## How to optimize solving process?...

I am able to get unlimeted numbers of equations describing my system. These equations are generally relate quotients of multivariate polynomials. Each additional equation I get is generally less than twice the length of the last, and it is not always the case that an equation is independant of the previous equations. Although I can get unlimited numbers of equations describing the system, it is not overdetermined.

I am interested in solving these equations for their variables. There are about 30 cases I am working on, the smallest number of evariables is six, the largest would be twenty.

I want to be able to solve these equations in the minimal time possible. But I don't understand the function solve well enough to do so.

How do I choose the equations to minimise the time taken for the command solve to proccess them?
How does the command solve work?

particularly:

1. if I process the command solve([Eq1,Eq2,Eq3...Eqn],variables) would the command solve([Eq[1],Eq[2],Eq[3]...Eq[n],Eq[n+1]],variables) take longer if Eq[n+1] is not indipendant of the previous equations?
2. Is there a way of checking whether Eq[n+1] is independant of the previous vequations, fast enough for it to be useful to check the equations before they are processed?
3. Does the ordering of the equations affect the speed of solve?
4. Is there a way of pre processing the equations before they are put into solve that will save it time? (for example factorising them, simplifying them etc...)

## How to find exact value of it?...

I try to find the exact (symbolic) value of

(-2*sqrt(7)-4)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))^2+4*EllipticE(-(1/8)*sqrt(2)*(-3+sqrt(7)))*sqrt(7)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))

I tried 'simplify' with different options and 'convert'. It would be pi=3.141... as numerical approximation suggests.

Many thanks.

## How to plot parametric integral ...

when the variable is in limits of integration?

hw2_example.mw

there exist an error :

Error, (in int) unable to compute a numeric answer for symbolic limits, q = -3.141592654+arccos(11./(1.+.1000000000*t)) .. 3.141592654-1.*arccos(11./(1.+.1000000000*t))

How to make this code work?

## How to check input in Maple TA?...

Assume the inequality xA,2+xB,2+xC,2 ≤ 110 has to be entered as "symbolic entry only".

How can I check that in Maple T.A.?

It seems that there are type conversions necessary. I attempted to use the MathML package without any luck.

1. Tried to transform \$ANSWER within the answer field using MathML[ExportPresentation]( x[A,2]+x[B,2]+x[C,2] <= 110) and compare it with evalb((\$ANSWER)=(\$RESPONSE)) in the grading code field
2. Tried to transform \$RESPONSE in the grading code: evalb((\$ANSWER)=( MathML[ImportContent] (\$RESPONSE)))

What’s the format of a symbolic entry? Is it really MathML!?

What is the correct way to do it?

3. expression type: Maple syntax?!
4. Text/Symbolic entry: Symbolic entry only

## Simplificating in Vector Algebra...

I want to work (cross products, differentiating and simplificating) of three dimensional vector functions.

But I'd like to work with them as vector, not as components. Is it available in Maple?

## different result for solve...

Why am I getting different results in these two cases ?

## Very hard integral...

How to calculate the integral

(symbolically or/and numerically) with Maple?

## How to define a symbolic Expectation Operator?...

Hello, i am recently doing a lot of my (really simple) equation manipulations with Maple and would like to include an expectation operator E( ) in my symbolic equations. As maple threads E() as a function, differentiating is not very convenient, as i have to replace all D(E) ... manually. I tried defining some properties of E() via the define() function, but when trying to set the behavior of d E(f(x))/dx I am not sure how to use (diff()=result) in the define() function. Any help or ideas are greatly appreciated!

## How to calculate that integral?...

Let us consider the definite integral

J:=int(abs(x-(-x^5+1)^(1/5)), x = 0 .. 1);

Maple fails with it, Mathematica 10.1 finds it in terms of  special functions. Let us look at the integrand:
plot(x-(-x^5+1)^(1/5), x = 0 .. 1);

We see the expression under the modulus changes its sign at the unique point of RealRange(0,1). Therefore

solve(x-(-x^5+1)^(1/5));

Then

J:= int(-x+(-x^5+1)^(1/5), x = 0 .. (1/2)*2^(4/5))+int(x-(-x^5+1)^(1/5), x = (1/2)*2^(4/5) .. 1);

which outputs a complicated expression

(1/8)*2^(4/5)*(4*hypergeom([-1/5, 1/5], [6/5], 1/2)-2^(4/5))+(1/2)*2^(4/5)*((1/2)*2^(1/5)-(1/4)*2^(4/5))-(1/25)*Pi*csc((1/5)*Pi)*(-(25/2)*sin((1/5)*Pi)*GAMMA(4/5)*2^(4/5)*hypergeom([-1/5, 1/5], [6/5], 1/2)/Pi+(5/4)*sec((3/10)*Pi)*cos((1/10)*Pi)*2^(3/5)*Pi^(1/2)*csc((3/10)*Pi)/GAMMA(7/10))/GAMMA(4/5).

