Maple 2023 Questions and Posts

These are Posts and Questions associated with the product, Maple 2023

I would like to write this equation:

That is a symbol that I want to be able to use (the S can be added after inserting the symbol). Sometimes, this helps the students to comprehend what they are doing. It could be added the symbols for double and triple integral. So it is some kind of suggestion, but for the moment, it is the actual symbol I would like to have.

I think that I could write it in LaTeX but I don't know if I can do it in Maple and ask him to convert it inside the document.

Thank you in advance for your help.

I try to understand why Maple throws 2 times an error but on a third attempt (with the same input) output is returned. Is that a new mechanism of suppression of error or warning messages and returning output up to a point where evaluation cannot further be performed.

With -sin instead of cos Maple returns output immediately. Does this mean that there is no information to the user available (yet) for this particular case?

three_times_entering_the_same.mw

A very easy example: 

solve({a > 0, ln(a) + ln(1 + a) >= 0}, a);
 = 
                        /    2         \ 
                        |---------- < a| 
                       <  (1/2)         >
                        |5      + 1    | 
                        \              / 

The output is . Clearly,  is also a solution to this inequality, so the solutions have been lost. But there is no warning message. Why?

Respected fellows, greetings!
I wonder if there is a way to increase the length of the legend in maple? I can easily do it in mathematica but I failed to find a way to do the same in maple. It would be so nice if someone could guide me about that please.

It says that one may specify the number of significant (decimal) digits when performing calculations. However, it appears that setting a higher precision does not yield more satisfactory results. Actually, the recommended solver (in the package) can report that a maximization succeeded, and yet the reported solution can be, in effect, incorrect.

restart;

kernelopts(version);

         Maple 2023.0, X86 64 WINDOWS, Mar 06 2023, Build ID 1689885

 

fun := ((2*(x+y+z))*(sqrt(y*z*(z+x)*(x+y))/(z+2*x+y)+sqrt(z*x*(x+y)*(y+z))/(x+2*y+z)+sqrt(x*y*(y+z)*(z+x))/(y+2*z+x))-9*x*y*z/(x+y+z)-2*(x*y+x*z+y*z))/(sqrt(x*y*z/(x+y+z))*(x+y+z-sqrt(27*x*y*z/(x+y+z))))

Digits := 5

Optimization['Maximize'](fun, assume = nonnegative, initialpoint = ({seq})(w = (rand())(), `in`(w, [x, y, z])))

Warning, no iterations performed as initial point satisfies first-order conditions

 

[2.56454435679811255, [x = HFloat(8.44225460865e11), y = HFloat(1.5121750086e11), z = HFloat(3.58747328735e11)]]

(1)

Digits := 10

Optimization['Maximize'](fun, assume = nonnegative, initialpoint = ({seq})(w = (rand())(), `in`(w, [x, y, z])))

Warning, no iterations performed as initial point satisfies first-order conditions

 

[2.54449612902387834, [x = HFloat(9.50923834782e11), y = HFloat(8.94868300574e11), z = HFloat(2.30179425858e11)]]

(2)

Digits := 15

Optimization['Maximize'](fun, assume = nonnegative, initialpoint = ({seq})(w = (rand())(), `in`(w, [x, y, z])))

Warning, no iterations performed as initial point satisfies first-order conditions

 

[2.53798179305501392, [x = HFloat(9.91986977089e11), y = HFloat(5.97663762096e11), z = HFloat(4.31192847449e11)]]

(3)

Digits := 20

Optimization['Maximize'](fun, assume = nonnegative, initialpoint = ({seq})(w = (rand())(), `in`(w, [x, y, z])))

[2.5281266501331255053, [x = 583804136381.99996354, y = 332585592469.99985371, z = 642614553072.00010884]]

(4)

Digits := 25

Optimization['Maximize'](fun, assume = nonnegative, initialpoint = ({seq})(w = (rand())(), `in`(w, [x, y, z])))

Error, (in Optimization:-NLPSolve) complex value encountered

 

Digits := 30

Optimization['Maximize'](fun, assume = nonnegative, initialpoint = ({seq})(w = (rand())(), `in`(w, [x, y, z])))

Warning, undefined value encountered

 

[Float(infinity), [x = 996095848033.138573379019582678, y = 0., z = 473765214257.250967995851222582]]

(5)


 

Download NMaxValue.mw

It is said that the approximate supremum of  is 3e0 (under the assumptions). 

fun:=`assuming`((2*(x+y+z)*(sqrt(y*z*(z+x)*(x+y))/(z+2*x+y\
)+sqrt(z*x*(x+y)*(y+z))/(x+2*y+z)+sqrt(x*y*(y+z)*(z+x))/(y\
+2*z+x))-(9*x*y*z/(x+y+z)+2*(y*z+z*x+x*y)))/(sqrt(x*y*z/(x+y+z))*(x+y+z-sqrt(27*x*y*z/(x+y+z)))),[(x,y,z)>~0]):

I am not sure if the toolbox performs better. But is there a way to obtain significantly accurate output natively?

