MaplePrimes Questions

I have defined a function II1norm of one variable. The variable has units "microns". It plots perfecting using a range defined in microns, but gives an error when I try to find the root using NextZero. If I just leave off the "microns" in the second argument, NextRoot just reports "FAIL". If I rewite the worksheet without units, then the NextZero executes fine. Why? How to I use units when finding roots?

I need to calculate the eigenvalues and eigenvectors of a big marix with enough Digits. When i apply the command Eigenvectors(K,M) for this purpose, it takes approximately 40 min to be calculated by maple. Where only 1/4 of cores of my CPU is used in this computation.

How is it possible to use all of my CPU cores to calculate the eigenvalues and eigenvectors of a big matrix faster?

change the txt to m for the following files.



This is so useful to see geometrical mapping diagram to visualize Complex analysis

Something that also can be made for Maple 

Mapping Diagram for Cauchy Integral Formula – GeoGebra

Using GeoGebra for visualizing complex variable. (

I highly encourage everyone interested in complex variable to read Tristan Needham „Visual Complex Analysis” and try to solve problems with or without aid of GeoGebra. I hope that in this workshop we will manage to get a feeling of complex functions and as a final point understand how complex integration works. It is a common misconception that complex integration can't be visualized, and using Tristan Needham's ideas we will try to explore this idea. It's a pity that we don't have a lot of time, thus we will skip a lot of important information and construct only some graphs. 

There is so much experimenting with Geogebra software and doing too this in Maple ?

  How do you transform vector expression (*) into [M,A] – 3[M,B] = 7[M,C] using Maple command?


  Thank you for your help !

How to find the eigenvalues and eigenvectors of a problem that have some zero diagonal elements which dont have the usual form of the standard eigenvalue problem? I have tested some ways, but the results was not accurate enough.
If it is possible please provide me an example with relatively large matrices (e.g. M>50)
Note that M>N.

Hello there, 

Would you allow me to ask one question?

Is there any way to get a saturated water vapor pressure value with a temperature outside of the range?

The range here means [273.06 K, 647.096 K]. The pressure value certainly exists (T<273.06 K), but the API only comes up with an error. 

Here is the Maple worksheet where I got into this issue:






T2 := (-40.0 + 273.15) * Unit('K');



xbb := 1: # 100% steam, saturated.

Pg2 := PropsSI("P", "T", T2, "Q", xbb, "water");

Error, (in ThermophysicalData:-CoolProp:-PropsSI) Temperature to QT_flash [233.15 K] must be in range [273.06 K, 647.096 K] : PropsSI("P","T",233.15,"Q",1,"water")





I'm new user in Maple and I have two question:

1. I have modeled transfer function in z term(without DynamicSystems). How quicky can I reearange it to difference equation to find coefficients?

2. I discretize transfer function of s to z using ToDiscrete(DynamicSystems) how here I can reearange this form to difference equation? 

I am studying the help pages for declare() statement in the PDEtool package. 
It can be used also for calculus(prime notation) for 1 variable and two variables (subscript notation) as i understand it now.

There is no input possible in Maple by using a prime notation and indexed functions notation?

Maybe with a alias ? ..remember that I can be chanced I (default) into the i for complex numbers 

Hello there, 

Would you allow me to ask these two questions?

1) is there any way to collect the expression 'eq14_2' w.r.t. DeltaP? The question is labeled as 'Q1' in the worksheet. 

2) Why does the 'DeltaP' term survive at the RHS of the expression 'eq14_2_3'? In other words, is it possible to cancel out the same term, 'DeltaP', in numerator and denominator?


eq14_1_3 := w[NET] = Delta*T[Sfg];

w[NET] = Delta*T[Sfg]


eq14_2 := w[NET] = -((v[2] + v[3])/2)((-DeltaP + P) - P) - ((v[1] + v[4])/2)((P - P) + DeltaP);

w[NET] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)



w[NET] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)


collect(expand(eq14_2), DeltaP, distributed); # Q1

w[NET] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)


Desired1 := w[NET] = DeltaP * (-v[2]*(-1)/2 - v[3]*(-1)/2 - v[1]*(1)/2 - v[4]*(1)/2);

w[NET] = DeltaP*((1/2)*v[2]+(1/2)*v[3]-(1/2)*v[1]-(1/2)*v[4])


eq14_2_2 := rhs(eq14_1_3) = rhs(eq14_2);

Delta*T[Sfg] = -(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP)


eq14_2_3 := eq14_2_2 / DeltaP; # Q2

Delta*T[Sfg]/DeltaP = (-(1/2)*v[2](-DeltaP)-(1/2)*v[3](-DeltaP)-(1/2)*v[1](DeltaP)-(1/2)*v[4](DeltaP))/DeltaP


Desired2 := w[NET]/DeltaP =  (-v[2]*(-1)/2 - v[3]*(-1)/2 - v[1]*(1)/2 - v[4]*(1)/2);

w[NET]/DeltaP = (1/2)*v[2]+(1/2)*v[3]-(1/2)*v[1]-(1/2)*v[4]




I am trying to plot the solution of the following complex-valued initial value problem (IVP), obtained numerically with dsolve:

odesys := {dy(x)/dx + I*y(x) = 0, y(0) = 1};

sol := dsolve(odesys,numeric,range=0..1);

In the Maple help page dsolve/numeric, they say that dsolve can solve complex-valued IVPs. When I try the code above, it seems to work (I don't get an error). But I can't find how to plot the real and imaginary parts of y(x). Indeed, odeplot(sol) yields an empty graph, and odeplot(Re(sol)) yields an error.

