313105478e-1), (28, 1) = HFloat(.27086\
2050050251268), (28, 2) = HFloat(.733662501574248171e-1), (29, 1) = HFloat(.281\
192579698492429), (29, 2) = HFloat(.790692668774930219e-1), (30, 1) = HFloat(.2\
91298987537688459), (30, 2) = HFloat(.848551001404823785e-1), (31, 1) = HFloat(
.301077456783919617), (31, 2) = HFloat(.906476349834729883e-1), (32, 1) =
HFloat(.311934779698492481), (32, 2) = HFloat(.973033067855470363e-1), (33, 1)
= HFloat(.321690567236180891), (33, 2) = HFloat(.103484821048735812), (34, 1) =
HFloat(.332106952763819130), (34, 2) = HFloat(.110295028074069587), (35, 1) =
HFloat(.341545746231155745), (35, 2) = HFloat(.116653496768597043), (36, 1) =
HFloat(.351864840603015094), (36, 2) = HFloat(.123808866052585217), (37, 1) =
HFloat(.361574304221105480), (37, 2) = HFloat(.130735977472976550), (38, 1) =
HFloat(.371723491356783953), (38, 2) = HFloat(.138178354026477046), (39, 1) =
HFloat(.381646176884422095), (39, 2) = HFloat(.145653804330495601), (40, 1) =
HFloat(.392034309045226126), (40, 2) = HFloat(.153690899468567871), (41, 1) =
HFloat(.402039314974874384), (41, 2) = HFloat(.161635610785466260), (42, 1) =
HFloat(.412270878592964851), (42, 2) = HFloat(.169967277335815153), (43, 1) =
HFloat(.422417719698492511), (43, 2) = HFloat(.178436729915274178), (44, 1) =
HFloat(.431741612864321611), (44, 2) = HFloat(.186400820278685764), (45, 1) =
HFloat(.442427846633165867), (45, 2) = HFloat(.195742399476460133), (46, 1) =
HFloat(.451985741507537675), (46, 2) = HFloat(.204291110526118674), (47, 1) =
HFloat(.462176450954773888), (47, 2) = HFloat(.213607071817150523), (48, 1) =
HFloat(.471930260201005036), (48, 2) = HFloat(.222718170493388323), (49, 1) =
HFloat(.482760611859296529), (49, 2) = HFloat(.233057808362762353), (50, 1) =
HFloat(.492138900603015073), (50, 2) = HFloat(.242200697486744360), (51, 1) =
HFloat(.502783342211055251), (51, 2) = HFloat(.252791089204919106), (52, 1) =
HFloat(.512484595175879409), (52, 2) = HFloat(.262640460292584976), (53, 1) =
HFloat(.523096241306532650), (53, 2) = HFloat(.273629677669022242), (54, 1) =
HFloat(.532252297286432086), (54, 2) = HFloat(.283292507966684481), (55, 1) =
HFloat(.542679976281407073), (55, 2) = HFloat(.294501556656788566), (56, 1) =
HFloat(.552752599396984956), (56, 2) = HFloat(.305535436140123740), (57, 1) =
HFloat(.562818642311557871), (57, 2) = HFloat(.316764824133425327), (58, 1) =
HFloat(.572847654070351764), (58, 2) = HFloat(.328154434773905379), (59, 1) =
HFloat(.582482394673366821), (59, 2) = HFloat(.339285740104419864), (60, 1) =
HFloat(.592897804422110597), (60, 2) = HFloat(.351527806488559302), (61, 1) =
HFloat(.602824445125628161), (61, 2) = HFloat(.363397311641021459), (62, 1) =
HFloat(.613271767035175941), (62, 2) = HFloat(.376102260242447139), (63, 1) =
HFloat(.622729109145728654), (63, 2) = HFloat(.387791543377432824), (64, 1) =
HFloat(.633181242613065298), (64, 2) = HFloat(.400918485997025453), (65, 1) =
