## plot3d for a complex function ...

I want to plot the argument for a complex function. The input (x,y) represented in polar coordinates (r,phi) by default puts the cut at -I*Pi. Likewise the argument function:

argument(f(x)) plots the range -Pi..Pi.

However the function f(x)=x^2 could typically be plotted with 2 riemann surfaces on top of each other. When phi becomes 2Pi f(x) becomes 4Pi and only then I want to identify the 0 with 4Pi again since the points are equivalent in the preimage.

On the other hand the function f(x)=sqrt(x) never surpasses its own domain. The values always stay within the argument range of (0,2Pi) (in fact it only goes till Pi, or -Pi/2..Pi/2 in maple) when the preimage is taken to be (0,2Pi). Thus when plotting a preimage value of (x,y) with argument phi and 2Pi+phi they will have the same value since phi=2Pi+phi and I see a step in the plot. This step is actually there since the function has a cut at this point.

This step in the plotting image is also shown for f(x)=x^2 (e.g. at phi=+-Pi/2) but it is not of importance since it just comes from the argument function being constrained to -Pi..Pi.

So is it possible to change this behaviour?

## How to change phase color wheel?...

In plots made with 'complexplot3d', Maple uses by default a color wheel for the argument of complex numbers in which positive numbers are painted cyan and negative numbers are red. Is there a way to change this to the other common convention (i.e. cyan negative and red positive numbers)?

Any help would be really appreciated, as it's not convenient to have graphs made with different conventions in the same document and I wouldn't want to remake all the ones I already have.

## Problem in Solve Command...

Dear All

I have updated my Maple 18, I am surprised to see that ordinary "solve" do not work and return error massage like;

"Error, (in coulditbe) invalid input: `coulditbe/internal` uses a 1st argument, obj, which is missing"

or like;

"Error, (in solve) invalid input: hastype expects 2 arguments, but received 1"

I am totally confused !!!

Can anybody help me out please !!!!

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Regards

## Heavy handling with complex numbers in modulus-arg...

Dear Maple users

An engineering student asked me how Maple is handling complex numbers in polar form. He told me that his fellow students are using another CAS, whereas he himself prefer Maple. When making calculations with AC currents having different phases the other students were using the easy notation depicted in the first line on the picture below. Obviously here the angle (argument) is measured in degrees. I tried to perform the same calculations in Maple, but found it to require a very heavy notation: the other three lines on the picture. Now my question is: Does it really have to be that messy, or maybe there are some package, which will accomplish the task in a more neat way? I mean it is a rather common operation in the engineering sciences.

NB! Of couse one can argue about the educational value of using the notation of the other CAS! From that viewpoint they will probably not learn anything ...

Regards,

Erik

## Error, (in isolate) cannot isolate for a function ...

Hello,

Im solving 4 ODE equations with BC. im trying to shoot the initial value but im having this error:

""Error, (in isolate) cannot isolate for a function when it appears with different arguments""

anyone could help me???

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 Error, (in isolate) cannot isolate for a function when it appears with different arguments
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## Modular Arithmetic...

How do I use msolve to solve y^2 + y - 11=0 in Zp for all primes p with 41=< p =<107 ?

Also, using the results make a conjecture describing the primes p for which there are solutions to y^2 + y - 11 = 0 in Zp

This was what I did.

41<=p<=107

msolve(y^2 + y - 11=0, p)

but I received this error, no implementation of msolve matches the arguments in call, msolve(y^2 + y - 11=0, p)

Any help is appreciated. Thanks

## Incorrect first argument error...

I'm attempting to plot several solutions of this differential equation (I have uploaded my worksheet). I have used this series of commands before without issue, but for some reason I keep getting the error message: "Error, (in plot) incorrect first argument" ect.. Does anyone have any insight into what might be going wrong? Thank you.

ass_1_#9.mw

## procedures and datatypes of the arguments...

Hi there!

I want to improve the way I code up my procedures. For instance I want to code them safe in the sense that they only accept the arguments when they have the correct type.

I know that in principle this is done with the double-colon operator in the following way:

proc(argument::argumenttype)::valuetype;

(Q1)Now, given that my argument is of a type such as set, list, Array, etc.:

(a) How would I specify the allowed types of the elements of that list (for all elements, and for specific ones)? And if the element of the list is a list again, how would I specify the type of that's elements? and so forth..

(b) How would I specify the allowed size of the listArray, etc. ?

(Q2) How do I specify the types of more than one output, if my proc returns more than one value?

(Q3) I know that there are special integer types, such as nonnegint, posint, negint. Is there also a way to specify that the ineger (or float) argument has to be greater than some given value, e.g. >2, or that it has to lie between two values, or out of a given set?

Thats all for now. Thanks for your help guys! : )

Gernot

## Integral with GAMMA functions...

I am trying to solve the following integral

beta^alpha*x^(alpha-1)*exp(-beta*x)/((1+x)*GAMMA(alpha))

with respect to x, between zero and infinity.

If i just integrate it the result that I obtain is

(alpha^2*beta^(alpha+1)*exp(beta)*GAMMA(-alpha-1, beta)+alpha*beta^(alpha+1)*exp(beta)*GAMMA(-alpha-1, beta)+beta-alpha)/beta

My problem is that the alpha is positive and consequently the GAMMA functions do not exist, since the argument...

## quick JacobiTheta1 ?...

I'd like to be able to get a quicker low accuracy computation of the argument of the complex-valued JacobiTheta1 function.

I only need as much accuracy as to get a decent plot, which means... I don't know... about 1e-3 relative accuracy?

If I can get a formula or approach that is "evalhf'able" then I can construct a procedure which does this action and writes results inplace to a float[8] Matrix.

The naive approach in the code below takes about 6min...

## What is the problem when in Dynamic systems maples...

Hello. I am creating a custom component similar to the one that maplesoft has as an example (the discretized counterflow heat exchanger), but with some diff. The problem is that when i execute dyamic systems i get an error saying:

Error, (in DynamicSystems:-ParseSystemInputs) cannot match the arguments to an appropriate system

Is this a problem on my equation (something that i may have forget) or is another thing? Are the arguments type of dynamic system in the right "type"?

I have written a procedure to overload a new "Subs" function. It uses a seq of equations as its first argument followed by the object to act upon (yes, it is to have subs functionality on these objects). I find the overloading works when I have just one equation in the argument list, but with more than one it never calls any of the procedures. The code worked with multiple equations before I overloaded it (i.e. the first proc was verified by itself). FWIW the objects (elemt or bm...

## Complex Numbers...

Hi all. I am trying to find the cube roots of -sqrt(6)-sqrt(18)*I in polar form. I have used the following commands but it does not convert the argument properly. Can anyone help? readlib(polar); sola:=solve(z^3=-sqrt(6)-sqrt(18)*I,z); polar(sola[1]); polar(sola[2]); polar(sola[3]); I have also used the following but it could not simplify the argument/angle. sola1 := simplify(convert(sola[1], polar)); Can anyone please suggest a fix to this? The argument...

## modules as arguments to procedures...

I have a module which is an argument to a procedure.

When I "trace" this procedure, the entire module is  printed (as it should).

Is there a way to NOT print the contents of the passed module? It is annoying when debugging.

Paul