Maple 2023 Questions and Posts

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

I have this overloaded function foo(). 

restart;

foo:= overload(  
        [
        proc(A::integer,$)option overload;
            print("first one, _passed = ", _passed," _npassed = ",_npassed);             
        end proc,

        proc(A::integer,B::integer,$)option overload;
            print("second one  _passed = ", _passed," _npassed = ",_npassed);
        end proc
       ]);

Which works OK. so I can now do 

foo(1)
foo(1,2)

But I wanted to indicate that the proc returns say ::integer , and this where I am stuck, I do not know where to add this ::integer

With non-overloaded proc's, this is the syntax

foo:=proc(A::integer,$)::integer;
     ......
end proc;

but I can't do this with the overloaded function. If I type

foo:= overload(  
        [
        proc(A::integer,$)option overload;
            print("first one, _passed = ", _passed," _npassed = ",_npassed);             
        end proc,

        proc(A::integer,B::integer,$)option overload;
            print("second one  _passed = ", _passed," _npassed = ",_npassed);
        end proc
       ])::integer;

Maple simply does not like it. typing foo(1) now it just echos the definition back.

And these give syntax errors

foo:= overload(  
        [
        proc(A::integer,$)::integer option overload;
            print("first one, _passed = ", _passed," _npassed = ",_npassed);    
        end proc,

        proc(A::integer,B::integer,$)::integer option overload;
            print("second one  _passed = ", _passed," _npassed = ",_npassed);
        end proc
       ]);

Tried many other variations and looked at help but see nothing to far.

Can one add ::type to indicate type proc returns with overloaded proc?

Maple 2023.2.1

I want to execute a function at least one time. So, I use do ... until ...

However, the function sometimes returns FAIL. So, I looked at help FAIL.

FAIL.mw

The while loop works. The until loop returns an error. evalb(testeq(...)=FAIL) seems overly complicated.

Tom Dean

I am starting a course on differential forms. They have introduced the wedge product by comparing it to the curl product. I can do it by hand. But I would like to do it in Maple. I tried to read the help page of with(difforms) but I cannot see how to do it. And to add to the complication, since my keyboard is in French, I don't know how to insert the circumflex accent right after &. Maybe I should just wait that more theory is done, but just for the principle, I would like to be able to do it. For example, the vectors are:

a=(1, 3,-2)

b=(5, 2, 8)

Thank you in advance for your help.

Mario

The attached integral is plotted quite quickly, but the search for the maximum and for the inverses of function values takes time. Can the search be accelerated or is the integrand simply too complicated?

Int(22.89730452*exp(-3.373250126*10^6*x^2)*sqrt(2)*(erf(1298.701299*sqrt(2)*(sqrt(2.500000000*10^(-7)-x^2)+(1/40)*y-0.1540000000e-2))+erf(1298.701299*sqrt(2)*(sqrt(2.500000000*10^(-7)-x^2)-(1/40)*y+0.1540000000e-2))), x = -0.5000000000e-3 .. 0.5000000000e-3, method = _d01ajc)

Int(22.89730452*exp(-3373250.126*x^2)*2^(1/2)*(erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)+(1/40)*y-0.1540000000e-2))+erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)-(1/40)*y+0.1540000000e-2))), x = -0.5000000000e-3 .. 0.5000000000e-3, method = _d01ajc)

(1)

plot(Int(22.89730452*exp(-3373250.126*x^2)*2^(1/2)*(erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)+(1/40)*y-0.1540000000e-2))+erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)-(1/40)*y+0.1540000000e-2))), x = -0.5000000000e-3 .. 0.5000000000e-3, method = _d01ajc), y = 0 .. .25)

 

unapply(int(op(1 .. 2, Int(22.89730452*exp(-3373250.126*x^2)*2^(1/2)*(erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)+(1/40)*y-0.1540000000e-2))+erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)-(1/40)*y+0.1540000000e-2))), x = -0.5000000000e-3 .. 0.5000000000e-3, method = _d01ajc))), y)

proc (y) options operator, arrow; int(22.89730452*exp(-3373250.126*x^2)*2^(1/2)*(erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)+(1/40)*y-0.1540000000e-2))+erf(1298.701299*2^(1/2)*((0.2500000000e-6-x^2)^(1/2)-(1/40)*y+0.1540000000e-2))), x = -0.5000000000e-3 .. 0.5000000000e-3) end proc

(2)

CodeTools:-Usage(Optimization:-Maximize(proc (y) options operator, arrow; int(22.89730452*exp(-3373250.126*(x^2))*(2^(1/2))*(erf(1298.701299*(2^(1/2))*((0.2500000000e-6-x^2)^(1/2)+(1/40)*y-0.1540000000e-2))+erf(1298.701299*(2^(1/2))*((0.2500000000e-6-x^2)^(1/2)-(1/40)*y+0.1540000000e-2))), x = -0.5000000000e-3 .. 0.5000000000e-3) end proc, 0 .. .15))