HFloat(.643192565125628168), (65, 2) = HFloat(.413696675832885441), (66, 1) =
HFloat(.653179519798995023), (66, 2) = HFloat(.426643485084845731), (67, 1) =
HFloat(.663610932663316611), (67, 2) = HFloat(.440379469950276936), (68, 1) =
HFloat(.673218644723618143), (68, 2) = HFloat(.453223343603505191), (69, 1) =
HFloat(.683058256080402049), (69, 2) = HFloat(.466568581199600096), (70, 1) =
HFloat(.693922356180904587), (70, 2) = HFloat(.481528236407658183), (71, 1) =
HFloat(.703758908944723593), (71, 2) = HFloat(.495276601919067749), (72, 1) =
HFloat(.713818626633165865), (72, 2) = HFloat(.509537031728459100), (73, 1) =
HFloat(.724049100402010093), (73, 2) = HFloat(.524247099792960136), (74, 1) =
HFloat(.733452896582914682), (74, 2) = HFloat(.537953151505867755), (75, 1) =
HFloat(.743477038793969869), (75, 2) = HFloat(.552758107213850214), (76, 1) =
HFloat(.753424876582914571), (76, 2) = HFloat(.567649044653980028), (77, 1) =
HFloat(.764065970854271415), (77, 2) = HFloat(.583796807817480334), (78, 1) =
HFloat(.773456275577889429), (78, 2) = HFloat(.598234610230820030), (79, 1) =
HFloat(.784290737889447254), (79, 2) = HFloat(.615111961539173691), (80, 1) =
HFloat(.794068004824120544), (80, 2) = HFloat(.630543996285359509), (81, 1) =
HFloat(.803742099396984933), (81, 2) = HFloat(.646001362343072816), (82, 1) =
HFloat(.814144858894472301), (82, 2) = HFloat(.662831851264300220), (83, 1) =
HFloat(.824589699698492495), (83, 2) = HFloat(.679948172848850008), (84, 1) =
HFloat(.834092958291457243), (84, 2) = HFloat(.695711063071394631), (85, 1) =
HFloat(.844184996783919672), (85, 2) = HFloat(.712648308795066465), (86, 1) =
HFloat(.854033840000000044), (86, 2) = HFloat(.729373799865145722), (87, 1) =
HFloat(.864710089949748739), (87, 2) = HFloat(.747723539660902548), (88, 1) =
HFloat(.873948014472361812), (88, 2) = HFloat(.763785132000183498), (89, 1) =
HFloat(.884558106633165808), (89, 2) = HFloat(.782443044010451172), (90, 1) =
HFloat(.894532151055276392), (90, 2) = HFloat(.800187769271579863), (91, 1) =
HFloat(.904409857085427094), (91, 2) = HFloat(.817957189593282674), (92, 1) =
HFloat(.914295420904522649), (92, 2) = HFloat(.835936116686978203), (93, 1) =
HFloat(.924378070251256290), (93, 2) = HFloat(.854474816761436551), (94, 1) =
HFloat(.935065509648241200), (94, 2) = HFloat(.874347507333725016), (95, 1) =
HFloat(.944864845025125577), (95, 2) = HFloat(.892769575364354528), (96, 1) =
HFloat(.954538047336683348), (96, 2) = HFloat(.911142883813328308), (97, 1) =
HFloat(.964878541407035106), (97, 2) = HFloat(.930990599667767538), (98, 1) =
HFloat(.975196525125628155), (98, 2) = HFloat(.951008262617099920), (99, 1) =
HFloat(.984457528241206137), (99, 2) = HFloat(.969156624910785136), (100, 1) =
HFloat(.995427854271356827), (100, 2) = HFloat(.990876613059277656), (101, 1) =
HFloat(1.00460731437185924), (101, 2) = HFloat(1.00923585608943966), (102, 1) =
HFloat(1.01534372402010042), (102, 2) = HFloat(1.03092287790700587), (103, 1) =
