# Items tagged with polynomialpolynomial Tagged Items Feed

### Hybrid of bernstein and block pulse...

July 11 2014
0 1

Hi all

Assume that we have construct new orthogonal Hybrid function of block pulse and bernstein poly nomials as follow:

and assume that we want to approximate a function as follows:

how can we do this with maple????Indeed we want to optimize using this hybrid functions

note that the degree of bernstein polynomials is fix or should be fixed...and

regards

Ph.D Candidate

Applied Mathematics Department

### recognizing the root of a polynomial...

July 02 2014
1 5

Hi everyone,

I have a maple program that generates a polynomial g(y)=(80y^8 + 68y^6 + 12y^4 -4y^2 -1). This polynomial has two real roots (irrational roots), call them +/- y*. My code does a sequential calculation, and often sI am left with a higher order polynomial in y that has the form h(y)= p(y)*g(y), where p(y) is also a polynomial in y. This polynomial h(y)=p(y)*g(y) is not in factored form (i.e. it would look like expand(p(y)*g(y)). Is there a way to instruct maple to recoginize that +/-y* is also a root h(y)=p(y)*g(y)? So far I've tried things like applyrule([g(y*)=0],h(y*)), but nothing seems to work (I suspect because Maple cannot recgonize that g(y) is a factor of h(y)). I am not interested in computing this numerically. I am just trying to find a way to instruct Maple to recognize symbolically that h(y*) =0.

Thanks a million for anyone who has any idea.

Best,

Justin

### how to solve this equation?...

July 01 2014
0 2

f1 := expand((a1*x^2+b1*x+c1)^n);
f2 := a1*x^2+b1*x+c1;

solve([coeff(f1, x, 4) = coeff(f2, x, 4),
coeff(f1, x, 3) = coeff(f2, x, 3),
coeff(f1, x, 2) = coeff(f2, x, 2),
coeff(f1, x, 1) = coeff(f2, x, 1),
coeff(f1, x, 0) = coeff(f2, x, 0)], [a1,b1,c1,d1]);

### which family of polynomials do it belong to?...

June 28 2014
0 0

m := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);

m2 := Determinant(m-Matrix([[1,0,0],[0,1,0],[0,0,1]]));

1. which family of polynomials do m2 belong to?

2. how to analyze m2?

### how to convert back to matrix form...

June 28 2014
0 0

restart;

with(combinat):

symMonomial := proc(test)

h := 0;

for i from 1 to nops(test) do

h[i] := choose(test,i);

od;

c := copy(test);

k := 0;

for k from 1 to nops(test) do

c[k] := 0;

for i from 1 to nops(h[k]) do

ki := 1;

for j from 1 to nops(h[k][i]) do

ki := ki*h[k][i,j];

od;

c[k] := c[k] + ki;

od;

od;

return c;

end proc;

sympoly := proc(test, number_of_roots)

with(combinat):

h := 0;

for i from 1 to nops(test) do

h[i] := choose(z,i);

od;

c := 0;

for k from 1 to nops(test) do

c[k] := 0;

for i from 1 to nops(h[k]) do

ki := 1;

for j from 1 to nops(h[k][i]) do

ki := ki*h[k][i,j];

od;

c[k] := c[k] + ki;

od;

od;

poly := x^number_of_roots;

for k from 1 to number_of_roots do

poly := poly + c[k]*x^(number_of_roots-k);

od;

end proc;

z := [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10];

sigma := symMonomial(z);

f := expand(sigma[1]*sigma[2]);

f := expand(sigma[1]*sigma[1]); # two lambda value are the same

f := expand(sigma[1]*sigma[1]*sigma[1]); # three lambda value are the same

f := expand(sigma[1]^2+2*sigma[1]*sigma[2]+sigma[2]);

f := subs(x1=3, f);

f := subs(x2=2, f);

f := subs(x3=3, f);

f := subs(x4=4, f);

f := subs(x5=5, f);

f := subs(x6=6, f);

f := subs(x7=7, f);

f := subs(x8=8, f);

f := subs(x9=9, f);

f := subs(x10=lambda, f);

evalf(solve(f, lambda));

if degree(f) = 2 then

f := f + lambda^3;

evalf(solve(f, lambda));

end if:

how to convert above f back to matrix form such as

m := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);

m-Matrix([[lambda,0,0],[0,lambda,0],[0,0,lambda]]);

m2 := Determinant(m-Matrix([[lambda,0,0],[0,lambda,0],[0,0,lambda]]));

after tested m2 can not be expressed in terms of shell like polynomial,

it seems that it is from symmetric polynomial and it is from a non-homogenous polynomial which homogenize with a lambda

if solve f for new eigenvalue,

can traditional eignvector method calculate new eigenvector for these new kind of eigenvalues method?

A*x = lambda*x

### How to get the roots?...

June 23 2014
0 3

Greetings everyone. I tried to get the roots of this polynomial by using allvalues command. But I got the roots in indeces instead of the value of the roots.

what should i do?

### Set monomials in which an unknown has a certain de...

June 20 2014
3 3

Hi all,

I would like to set equal to zero some monomials in a polynomial. In particular those monomials in which an unknown has a certain degree.

For example for the polynomial

poly := x^2*y+x*y*z+x*z

i would like to set equal to zero the monomials in which x has degree 1, that is x*y and x*z.

Is there a way to do it?

Manuele

### Operational Matrices...

June 06 2014
0 0

Hi All. Hope all is well.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of polynomials of arbitrary form[say bij(t)](a.e Taylor series, or Bernstein series,…)

for Example with N=4, M=3 and by Taylor series we have:

now we want to approximate a function, asy f(t), in this interval with following form:

If we have:

(Tau is a constant number)
then: How can  we find L and Z matrices using maple? Is it any way? (or other softwares?)

Regards

Ph.D Candidate

Applied Mathematics Department

### Got quantifier elimination?...

April 22 2014
2 5

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?

### how to convert function into this form...

March 29 2014
0 2

x*(y+z)/x

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

### How to solve it with Maple?...

March 29 2014
1 5

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.

### Why are polynomials including constants not factor...

March 22 2014
2 3

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)

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

### Reduce the exponents of a polynomial mod p...

February 10 2014
1 6

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

### Procedure to produce array of parameters and numer...

February 07 2014
1 3

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;

### How do I solve a equal degree splitting problem...

January 17 2014
0 5
$u_{tt} = c^2 u_{xx}, \,$
$u(t,0)=0, \quad u(t,L)=0,$

as well as the initial conditions

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

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