RE: How to translate the phase index information f...

Hello there,

Is there any API that would translate the numerical information to a more informative string?

Or, is there the implementation of the original CoolProp API, 'PhaseSI()', which comes up with a string, instead of the numerical value?

Thank you,

In Kwon Park

How is possible to plot two functions in one coord...

How is possible to plot two functions in one coordinate system but with different domains?

For example I want to see the both functions f1=x*exp(-x^2-y^2) and f2=exp(-x^2-y^2) in one coordinate system but with different domans as below:
f1: -3<x<3, -2<y<2

f2: -1<x<1, -1<y<2

Unexpected bug in solve...

It's sad when a bug is found for such a simple problem!

```sys := [x*y*z = 0, x*y*z + x*z + z = 0, x*y*z + x*y + x = 0]:
solve(sys, {x,y,z});    # OK
#         {x = 0, y = y, z = 0}, {x = x, y = -1, z = 0}

solve(sys, [x,y,z]);    # ???
#                               []
```

Converting floats to rationals - sometimes...

Under certain special circumstances it seems that Maple is converting floats to rationals - I noticed this in Maple 2021 when a^0.5 evaluated to sqrt(a). Prior to Maple 2017, a^0.5, evaluates to a^0.5.

Can anyone think of a reason for this change?

I'm not quite sure why it bothers me, but it does

See the attached for Maple 2016 and Maple 2017.

 > restart;   interface(version);   a^0.5;   a^(-0.5);
 (1)
 >

 > restart;   interface(version);   a^0.5;   a^(-0.5);
 (1)
 >

How to avoid float undefined...

Greetings of the day.

If I am considering the value of "gam=0.5,0.7,0.9" in the code other than 1, I am unbale to draw figure using this code. Also, I can not evaluate the values of  A1[200]; A1[400]; A1[600]; A1[800]; A1[1000]. It is showing float undefined.

 >

 (1)

 >
 (2)
 >
 >

How can I find three numbers a, b, c so that the s...

The system of equations x*y*z + y*z + y = 21, x*y*z + x*z + z = 30, x*y*z + x*y + x = 12

has three solutions, one of them is not an integer solution.

solve({x*y*z + y*z + y = 21, x*y*z + x*z + z = 30, x*y*z + x*y + x = 12}, {x, y, z})

How can I find three numbers a, b, c so that the system of equations

x*y*z + y*z + y = a, x*y*z + x*z + z = b, x*y*z + x*y + x = c

has three  solutions (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3), where x1, y1, z1, x2, y2, z2, x3, y3, z3 are nine integer numbers.

Document Section Numbering and header layouts...

Hi,

Happy New Years All

Can anyone explain two document formating features I am trying to implement?

1.)  Sections.  I select numbering with follow previous selected and I get three sections with a 1. in front of them vs 1, 2, 3.

I would expect Technical to become 3.1 when properly following Section 3. header.   Also, I have seen how to manually type the section number, but that seems to defeat the document layout and formatting if it gets "jumbled up".

2.)  Headers.   Can you suppress headers on pages 2 through X to have a unique cover page header?   This would be similar to word (headers and footers linked to previous section, or not(?) with section breaks as new pages)

Thanks,
Bill

question on syntax of old Maple code. ...

I am translating old Maple code to run on Maple 2021.2. This code from 1985. I think it was Maple 3 then. I'll put a link to the paper and page number.

It uses this syntax

Btw, the " above is meant to be % in new Maple. I do not know what w='@W' is supposed to translate to.

The paper is

A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS

by  Carolyn J. Smith.

https://cs.uwaterloo.ca/research/tr/1984/CS-84-35.pdf

The above is at page 67. Near the end.  The code also uses some old functions, which are not given in the listing, I searched but could not find these.. One is called Lsolve (to solve linear equations, but I can replace this with solve) and  on page 77 it uses these

Functions required: scanmap, expcontract, lncontract, explnsimp

These are not given in the source code in the paper. I assume these are old Maple function which no longer exist?. But I can just use simplify for now in their place.

My question is on the use of `@W` and what it could mean? This syntax @ is used in many places in this old Maple code.