HFloat(1.02559058693467331), (103, 2) = HFloat(1.05183605200900776), (104, 1) =
HFloat(1.03473981497487433), (104, 2) = HFloat(1.07068648469423722), (105, 1) =
HFloat(1.04502907879397000), (105, 2) = HFloat(1.09208577552497355), (106, 1) =
HFloat(1.05538654653266328), (106, 2) = HFloat(1.11384076260214138), (107, 1) =
HFloat(1.06569478703517584), (107, 2) = HFloat(1.13570537911394887), (108, 1) =
HFloat(1.07525184552763808), (108, 2) = HFloat(1.15616653131059177), (109, 1) =
HFloat(1.08514762603015091), (109, 2) = HFloat(1.17754537027887229), (110, 1) =
HFloat(1.09538185638190955), (110, 2) = HFloat(1.19986141129067825), (111, 1) =
HFloat(1.10558326542713559), (111, 2) = HFloat(1.22231435679252809), (112, 1) =
HFloat(1.11607666854271348), (112, 2) = HFloat(1.24562713006540182), (113, 1) =
HFloat(1.12531926371859292), (113, 2) = HFloat(1.26634344529615617), (114, 1) =
HFloat(1.13572423678391954), (114, 2) = HFloat(1.28986954201841653), (115, 1) =
HFloat(1.14617193366834180), (115, 2) = HFloat(1.31371010152902579), (116, 1) =
HFloat(1.15624022552763828), (116, 2) = HFloat(1.33689145912820373), (117, 1) =
HFloat(1.16538319909547727), (117, 2) = HFloat(1.35811800073400879), (118, 1) =
HFloat(1.17625507899497483), (118, 2) = HFloat(1.38357601086147453), (119, 1) =
HFloat(1.18546498733668337), (119, 2) = HFloat(1.40532723620116284), (120, 1) =
HFloat(1.19617830020100513), (120, 2) = HFloat(1.43084252587176586), (121, 1) =
HFloat(1.20566139738693479), (121, 2) = HFloat(1.45361940514901633), (122, 1) =
HFloat(1.21606585798994971), (122, 2) = HFloat(1.47881617096883256), (123, 1) =
HFloat(1.22597336492462317), (123, 2) = HFloat(1.50301069150460331), (124, 1) =
HFloat(1.23631080904522617), (124, 2) = HFloat(1.52846441656206178), (125, 1) =
HFloat(1.24580380974874383), (125, 2) = HFloat(1.55202713238448431), (126, 1) =
HFloat(1.25604329346733667), (126, 2) = HFloat(1.57764475506427404), (127, 1) =
HFloat(1.26667923929648252), (127, 2) = HFloat(1.60447629526471558), (128, 1) =
HFloat(1.27593786140703536), (128, 2) = HFloat(1.62801742617195888), (129, 1) =
HFloat(1.28593742693467328), (129, 2) = HFloat(1.65363506599136811), (130, 1) =
HFloat(1.29626795658291449), (130, 2) = HFloat(1.68031061526364467), (131, 1) =
HFloat(1.30637436442211063), (131, 2) = HFloat(1.70661398001927345), (132, 1) =
HFloat(1.31615283366834168), (132, 2) = HFloat(1.73225828157320549), (133, 1) =
HFloat(1.32701015658291466), (133, 2) = HFloat(1.76095595567421159), (134, 1) =
HFloat(1.33676594412060301), (134, 2) = HFloat(1.78694318936064711), (135, 1) =
HFloat(1.34718232964824125), (135, 2) = HFloat(1.81490022931646267), (136, 1) =
HFloat(1.35662112311557781), (136, 2) = HFloat(1.84042087168337165), (137, 1) =
HFloat(1.36694021748743699), (137, 2) = HFloat(1.86852555818460164), (138, 1) =
HFloat(1.37664968110552777), (138, 2) = HFloat(1.89516434448795135), (139, 1) =
HFloat(1.38679886824120602), (139, 2) = HFloat(1.92321110095508985), (140, 1) =
HFloat(1.39672155376884422), (140, 2) = HFloat(1.95083109876245442), (141, 1) =
