Let Poly2 denote the vector space of polynomials

(with real coefficients) of degree less than 3.

Poly2 = {a1t^2+ a2 t+ a3 |a1; a2; a3 €R}

You may assume that {1,t; t^2}is a basis for Poly2.

(1) Show that L1 = {t^2 + 1; t-2 ; t + 3}and L2 = {2 t^2 + t; t^2 + 3; t}

are bases for Poly2.

(2) Let v = 8t^2- 4t + 6 and w = 7t^2- t + 9. Find the coordinates for

v and w with respect to the basis L1 and with respect to the basis L2

(3) find the coordinate change matrix P from the basis L1 to the basis L2.find P^-1

Just I answer part (1) can you help me to answer 2 and 3 

I am considering to write a wrapper for plot and related commands (could redefine the commands or introduce a new name) which facilitates export of Maple plots to postscript. The command should interpret some of the options and remove them from the options sequence before submitting the remaining ones to the original plot().
E.g. it should recognize a title="TITLE" parameter and process TITLE (e.g. write it to a specific file). Similarly I would want to be able to pass additional parameters, e.g. filename="FILE" in order to specify how the output file name should be set. Is this a sensible approach. How can I realize this detailed option 'parsing' in Maple?

how to calculate hlibert series as in maple with Gröbner Bases

would like to know the algorithm and try in another programming language such as F#

i find the algorithm in book Singular introduction to commutative algebra

page 320 and 322 

1. is it equal to the hilbert series function in maple?

eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eq3a := Homogenize(eq3, h);
T3:=lexdeg([a,b,c,h]);
GB := Basis([eq1a,eq2a,eq3a], T3); #a

MonomialHilbertPoincare(LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3));

F:=[LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3)];
InterReduce(F, ???);

 2. what is the maple function for degree reverse lex ordering ?

eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eq3a := Homogenize(eq3, h);
David Cox using Algebraic Geometry page 82 use resultant to eliminate variable h
eq1b := eq1a - x;
eq2b := eq2a - y;
eq3b := eq3a - z;
T2:=lexdeg([a,b,c],[x,y,z]);
GB := Basis([eq1b,eq2b,eq3b], T2);
r1 := resultant(eq1b, eq2b, h);
r2 := resultant(eq1b, eq3b, h);
r1 = r2

page 82 teach how to eliminate, after do question 2, discover r1 and r2 are the same.

how to eliminate the variable h with resultant after homogenize ideal with variable h

 Do Hilbert series function classify all or only some type or some form of ideals?

Let Poly2 denote the vector space of polynomials

(with real coefficients) of degree less than 3.

Poly2 = {a1t^2+ a2 t+ a3 |a1; a2; a3 €R}

You may assume that {1,t; t^2}is a basis for Poly2.

(1) Show that L1 = {t^2 + 1; t-2 ; t + 3}and L2 = {2 t^2 + t; t^2 + 3; t}

are bases for Poly2.

(2) Let v = 8t^2- 4t + 6 and w = 7t^2- t + 9. Find the coordinates for

v and w with respect to the basis L1 and with respect to the basis L2

Hi everyone

Right now I am working on a command that calculates the molar mass of molecules. Mostly it is working like a charm but in some cases the interpretation of the input goes wrong.
The command converts the input to a string, e.g.:

f:=convert(Ca₃(PO₄)₂, string) = "Ca[3](PO[4])[2]"

f := StringTools:-Remove("[]_*^+-", f) = "Ca3(PO4)2"

However, sometimes information such as parentheses is lost (which is understandable considering the fact that maple does not know chemical syntax):

f := convert(NH[3][3]*PO[4], string) = "NH[3][3]*PO[4]"

f := StringTools:-Remove("[]_*^+-", f) = "NH33PO4"

In special cases it goes completely nuts (I am aware this is not a real molecule):

f := convert(Al(OH)₂(NH₃)₂, string) = "Al(`#msub(mfenced(mi("OH")),mn("2"))`)(NH[3])[2]"

The problem could of course simply be solved by typing the input as a string with no subscripts but is looks much nicer with the correct chemical syntax as input.