How do I open .mw files?...

Hey all! I recently reinstalled my PC and therefore had to reinstall Maple. I did so and it worked out great, however, minor problem. My PC doesn't recognise .mw files as associated to Maple. I have tried a few different files, but I don't know which one to select as standard program for opening .mw files. Would anyone by chance know which file is the "opener" file, if that´s what that's called.
Thank you for the help in advance :D

(PS: I do know that I can just open the file through Maple by clicking files -> open and locating the file. But I'd rather access them by just doubleclicking from the directory.

How to prove this sum is equal to product ?...

Try to prove those two expressions : a sum and product
First to know if they are correct defined for some values ?

Eulers productformule in Maple

 >

Eerst de Euler identiteit in Maple opschrijven
via info over series

 -Series Absolute convergence for Diverges for

 > restart;

=

 > product(f,i=k..n);
 > product(1/(1 - p^(-s)), i = 1 .. p);
 (1.1)
 > sum(1/n^p, n = 1 .. infinity);
 (1.2)
 > sum(1/n^p, n = 1 .. 4);
 (1.3)
 > product(1/(1 - p^(-s)), i = 1 .. 4);
 (1.4)
 > Product(1/(1 - p^(-s)), i = 1 .. 4)= product(1/(1 - p^(-s)), i = 1 .. 4);
 (1.5)
 > sum(1/n^p, n = 1 .. infinity) = product(1/(1 - p^(-s)), i = k .. p);
 (1.6)
 >

How to prove this  =

For the sum i got some terms , but for the product i don't see factors as i use the commands

Why does this proc does not provide an answer...

I am trying to start writing small procedures in Maple. In the attached document I do not get an answer and I do not understand why. For clarity I have also added a working construct from another program so anyone willing to help me out can better understand what I am after.

CDI_T_cor.mw

are these error messages to be expected from pdsol...

I was trying Maple 2021.2 on this pde I saw on the net, and noticed it gives some error messages.

Are these to be expected and known?

 > interface(version);

 > Physics:-Version();

 > restart;
 > PDE := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]); bc := D[2](u)(t,0,y)=0,D[2](u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0; ic := u(0, x, y) = f(x,y); sol := pdsolve([PDE, bc,ic], u(t,x,y))

Error, (in assuming) when calling '`assume/NormalizeBoolean`'. Received: 'invalid input: type expects 2 arguments, but received 3'

 > restart;
 > PDE := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]); bc := D[2](u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0; ic := u(0, x, y) = f(x,y); sol := pdsolve([PDE, bc,ic], u(t,x,y))

Error, (in PDEAdvisor/2nd_order/Series/ThreeVariables) invalid input: has expects 2 arguments, but received 1

 > restart;
 > pde := diff(u(t, x, y), t) = VectorCalculus:-Laplacian(u(t,x,y),'cartesian'[x,y]); bc := D[2](u)(t,0,y)=0,D[2](u)(t,1,y)=0, u(t, x, 0)=0,u(t, x, 3)=0; sol := pdsolve([pde,bc], u(t,x,y))

Error, (in PDEAdvisor/2nd_order/Series/ThreeVariables) invalid boolean expression: NULL

 >

Riemanns formidable formula gives differences...

Some small differences is unavoidable ?

 >

Its not symbolic that's why i don't get he same answers ?
Later on i will investigate some values for for this formula

Riemanns formidabele formule

 > restart:

Volgens het boekje de riemanns hypothese : de functionaal vergelijking  (zonder bewijs)

 (1.1)
 > Zeta(-z) = -2*z!*sin(Pi*z/2)*Zeta(z + 1)/(2*Pi)^(z + 1);
 (1.2)
 > verg:=%;
 (1.3)
 > verg2:= subs(z=2+3*I,verg);
 (1.4)
 > verg3:= eval(verg,z=2.+3*I);
 (1.5)
 > evalf(rhs(verg3));
 (1.6)
 > lhs(verg3)=evalf(rhs(verg3));
 (1.7)
 > lhs(verg3)- evalf(rhs(verg3));
 (1.8)
 >

How to interpret results from showprofile() ?...