HFloat(1.40710968592964836), (141, 2) = HFloat(1.97995766823703367), (142, 1) =
HFloat(1.41711469185929650), (142, 2) = HFloat(2.00821404988346908), (143, 1) =
HFloat(1.42734625547738680), (143, 2) = HFloat(2.03731733302531737), (144, 1) =
HFloat(1.43749309658291469), (144, 2) = HFloat(2.06638640272353680), (145, 1) =
HFloat(1.44681698974874351), (145, 2) = HFloat(2.09327940182561578), (146, 1) =
HFloat(1.45750322351758776), (146, 2) = HFloat(2.12431564656415928), (147, 1) =
HFloat(1.46706111839195996), (147, 2) = HFloat(2.15226832509746835), (148, 1) =
HFloat(1.47725182783919595), (148, 2) = HFloat(2.18227296285424543), (149, 1) =
HFloat(1.48700563708542721), (149, 2) = HFloat(2.21118576472383710), (150, 1) =
HFloat(1.49783598874371848), (150, 2) = HFloat(2.24351264917587256), (151, 1) =
HFloat(1.50721427748743708), (151, 2) = HFloat(2.27169487826197702), (152, 1) =
HFloat(1.51785871909547732), (152, 2) = HFloat(2.30389509113416313), (153, 1) =
HFloat(1.52755997206030147), (153, 2) = HFloat(2.33343946824086901), (154, 1) =
HFloat(1.53817161819095460), (154, 2) = HFloat(2.36597192700818004), (155, 1) =
HFloat(1.54732767417085437), (155, 2) = HFloat(2.39422293125498564), (156, 1) =
HFloat(1.55775535316582903), (156, 2) = HFloat(2.42660174031679654), (157, 1) =
HFloat(1.56782797628140713), (157, 2) = HFloat(2.45808456321065272), (158, 1) =
HFloat(1.57789401919598005), (158, 2) = HFloat(2.48974953581444369), (159, 1) =
HFloat(1.58792303095477383), (159, 2) = HFloat(2.52149955223659550), (160, 1) =
HFloat(1.59755777155778911), (160, 2) = HFloat(2.55219083346468922), (161, 1) =
HFloat(1.60797318130653277), (161, 2) = HFloat(2.58557775180105187), (162, 1) =
HFloat(1.61789982201005023), (162, 2) = HFloat(2.61759983406015229), (163, 1) =
HFloat(1.62834714391959801), (163, 2) = HFloat(2.65151442111111191), (164, 1) =
HFloat(1.63780448603015083), (164, 2) = HFloat(2.68240353446048641), (165, 1) =
HFloat(1.64825661949748747), (165, 2) = HFloat(2.71674988371728521), (166, 1) =
HFloat(1.65826794201005034), (166, 2) = HFloat(2.74985256749824769), (167, 1) =
HFloat(1.66825489668341720), (167, 2) = HFloat(2.78307440030819908), (168, 1) =
HFloat(1.67868630954773868), (168, 2) = HFloat(2.81798772586300617), (169, 1) =
HFloat(1.68829402160804021), (169, 2) = HFloat(2.85033670339744960), (170, 1) =
HFloat(1.69813363296482422), (170, 2) = HFloat(2.88365783540631249), (171, 1) =
HFloat(1.70899773306532654), (171, 2) = HFloat(2.92067325162242497), (172, 1) =
HFloat(1.71883428582914588), (172, 2) = HFloat(2.95439130214179002), (173, 1) =
HFloat(1.72889400351758793), (173, 2) = HFloat(2.98907447539907345), (174, 1) =
HFloat(1.73912447728643227), (174, 2) = HFloat(3.02455394749680639), (175, 1) =
HFloat(1.74852827346733686), (175, 2) = HFloat(3.05735112311466573), (176, 1) =
HFloat(1.75855241567839204), (176, 2) = HFloat(3.09250659868830802), (177, 1) =
HFloat(1.76850025346733686), (177, 2) = HFloat(3.12759314651403475), (178, 1) =