First Question

 

Let's define a function:

f := proc (x) options operator, arrow; a*x/(4*x^2+b) end proc

proc (x) options operator, arrow; a*x/(4*x^2+b) end proc

(1.1)

now define a new function that is the derivative of f.

g := proc (x) options operator, arrow; diff(f(x), x) end proc

proc (x) options operator, arrow; diff(f(x), x) end proc

(1.2)

g is not what I expected. I expect:

g := proc (x) options operator, arrow; a/(4*x^2+b)-8*a*x^2/(4*x^2+b)^2 end proc

NULL

and if i try to calculate g(0), the result is:

g(0)

Error, (in g) invalid input: diff received 0, which is not valid for its 2nd argument

 

NULL

instead of

a/b

a/b

(1.3)

Second Question

 

I need to define an integral function in which the variable is an integration boundary:

 

h := proc (x) options operator, arrow; int(f(t), t = 0 .. x) end proc

proc (x) options operator, arrow; int(f(t), t = 0 .. x) end proc

(2.1)

if I try to calculate :

h(x)

int(a*t/(4*t^2+b), t = 0 .. x)

(2.2)

how can i do the calculation and display the explicit form of the function, and assign to a name ?

  (1/8)*a*ln(4*x^2+b)-(1/8)*a*ln(b)

(1/8)*a*ln(4*x^2+b)-(1/8)*ln(b)*a

(2.3)

Third Question

 

is there a way to write a system of equation in text mode (or math) in the usual math notation with a big curly bracket followed by the list of equation ? graphically similar to the piecewice operator that seems to be not useful for this purpose?

About the first and the second question i read on the web something but i don't understand deeply what is the reason of the behaviour. I would like to understand really that. Thanks a lot.

Download Questions.mw

In the end of numerics - Mathematica Stack Exchange,  claimed that "I don't know if it also has generalized precision tracking". (Another answer additionally claimed that Mma chooses "significance arithmetic" to track the precision.) So, the question is simple: Does Maple always (automatically) keep track of the accuracy of inexact numbers through a computation?

I beleave this must be wrong - plea

NULL

int(int(x^2+1, x), x)

(1/12)*(x^2+3)^2``

(1)

int(x^2+1, x)

(1/3)*x^3+x

(2)

int((1/3)*x^3+x, x)

(1/12)*(x^2+3)^2

(3)

NULL

NULL


Download Bug_in_Maple_2023.mw

se see attachment !

Any workaround for this serious error in Maple 2023? Is this new bug? The problem is can't be cought so whole program crashes. Is this related to the new changes made in 2023 to simplification of of trig functions?

restart;

711624

interface(version);

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

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1463. The version installed in this computer is 1462 created 2023, June 10, 2:26 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2023\Physics Updates\lib\`

expr:=-1/7-(-1/7*I*7^(5/7)*exp(2/7*I*Pi)*sin(1/7*Pi)-1/7*cos(1/7*Pi)*7^(5/7)*exp(2/7*I*Pi))^(7/2);
simplify(expr);

-1/7-(-((1/7)*I)*7^(5/7)*exp(((2/7)*I)*Pi)*sin((1/7)*Pi)-(1/7)*cos((1/7)*Pi)*7^(5/7)*exp(((2/7)*I)*Pi))^(7/2)

Error, (in trig/normal/sincosargs) too many levels of recursion

 

Download simplify_error_june_13_2023.mw

Update

I just tried it in 2022, and it completes instantly with no error.

interface(version)

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

expr:=-1/7-(-1/7*I*7^(5/7)*exp(2/7*I*Pi)*sin(1/7*Pi)-1/7*cos(1/7*Pi)*7^(5/7)*exp(2/7*I*Pi))^(7/2);
simplify(expr);

-1/7-(-((1/7)*I)*7^(5/7)*exp(((2/7)*I)*Pi)*sin((1/7)*Pi)-(1/7)*cos((1/7)*Pi)*7^(5/7)*exp(((2/7)*I)*Pi))^(7/2)

-1/7-(1/7)*(-(-1)^(3/7))^(1/2)*(-1)^(2/7)

 

Download simplify_ok_2022.mw

Hi community!