[HFloat(0.0356073228322897), Vector[column](%id = 36893490875463313756)]

(3)

CodeTools:-Usage(fsolve((proc (y) options operator, arrow; int(22.89730452*exp(-3373250.126*(x^2))*(2^(1/2))*(erf(1298.701299*(2^(1/2))*((0.2500000000e-6-x^2)^(1/2)+(1/40)*y-0.1540000000e-2))+erf(1298.701299*(2^(1/2))*((0.2500000000e-6-x^2)^(1/2)-(1/40)*y+0.1540000000e-2))), x = -0.5000000000e-3 .. 0.5000000000e-3) end proc)-0.5e-2, 0 .. .15, maxsols = 2, method = subdivide))

0.2456248637e-1, 0.9863751363e-1

(4)

Download slow_maximize_and_fsolve.mw

I wanted to debug some code from worksheet A.  So added DEBUG(); command in the code where I want to start the GUI debugger from, and then run the command from the worksheet. All is working OK. the debugger GUI comes up and I can step in. 

Now I wanted to debug some other code from worksheet B. But without closing the currect debugger which is open and running.

It turned out this is not possible.  When running debugger from worksheet B, it uses the same debugger GUI that was up and running. I think it closed that session automtically also.

So basically using same Maple process, one can't open two debgging sessions at same time? Is there a way around this.

I run each worksheet using its own math engine. So each is separated from each other.

But this is first time I wanted to debug two things at same time, i.e. side by side, thinking I will be able to open two GUI debuggers at same time.

I know ofcourse I can open two separate Maple processes and then I will be able to do this. I think I am allowed to have two Maple's open at same time. Will try that next.

But it will be better if one is able to open two debuggers from same Maple at same time. I do not see why this should not be possible.

Any suggestions if there is a workaround? May be some hidden setting that allows this?

Maple 2023.2.1 on windows 10

Plots of physical quantities has significantly improved with Maple 2022. The updated useunits option makes unit conversion errors in plots very unlikely. A lot of time is saved when creating plots of physical quantities where values and units must be correct.

One final source of user errors remains: The manual entry of incorrect units in labels.

Below is a way to avoid such errors by computing labels with units for three prevalent axis labeling schemes.


Other desireable labels are given as a suggestion for future plot label enhancements where plot commands could provide formating functionality.

The rendering on this website adds double brakets ⟦ ⟧ wherever units are used. You have to open the document to see how Maple renders.

NULL

Simple plot example: Solar irradiance in space

G__0 := 1361*Unit('W'/'m'^2)

1361*Units:-Unit(W/m^2)

(1)

G__0*sin(2*Pi*t/(24*Unit('h')))

1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h))

(2)

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'))

 

This plot has inconsistent axis labeling:

• 

The vertical axis has units but no name

• 

The horizontal axis has a name and units but they are not easily distinguishable. Misinterpretation is possible. Due to the close spacing the label could be read as a product of the dimension "time squared" (the time t times hours h is of the dimension time squared). Or the reader confounds name and units. (The use of italic fonts for names and roman fonts for units might not be noticeable and is a convention that is not used everywhere.)

 

The above labeling should be improved for communication, documentation or publication purposes.

 

A quick attempt using strings and the options useuints and labels.

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = ['d', kW/m^2], labels = ["Time t in days", "Exposure G in kV/m^2"])

 

Axes are now consistent and can be interpreted unambiguously. Formatting can still be improved.

 

Unfortunately, using the options useunits (for unit conversion) and labels this way introduces a new source of user error when labels are entered with the wrong units.

 

A way to address this and to ensure unit error-free plotting of expressions of physical quantities is the following:

 

Step1: Define two lists, one for the units to display and the other for the names to display

a := [Unit('s'), Unit('W'/'cm'^2)]; b := [t, G]

[t, G]

(3)

Step2: Compute labels from the lists

This step avoids the labeling error: No manual entry of units in labels required.

c := [b[1]/a[1], typeset(b[2]/a[2])]; d := [typeset(b[1], "  ", "⟦", a[1], "⟧"), typeset(b[2], "  ⟦", a[2], "⟧")]; e := [typeset(b[1], "  ", "(", a[1], ")"), typeset(b[2], "  (", a[2], ")")]

[typeset(t, "  ", "(", Units:-Unit(s), ")"), typeset(G, "  (", Units:-Unit(W/cm^2), ")")]

(4)

NULL

 

Dimensionless labels

 Double brackets

Parenthesis

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = a, labels = c)