HFloat(1.77914134773869348), (178, 2) = HFloat(3.16534393523345470), (179, 1) =
HFloat(1.78853165246231161), (179, 2) = HFloat(3.19884547185956691), (180, 1) =
HFloat(1.79936611477386954), (180, 2) = HFloat(3.23771841499641022), (181, 1) =
HFloat(1.80914338170854272), (181, 2) = HFloat(3.27299977557982169), (182, 1) =
HFloat(1.81881747628140711), (182, 2) = HFloat(3.30809701202666684), (183, 1) =
HFloat(1.82922023577889470), (183, 2) = HFloat(3.34604667098299524), (184, 1) =
HFloat(1.83966507658291456), (184, 2) = HFloat(3.38436759399882092), (185, 1) =
HFloat(1.84916833517587942), (185, 2) = HFloat(3.41942353181713354), (186, 1) =
HFloat(1.85926037366834174), (186, 2) = HFloat(3.45684913709334163), (187, 1) =
HFloat(1.86910921688442211), (187, 2) = HFloat(3.49356926464229778), (188, 1) =
HFloat(1.87978546683417092), (188, 2) = HFloat(3.53359340132096200), (189, 1) =
HFloat(1.88902339135678377), (189, 2) = HFloat(3.56840937309308481), (190, 1) =
HFloat(1.89963348351758787), (190, 2) = HFloat(3.60860737170116597), (191, 1) =
HFloat(1.90960752793969868), (191, 2) = HFloat(3.64660091076396720), (192, 1) =
HFloat(1.91948523396984938), (192, 2) = HFloat(3.68442356342828736), (193, 1) =
HFloat(1.92937079778894471), (193, 2) = HFloat(3.72247167536074919), (194, 1) =
HFloat(1.93945344713567835), (194, 2) = HFloat(3.76147967360646573), (195, 1) =
HFloat(1.95014088653266326), (195, 2) = HFloat(3.80304947732640164), (196, 1) =
HFloat(1.95994022190954786), (196, 2) = HFloat(3.84136567345884794), (197, 1) =
HFloat(1.96961342422110564), (197, 2) = HFloat(3.87937704087198920), (198, 1) =
HFloat(1.97995391829145739), (198, 2) = HFloat(3.92021751855769507), (199, 1) =
HFloat(1.99027190201005011), (199, 2) = HFloat(3.96118224393070228), (200, 1) =
HFloat(2.), (200, 2) = HFloat(4.)},datatype = float[8],storage = rectangular,
order = Fortran_order,shape = []),COLOUR(RGB,.47058824,0.,.54901961e-1,
_ATTRIBUTE("source" = "mathdefault"))),AXESLABELS(x,""),VIEW(0. .. 2.,DEFAULT,
_ATTRIBUTE("source" = "mathdefault")))

I also opened an old worksheet with plots and pressed the "!!!" buttom, but maple didn't plotted anything, but 3 years ago, it worked with the old version of maple.  Does anybody knows what the problem is?

restart

with(Physics)

Setup(spacetime)

[spacetimeindices = greek]

(1)

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1142 and is the same as the version installed in this computer, created 2022, February 12, 11:16 hours Pacific Time.`

(2)

Define(t[mu])

{Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], t[mu], Physics:-LeviCivita[alpha, beta, mu, nu]}

(3)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

(4)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

(5)

NULL

SumOverRepeatedIndices(t[mu]*t[`~&mu;`])

t[mu]*t[`~&mu;`]

(6)

NULL

Download greek-index.mw

How to find the axis and focus of a parabola whose equation we know ? Thank you.

4 5 6 7 8 9 10 Last Page 6 of 27