At the same time we have

int(abs(x-(-x^5+1)^(1/5)), x = 0 .. 1, numeric);

0.5000000000

How to obtain 1/2 symbolically?

## Degree of a Polynomial...

can I extract a certain non numeric degree from an expression?

for example, I want to get degree "n-1" from "x^(n-1)+y".

any thoughts?

## Standalone execuatable...

Hello,

I wonder if it is possible to create standalone executables in Maple that would run in a  computer without Maple. Also if it is possible can we do that with Matlab code in it too?

Matlab does not allow to create standalone executable is you use symbolic toolbox and I want to find a solution for that. What I will need to take second derivatives and get the coefficients of polynomials.

## combstruct package

by:

Greetings to all.

I am writing to alert MaplePrimes users to a Maple package that makes an remarkable contribution to combinatorics and really ought to be part of your discrete math / symbolic combinatorics class if you teach one. The combstruct package was developed at INRIA in Paris, France, by the algorithmics research team of P. Flajolet during the mid 1990s. This software package features a parser for grammars involving combinatorial operators such as sequence, set or multiset and it can derive functional equations from the grammar as well as exponential and ordinary generating functions for labeled and unlabeled enumeration. Coefficients of these generating functions can be computed. All of it easy to use and very powerful. If you are doing research on some type of combinatorial structure definitely check with combstruct first.

My purpose in this message is to advise you of the existence of this package and encourage you to use it in your teaching and research. With this in mind I present five applications of the combstruct package. These are very basic efforts that admit improvement that can perhaps serve as an incentive to deploy combstruct nonetheless. Here they are:

I hope you enjoy reading these and perhaps you might want to feature combstruct as well, which presented the first complete implementation in a computer algebra system of the symbolic method, sometimes called the folklore theorem of combinatorial enumeration, when it initially appeared.

Best regards,

Marko Riedel.

## How to calculate eigenvalues of complex symbolic M...

Hello,

first of all, this is my very fist question in this forum, so please excuse some formal mistakes I may make...

Using Maple 18.01 on Windows 7 64bit

To the topic: I want to calculate the eigenvalues of a complex matrix like this (just as an example):

M := Matrix(2, 2, {(1, 1) = a+2.5*I, (1, 2) = 1-I*a, (2, 1) = 4, (2, 2) = a})

When I try to calculate

Eigenvalues(M)

I get

Error, (in LinearAlgebra:-Eigenvalues) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values

Strange, because if I replace the "2.5" with just "2", so an integer instead of a float, I get results:

I don't understand this strange behavior, since Mathematica i.e. calculates everything just fine...:

Thanks in advance for any suggestions.

## Syntax error with symbolic parameters...

Hi everyone,

I have to create a double wishbone suspesione model that can be edited by different users, only introducing some reference point values (called Hard Points). So I need some tool that, in some way, passes from the entered reference point values to the actual values of the bodyframes link.

I found an already done model (from this link) that seems to be perfect to me because contains an attached Maple document that does exactly what I need working on the base of symbolic parameters applied to the MapleSim model. Now my problem is that I need to deeply change the model and so having the possibility to change the parameter set and insert for example nex parameters. But when I try to do that some problems come out with the Maple document: the syntax of the nex parameter set is different from the default (in the sense of already built in the model I downloaded) one and there are some syntax errors. Below I'll put a screenshot of the error.

under the XData code line, you can also see the syntax of one of the parameters that is very long and complicated: below I'll insert another image from which it can be seen the syntax with the original parameter set.

Now if you another idea for solving the initial problem, that would be great! Instead do you have an idea on how to fix the problem with the downloaded model? In my opinion there is a different MapleSim version problem, in the sense that could be thatn the model I downloaded has been done in another MapleSim version in which the parameter set syntax was different.

## How do I increase the memory allocation in Maple?...

Hi,

I am trying to find the inverse of 8x8 generic symbolic matrix. Everytime I evaluate the program I get the following error:

Error, (in expand/bigprod) Maple was unable to allocate enough memory to complete this computation. Please see ?alloc

Can anyone guide me how to increase the memory allocation? And would that solve the problem for me?

Any help is appreciated.

Thanks!!

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