In the mw file attached, I have worked a numerical solution to get the standard parameters of minimum and maximum of the distribution Triangular(a,b,c) given 2 quantiles (and its values) and c.  The code works and was simple.  Now, how do I solve this more elegantly to have the reparameterization directly inputed instead of indirectly by solving a & b first (like the attached file does)? Thanks people,altTriangular2.mw

From help it says

But in the following it works on list type. Why? Should have not given an error?

158332

restart;

158332

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

3

T:=[ [1,2],[3,4],[6,6]];
whattype(T);
type(T,Matrix);
LinearAlgebra:-RowDimension(T);

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

list

false

3

T:=Matrix([[1,2],[3,4],[6,6]]);
whattype(T);
type(T,Matrix);
LinearAlgebra:-RowDimension(T);

T := Matrix(3, 2, {(1, 1) = 1, (1, 2) = 2, (2, 1) = 3, (2, 2) = 4, (3, 1) = 6, (3, 2) = 6})

Matrix

true

3

 

Download row_dim_june_13_2023.mw

Where do you think label="dontexpand" is coming from in the following? I never seen this before. Is this a bug?

When using PDEtools:-Solve no such error shows up. Worksheet below

998948

interface(version);

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

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1462 and is the same as the version installed in this computer, created 2023, June 10, 2:26 hours Pacific Time.`

restart;

998948

sol:=sum((-2*_R^2+1)/(6*_R^2+4*_R-1)*ln(y(x)/x-_R),_R = RootOf(2*_Z^3+2*_Z^2-_Z+1))-ln(x)-c[1] = 0;
solve(sol,y(x))

sum((-2*_R^2+1)*ln(y(x)/x-_R)/(6*_R^2+4*_R-1), _R = RootOf(2*_Z^3+2*_Z^2-_Z+1))-ln(x)-c[1] = 0

Error, (in solve) cannot solve expressions with sum((-2*_R^2+1)/(6*_R^2+4*_R-1)*ln(y(x)/x-_R),_R = RootOf(2*_Z^3+2*_Z^2-_Z+1,label = "dontexpand")) for y(x)

PDEtools:-Solve(sol,y(x))

y(x) = exp(-c[1])+_R*x

 

Download dontexpand_june_10_2023.mw

Maple has a myriad of kernel functions for doing different kinds of symbolic replacements to whole expressions: subs, eval, algsubs, applyrule, `simplify/siderels`, `simpl/eval`,  Physics:-Substitute, MTM:-subs, MmaTranslator:-Mma:-ReplaceRepeated, PDEtools:-dsubs, liesymm:-wsubs, student:-powsubs, etc. But if I need to apply transformation rules over and over again until the result no longer changes within  iterations in a singular clean built-in command (so, without explicit while / until / MmaTranslator:-Mma:-FixedPoint) elegantly, only four can be called: eval['recurse']algsubs, applyrule, MmaTranslator['Mma']['ReplaceRepeated']. The difference between applyrule and algsubs has been elucidated in this help page:

applyrule … does not do mathematical transformations as algsubs does.

However, I cannot find any explanation for the potential distinctions between eval['recurse'] and MmaTranslator['Mma']['ReplaceRepeated'] in their documentation. Does anyone know?

Besides, is it possible to use an "operator" form (like ) instead of a "functional" form (like ) to perform (single or repeated) substitutions in Maple?

How can one set their own symbols for DynamicSystems continuoustimevar?  If I try to use DynamicSystems:-SystemOptions('continuoustimevar'=x): or DynamicSystems:-SystemOptions('continuoustimevar'=y): Maple complains that these letters are already assigned. Why can not one have their own choice of which letters to use?  Is there a workaround?


 

858904

interface(version);

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

restart;

858904

DynamicSystems:-SystemOptions('continuoustimevar'=t):

restart;

858904

DynamicSystems:-SystemOptions('continuoustimevar'=x):

Error, (in DynamicSystems:-SystemOptions) cannot assign x to continuoustimevar, already assigned to statevariable

restart;

858904

DynamicSystems:-SystemOptions('continuoustimevar'=y):

Error, (in DynamicSystems:-SystemOptions) cannot assign y to continuoustimevar, already assigned to outputvariable

restart;

858904

DynamicSystems:-SystemOptions('continuoustimevar'=XXXXXX):

 


 

Download dynamics_june_9_2023.mw

 

Can one evaluate dirac spinor products using the Standard Model package? How far can I take the evaluation in the package? See maplesheet with commentary.

Evaluating_spinor_products_with_the_standard_model_package.mw

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