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I often use RegularChains and SolveTools package. SemiAlgebraic is extremelly useful to deal with polynomial equations. However, I need some similar to Mathematica's Resolve that allows me to eliminate some variables from the description of the set. Say we have some set decribed by: for all 0<x<1, p(x,z)> 0 where p is a polynomial in x and z. Is there any Maple command that allow us to remove x and give the set only n terms of z?

x*(y+z)/x

convert any polynomial to Divide(Mult(x, Plus(y+z)), x)

 

The equation

x^7+14*x^4+35*x^3+14*x^2+7*x+88 = 0

has the unique real root

x = (1+sqrt(2))^(1/7)+(1-sqrt(2))^(1/7)-(3+2*sqrt(2))^(1/7)-(3-2*sqrt(2))^(1/7).

Here is its verification:

Is it possible to find that in Maple? I unsuccessfully tried the solve command with the explicit option.

 

 

 

Hello,

I have trouble in using the function factors. For example, I expect

factor(Pi*(t^2+1), {I});

to output

-Pi*(-t+I)*(t+I)

but instead the result is

Pi*(t^2+1)

This problem does not appear if Pi gets replaced by a general symbol:

factor(pi*(t^2+1), {I});

produces (as I expect it should)

-pi*(-t+I)*(t+I)

The problem seems to be tied to symbols representing constants, as for example replacing Pi by Catalan also results in no factorization being performed. It further seems to be tied to specifying a splitting field, because

factor(Pi*(t^2-1));

results in

Pi*(t-1)*(t+1)

Is this behaviour intended? Probably the reason is that the polynomial does not have algebraic coefficients (as it includes Pi). Indeed,

factor(Pi*(t^2-1),{});

produces the error message

Error, (in factor) expecting a polynomial over an algebraic number field

But why does this error then not appear for the call factor(Pi*(t^2-1))? If this would assume complex coefficients, it should factor using I. Considering coefficients in an algebraic number field, also the original call factor(Pi*(t^2+1), {I}); should raise an error!?

Thanks,

Erik

Dear Maple experts:

I have a very simple question:

I have a polynomial p(x) with integer coefficients and a prime p.  I want to reduce the exponents of this polynomial mod p.  So for example, if p(x) = 1 + x^3 + x^17 + x^19 and p is 17. Then I want Maple to output 1+x^3+1+x^2.

I know how to reduce the coefficients mod p, but not the exponents. Can someone suggest how I might go about doing this.  Thank you very much for your help.

Best wishes

Sunil

I have defined the following procedure, S(x,a,b,s), in Maple with the goal of creating an exportable two column, multi-row array, containing the least positive real root of a high order polynomial f(x,y)=0 in the 2nd column, and a parameter y in the first column.

The procedure takes four numerical arguments (x,a,b,s) and varies parameter y from the initial non-negative value of a, by stepsize s, until the value min(b,1) is reached.

Unfortunately, the output 4x2 array only has the last calculated [y,solution] entries in the first row. Successive rows are filled with zeros.

Is there anyone kind enough to point out the error in the way I have defined this procedure? Many thanks in advance. Procedure is:

S := proc (x, a, b, s
   global Ry;
   for y from a by s to b while y < 1
     do R := Array(1 .. ceil((min(b, 1)-a)/s), 1 .. 2, [[y, FindMinimalElement(select(type, [fsolve(f(x) = 0)], positive))]])
     end do;
     end proc;

 u_{tt} = c^2 u_{xx}, \,
 u(t,0)=0, \quad u(t,L)=0,

as well as the initial conditions

 u(0,x)=f(x), \quad u_t(0,x)=g(x).

 

I have an equation as follows:

By inspection one can see that the last three terms can be simplified (factored) to

How can I coerce Maple to do this? None of the available tools seem to be getting close to this. A partial solution is like this: Writ a procedure as follows:

Fac:=proc(xpr,a,b);
  tmp:=xpr+(a^2+2*a*b+b^2);
  return tmp-(a+b)^2;
end proc;

and then call it:

Fac(lhs(eq),k0,2*Pi*n/L)=rhs(eq);

to get

which is what I want. But procedure Fac() is not general at all; e.g. it fails if the overall sign of the polynomial terms are different. There does not seem to be any way in Maple to determine the sign of a term in the sum of lhs(eq), I can only find ways to determine signs of a simple indeterminate. I'd like to make this procedure more general (which is trivial enough for a human) but I just cannot find any tools in Maple to support this.

Any ideas out there?

Mac Dude.

 

Hi everyone,

I have a very complicated function y with only one independent variable x, and want to fit or approximate it by a simpler function, say polynomial. Many books or maple reference seem to tell how to fit a set of data instead of a given function. But the argument x in the function is assumed to be continuous other than discrete, so I don't know whether it is possible to express datax in form of x's range such as 0..1, and express datay in form of the function. After that , maybe I can fit the two created data sets by a polynomial function.

Or, does anyone have a better or more direct way to do the fitting linking two fucntions?

I am appreciated for your help.

Best,

GOODLUCK

Say I have a polynomial x^5 + 4xy^4 + 2y^3 +  x*y^2 + x^2 + y + 3

Can I truncate it up to total degree 3 (for example), so 2y^3 +  x*y^2 + x^2 + y + 3

 

 

Two questions:

The algortihms that Groebner[Basis] uses at each step computes some "tentative" or "pseudo-basis". The "tentative" basis is not a Groebner basis but it is in the ideal generated by the original system of polynomial eq.

1) Is this correct ? Provided this is correct, then

2) How can one retrive the last "tentative" basis?
 If I just use timelimit I can abort the computations but how can one retrive the last computation?

 

I have been struggling (reading Ore/Weyl Algebra documentation) to understand how to input a PDE system with polynomial coeff. in Weyl algebra notation so I can compute a Groebner basis for it. I would be very grateful if someone could  show, using the simple example below, which differential operators in Ore_algebra[diff_algebra] should one declare to express the system in Weyl algebra notation. The systems I'm working are more complicated but all have many dependent variables, f and g functions in this example:

pdesys:= [ x*diff( f(x,y,z),x)- z*diff( g(x,y,z),y) = 0, (x^2-y)*diff( f(x,y,z),z)- y*diff( g(x,y,z),z) = 0 ]

I've been playing around with the Basis command in the LinearAlgebra package. It's very easy to get a Basis for any subspace of R^n. However, if you're dealing with finite-dimensional polynomial or matrix spaces, the Basis command doesn't work. Due to some basic isomorphism theorems, we can always associate these vectors with those in R^n. I was wondering if there is a way to get Maple, via the Basis command, to handle "other types" of vectors. For example, how might one get Maple to return a basis of {x^2+x+4,x+3,2x^2-x-5,5x^2+x-7} in P_2, the space of polynomials of degree less than or equal to 2, or, a basis for {[[2,3],[5,6]],[[3,2],[0,1]],[[1,1],[0,5]]} in M_{2,2}, the space of 2 x 2 matrices, without converting to R^n?

Hello, I have a quadratic eigenvalue problem. I used to solve it using "polyeig" function in matlab. May I know if there is such a function in maple too? I cant seem to find it.Thanks.

When defining a polynomial as follows

p:=x->x^(r+1)-(r+1)*Sum((-1)^(r+k)*(r+k)!*(r+1)!*r!/((k!)^2*(r-k+1)!*(2*r+1)!)*x^k,k=0..r);

the result of

simplify((eval(p(1),r=1)));

is given as 1 whereas hand evaluation and also plotting the polynomial clearly shows that the result is 0. How can this behaviour be explained?

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