Does someone know how to do this? Thanks in advance for your help.



diff([f, g], t):  #ok

a := [alias()]:
diff(a, t);
      [0, 0]

More generally, how can we differentiate a list of aliases without naming them explicitely?

Thanks in advance

I must feed the not trivial zeros numbers into this aproximation formula ?


Riemann hypothese and staircase of primes













numelems(select(isprime, [seq(1 .. 10000)]))



The prime counting function is approximated by Li(x) and x/ln(x).

plot([PrimeCounting(x), Li(x), x/ln(x)], x = 1 .. 500, legend = [pi(x), Li(x), x/ln(x)])

The staircase of primes approximated by two functions
Interesting is the video: How i learned to love and fear the Riemann Hypothesis


for n from 1 to 30 do
 if is(n,prime)
     then ps[n]:=plot([[n,y],[n,y+1],[n+1,y+1]]):
     else ps[n]:=plot([[n,y],[n+1,y]]):
 end if ;

plot([PrimeCounting(x)] ,x = 1 .. 35, legend = [pi(x)]):

plot([PrimeCounting(x), Li(x), x/ln(x)], x = 1 .. 35, legend = [pi(x), Li(x), x/ln(x)])





Prime counting function
What found RIEMANN for the prime counting function in relation to the zeta function after he defined the zeta function?


He found further a function what follows exactly the shape of the prime counting function

Final discovery v. Riemann.  

- step in the omhoog in de priemtelfunctie = log(p) (zie video)


Using the logarithmic primecount function( from Chebyshev) (approximation)
Further  analyse with this Chebyshev approximation formula in relation to the not trivial zero points from Riemann zeta function ( zeros) gives another real function for approximating the primecounting function what uses the non trivial zeros from Riemanns zeta function  in this function:


"(not trivial zeros ) u[k ] = "i*w[k]+v[k]   
Number now all nottrivial zeros in the upperhalfplane from down to bottom,  as u[1], u[2], u[3, () .. ()]

"`&varphi;`(x)  := x-ln(2Pi)-1/(2 )ln(1-1/(x^(2))) - (&sum;)2/(|u[k]|) x^(v[k]) cos(w[k] ln(x)-alpha[k])"


Its only alpha[k] that must be calculated out of the not trivial zeros and i must have a list of  serie of not trivial zeroes from the zeta function. => see Hardy's Z(t) ? from this ..... alpha[k]  can be calculated ?
All not trivial zeros are complex numbers laying on a line ,but  orginating from (0,0) in the complex plane as  vectors to the points    

varphi(x):= x - ln(2*Pi) - 1/2*ln(1 - 1/x^2) - sum(2*x^v[k]*cos(w[k]*ln(x) - alpha[k])/abs(u[k]), k = 1 .. infinity);

x-ln(2*Pi)-(1/2)*ln(1-1/x^2)-(sum(2*x^v[k]*cos(-w[k]*ln(x)+alpha[k])/abs(u[k]), k = 1 .. infinity))


This formula seems to be correct .
Now how to make a plot ?
Hardy's Z(t) function shows the not trivial zeros in the upperhalfplane of the critical strip of the Riemann zeta function  as zeros in this Z(t) real function : derived from a alternating serie ?


I wish to solve a diffrential equation of the type:


where coefficients a_1,a_2,...are constants with respect to x.

I am trying to convert this equation in normal Weirstrass Form.

Can someone please help



Is there a direct way to have the int command return the anti-derivative plus an arbitrary constant of integration? I am imagining the process to look like:
int(f(x), x) = F(x)+c1


Consider the integral of f(x)=x.f := x



Int(f, x); int(f, x)



Notice that the output has no intregration constant or the constant has been assigned the value of zero and is not displayed in the output.

Maple 2021 Help states, "Indefinite integration  is performed if the second argument x is a name. Note that no constant of integration appears in the result. Definite integration is performed if the second argument is of the form x=a..b where a and b are the endpoints of the interval of integration."

I'd like Maple to output the anti-derivative plus an arbitrary constant in the same way dsolve outputs a general solution of an ode with arbitrary constants. My first work around was to just use dsolve.  

There is a sense in which performing an integration is equivalent to solving an ode:
diff(h(x), x) = g(x); int(diff(h(x), x), x) = int(g(x), x); h(x) = int(g(x), x)+c1; h(x) = G(x)+c2

Is there a way to force int to output arbitrary constants of integration or should I stick to just using dsolve if I want that effect?


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