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

Why can't maple 15 solve this eqn. [n= 10]

solve(ithprime(n)=29,n);

 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 Maple friends.

If Maple solves an equation and spits out an answer like this,

{x = 4/3+(1/3)*sqrt(7)}, {x = 4/3-(1/3)*sqrt(7)}

how can I get a decimal answer, other than by using my calculator?

Thanks in advance.

Hi Maple friends.

As per usual, I am unable to find the solution in Maple Help. Can someone please advice me on how to shade an area under a curve, preferably using the context menu, since that is what I prefer to use at this stage.

Thanks in advance.

 V = {(2a + b + c, 3a + b + 2c, 2a + c, b + 7c)|a, b, c ∈ R} forms a subspace of R^4 
 
 Show that {(2, 3, 2, 0),(1, 1, 0, 1),(0, 1, 1, 6)} is an (ordered) basis B for V . 

toally confused on how to do this??..please help!!

hello,

Let

j = exp (2 * I * Pi / 3);

Which option on Maple giving all possible values ​​(lambda ^ 3) ^ (1/3):

lambda lambda * j, j ^ 2 * lambda.

Thank you,

Gerard.

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 

Like for instance if I have a formula: ((x^2+y^3)*a1+(x+y^3)*a2)/x^2 and other similar forms as entries for a matrix M, I want to change each entries to a form like this: ((x^2+y^3)/x^2)*a1 + ((x+y^3)/x^2)*a2, what would be the right way to do this?

Thanks for any answers in advance!

Hi all

Assume that we have following vectors:

> V1 := [1/9, -5/9, 7/9, 1/9, -5/9, 7/9, 1/9, -5/9, 7/9];

>  V2:=t*V1;

and we want to compute the integral of V2, namely:

>  Int(seq(V2[i],i=1..9),t=0..1);
>

            [       5 t  7 t         5 t  7 t         5 t  7 t]
      V2 := [t/9, - ---, ---, t/9, - ---, ---, t/9, - ---, ---]
            [        9    9           9    9           9    9 ]

Error, (in print/Int) invalid input: IntegrationTools:-GetOptions expects its 1st argument, v, to be of type Integral, but received Int(1/9*t,-5/9*t,7/9*t,1/9*t,-5/9*t,7/9*t,1/9*t,-5/9*t,7/9*t,t = 0 .. 1)

 how we integrate from V2? why answer is wrong in my code?

thanks a lot

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

i have the following equation:

1.003225155^(l)-((∫)[0]^1[((((0.6 r^2+1)^1.813666667)/((0.375 r^2+1)^2.666666667))^())^(l)r ⅆr)=0

and throws me the error:

Error, Got internal error in unknown : "invalid input: lhs received sattr, which is not valid for its 1st argument, expr"

do  you know the meaning of the error and why this equation cant be solved for l?

Hello,

Is it possible to install on the same machine both the version 32bits and 64bits ?

For example, for some software (like visio) it is possible to have several version of the softwares.

In fact, it can be useful for me because with 32 bits I can communicate with 32bits softwares and with 64bits I can do quicker some calculations.

Thank you for help.

I want to find the greatest value of this expression 

f:=(x,y,z)->sqrt((x+1)*(y^2+2)*(z^3+3))+sqrt((y+1)*(z^2+2)*(x^3+3))+sqrt((z+1)*(x^2+2)*(y^3+3));

with x>0, y>0 , z>0,x+y+z=3.

I tried

restart:

 f:=(x,y,z)->sqrt((x+1)*(y^2+2)*(z^3+3))+sqrt((y+1)*(z^2+2)*(x^3+3))+sqrt((z+1)*(x^2+2)*(y^3+3));

DirectSearch[GlobalOptima](f(x,y,z), {x>0, y>0 , z>0,x+y+z=3},maximize);

I got the output

[HFloat(infinity), [x = .591166078050740e52, y = .183647204560715e52, z = .786638021216969e52], 1249]