Do any of you know a way to translate the input charactor by charactor into a (understandable) string?

Thanks in anvance,
Mads 

why not maple use NoSQL object database to save objects to prevent out of memory?

I have an indexed equation that contains serval definite integrals in it. I want maple to evaluate the equation for different indices. But when I set the parameter "N=100" in the code, it takes maple lots of time for the evaluation. I am looking for some tricks to make the code numerically more efficient. I will be so thankful for any opinion and help.
you can find my code below. The code is so simple and just contains few lines. I will appreciate any help.

Numerical_Performance.mw

Thanks in advance.

Hi all

I have written the following code in maple to approximate arbitrary functions by hybrid of block-pulse and bernstein functions but it doesn't work properly especially for f(t)=1.0, so what is the matter?

bb1.mws

best wishes

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

In using the Maple 17 VectorCalculus package I was suprised to find that the Norm of a free vector is not the same as the Norm of a "corresponding" RootedVector, i.e.the same vector with a different root. Am I missing something ? Thanks for an explanation.

restart;
with(VectorCalculus):

P:=<1,2,3>; # free vector
PP:=RootedVector(root=[-1,2,-3],P)

Norm(P);
Norm(PP);

This seems such a simple/basic question I'm almost too embarassed to ask.

Anyway. this is causing me some headaches

> A := <0|0>;

         A:= [0 0 ]

> B := A:

> A(1,1) := 2 ;

         A:= [2 0 ]

> B;

         B:= [2 0 ]

What do I do to prevent the elements of B changing if A changes, after using the assignment B:=A (or should I not be using this assignment?)  I mean, I would like the same behaviour as 

> a := 0;

         a:=0

> b := a;

         b:=0

> a := 2;

         a:=2

> b;

         b:=0

which seems to work as I "expect"...

It puzzles me that some of the choices for Clickable Math don't return a result. The image below shows four choices for clickable math. I would like it to "factor" exactly as shown in the upper left choice, but nothing happens after clicking the choice. (No matter how many times I try.) The choices "2D Plot" and "Isolate" return results ("Complete the square", in this case, also does not work).

My guess is that I'm asking it to operate on only the denominator of the rhs of the equation, but then why is the choice displayed at all. I've noticed this for some time in certain cases (like since version 17 was release).

Is there a way to make the choice return a result ? In this case, I don't find an equivalent command (factor, the denominator) using a right click. (In this case, I'll use another command "covert" "parfrac" . . .)

I want Clickable Math to make it easy.

Thanks. Cheers !

I was under the impression that I could declare the type of the return value from a procedure to be a tuple of two posints as follows:

  foo := proc () :: posint, posint; 12, 13; end proc;

and then use it for multiple assignment as

  i, j := foo();

Of course, I have to set

  kernelopts(assertlevel = 2):

if I want Maple to actually check that foo returns two posints as promised.

All this seems to work as expected, including getting an error message if the returned value has the wrong type.

So, why does Maple IDE claim that this is a syntax error? Is there a difference between the syntax accepted by Maple and Maple IDE, and if so which is correct?

Hello,

I could obtain the simulation of my multibody with kinematic closed chain (CKC).

However, it seems that from a specific time (around 12s) in my model I believe that I have some numerical instabilities. Indeed, I could compare my simulation results with another mulbody software. I obtain the same simulation until 12s and after in MapleSim, it appears many perturbations as you can see on the figures belows.

So, I think that I tune the numerical solver. This numerical solver must solve DAEs equations since my model contains 4 kinematic closed loops.

If i read correctly the help menu, there are the following methods to solve the DAEs :

- use specific DAE numerical solver (3 differents solvers are used : ck45 method, RKF45 method and Rosenbrock method

- use reformulation equations techniques (Baumgarte, Projection) which can be associated (I believe) with a classic solver like (RK4).

For the moment, I have obtained my results with the rosenbrock solver with error absolute : 1.0*10^(-4) and eror relative :error absolute : 1.0*10^(-4) 

Do you have some ideas or advices so as to find a better method to solve my multibody systems with kinematic closed loops ? This method should  prevent the creation of numerical instabilities.

Thanks a lot for your help