I am working on a modelling (simulation) program for an rf system involving DDSs, rf mixers and other components. Each component is programmed as a submodule with methods (procs) and other exports, the whole shebang wrapped into a main package loaded using with(). A loop simulates a number of scenarios with differing starting conditions. Most calculations are numeric in nature.

The code runs but is too slow and in addition seems to keep allocating memory as the main loop runs. I suspect these two are related. I am using profile() to get an idea where the time is spent and where the memory gets eaten up.

I am doing the following:

```profile(DDS__Boo:-SetTW,rf__Boo:-cycles,rf__SR:-cycles); # profile these three methods (procs):
.
.
.
# the main loop:
# Loop over injection cycles

for cycle from 1 to Cycles do
tStartRamp:=(cycle-1)/2;
c__B0:=cB0f(tStartRamp,tStartRamp);
cB0List[cycle]:=c__B0;
WBsum:=0;
DDS__Boo:-ResetTW(tStartRamp);
#
targetBucket:=targetList[cycle];
delta__r:=trunc((r__end-0)/(Points-1));

for ii from 0 to Points-1 do
r:=ii*delta__r;
DDS__Boo:-SetTW((r-delta__r/2)/f__clk,eval(W__Boo+ramp));
WBsum:=evalf(WBsum+eval(ramp)*delta__r);
end do:

BooRfPeriods:=evalf(rf__Boo:-cycles((c__ex+targetBucket)/f__SR));
SRRfPeriodsList[cycle]:=evalf(rf__SR:-cycles((c__ex+targetBucket)/f__SR));
BooRfPeriodsList[cycle]:=BooRfPeriods-evalf(rf__Boo:-cycles(c__B0/f__SR)); # rf periods cB0 to extr.
evalf(BooRfPeriodsList[cycle])/432; # Booster turns c__B0 to extr
targetErrors[cycle]:=(%-round(%))*432; # targeting error in bucket width
DocumentTools:-SetProperty(RotaryGauge0,'value',cycle,'refresh');
end do:
# end loop

showprofile();
function           depth    calls     time    time%         bytes   bytes%
---------------------------------------------------------------------------
SetTW                  1    10240  230.877    51.52   22851828384    72.80
cycles                 1      110  108.607    24.24    4269176160    13.60
cycles                 1      110  108.607    24.24    4269176160    13.60
---------------------------------------------------------------------------
total:                 3    10460  448.091   100.00   31390180704   100.00

```

My question is: how do I interpret the table of results?

"time" is in seconds? (this should really be written in the Help files). Also, SetTW() and cycles() call other routines from the package, are they included in the times reported or not?

"bytes" is my biggest concern. "SetTW" has a whopping 22 GB against it. Since the total allocation goes up to about 290 MB in this particular run (per Maple's info line) this cannot be the total memory used. Can this be the total allocation (and most of it ending up as garbage and cleaned out)?? Even the 4 GB against cycles seems out-of-line.

The two lines for "cycles" are exactly the same even though the routines differ (belong to different instances of the module and operate on differnt parameters). Is profile aware of that, or not?

I realize that people like to see the whole program or worksheet; but given that this is dependent on a large-ish package and the sheet itself is of some size and difficult to penetrate for the uninitiated I want to spare you from trying to read it. Right now I need to understand what showprofile() is reporting. Once I better understand profiling, and if I need more help, I will try to make a MWE, but I am not that far yet. I did check the Programming Guide but I did not find the info I am looking for.

Thanks much for any insight you can share.

Mac Dude.

DEplot warnings...

I have the following warnings. Could you help me fix the problem?

 > restart;
 > deS:=diff(x(t),t)=-0.5*x(t)*y(t)
 (1)
 > deI:=diff(y(t),t)=0.5*x(t)*y(t)-0.15*y(t)
 (2)
 > with(DEtools):
 > DEplot([deS,deI],[x(t),y(t)],t=0..40,x=0..1,y=0..0.6,[[x(0)=0.99,y(0)=0]])
 Warning, plot may be incomplete, the following errors(s) were issued:    incorrect number of arguments, got 51, expected 50
 >
 >