Items tagged with polynomial polynomial Tagged Items Feed

Hi EveryOne!

I have polynomial: p(x) = x^4 + 27x^3 + x^2 + 16x +1 over finite field F=GF(2^8)/f(x)=x^8 + x^4 +x^3 +1

The factors of this polynomial are: (x + 37)(x + 217)(x^2 + 213x +30) (in maple)

Hence there two roots of p(x): x = 37 and x = 217 in GF(2^8). The factor x^2 + 231x +30 is of degree 2. There are not roots in F. But in extension field GF((2^8)^2) of F, also there are two roots of factor x^2 + 213x + 30 (for example: x = 256 and x = 256^256 = 487).

How to find these roots of p(x) in extension field GF((2^8)^2) by maple? Please help me! Thanks a lot.

I have two polynomials, say


x(t) = a[0] + a[1]t + a[2]t^2

y(t) = b[0] + b[2]t + b[3]t^2


with the following conditions, x(0) = 2 and y(0) = 1. The polynomial are related by


x'(t) = y(t)

y'(t) = x(t)


and x(0) = 2, y(0) = 1.


One can show that the solution is x(t) = 2 + t + t^2 + O(t^3) and y(t) = 1 + 2t + 0.5t^2 + O(t^3).


I am trying to write something so that it works on a larger system. I have a set of nonlinear DEs which i want to solve this way. Here is a sample code of a much simplifed problem.


See the uploaded file for details.


edit: link is reparied. I uploaded the wrong file initially


edit2: Some improvements were made, but Maple still not returning.

hi can i write a function or procedure or summation so that i can write down the following polynomial ? i just want to create a set of polynomials which their summation of power ( power of x + power of y ) be less than three or equal to three ? the coefficients priority is not important , for example it is not important that a1 multiplies to x or y , i just want to create this polynomial with some coeeficients. tnx for help










OK, what am I doing wrong here?

This polynomial can be factored by almost anyone who knows algebra:


but Maple refuses:

 x2  + y2  + 2 xy

but if I pose the question this way:

ans := expand((x+y)^2);


(x + y)2

I get the expected result.  What is wrong with how I am using the factor?

I am trying to simplify sums of a few LaguerreL polinomials of different n using the identities in the function advisor such as recurrsion relations. How does one go about in using the FunctionAdvisor identities when trying to simplify expressions containing orthogonal polynomials? 




Hello, everyone!

I was given this week's Maple assignment in my class and I've come across a problem. I'll say this now so I don't get sent away, I am NOT asking for the answer. For this question there is a part A and part B, but also a preliminary check to make sure our code is wokring (as seen in the picture link). The issue I'm here for is that I can't figure out the code for the preliminary check... I've been here for hours and I'm stumped.


This is my attemp so far; 


f := x^(6*ln(x))


T2 := convert(%, polynom)

f_value := evalf(subs(x = 5, T2))


I'm very confused what to do next in order to get that preliminary test amount of 5121425.461.

Thanks in advance! :)

I am fitting polynomial differential equations to data, and I came across some troubling behavior. I have sets of coordinates in x, y, z, and values w at these coordinates. The x,y,z coordinates and the data at these coordinates are concatenations of three subsets of data each, and depending on the order of the concatenation, I get different polynomials from the stats fit command. The difference is not trivial -- it makes a huge differentce in the stability of the differential equations. I have written a demonstration worksheet to show this problem.

John Starrett

hypersurface is a homogenous polynomial

f(x,y) = 0

i do not understand how sampling hypersurface can generate this kind of polynomial


Dear people in Mapleprimes,


I have a question about the ordering of monomials in a polynomial.

I hope you will help me understand how Maple works about it.

I inputed the polynomial as is written in black below.

Then, the outcome was blue, which ordering I could understand well: total degree ordering where at first 

those who have the order of 6 are collected which are 14 x^3*y^3, 6x*y^5, and then the following was those which 

have the order of 5: 21*x^5, -35 x^4*y, 9*x^3*y^2,-15*x^2*y^3, ... and so on.

And, among those who have the same order, lexical ordering was done, that is among 14 x^3*y^3, 6x*y^5, one which 

came first was the one with the larger degree about x, and among 21*x^5, -35 x^4*y, 9*x^3*y^2,-15*x^2*y^3, 

the first was 21*x^5, the second was -35*x^4*y, and so one, which was the ordering following the exponent about x.


And, then, I calculated Factor(polynomial) mod 7, which meaning I know.

Then, the result was 2*(x*y+2)*(3*y^3+x^2+3x*y)y.

I can understand the ordering among x*y and 2 in x*y+2, and that among 3y^3, x^2 and 3x*y in 3y^3+x^2*3x*y.

But, I can't understand why (x*y+2) comes at the first term, with 3 y^3+x^2+3x*y following it, and with y coming last.


This might be a trivial question. But, I hope you will teach me about this.


Best wishes.




polynomial := 14*x^3*y^3+6*x*y^5+21*x^5-35*x^4*y+9*x^3*y^2-15*x^2*y^3+12*y^4+18*x^2*y-30*x*y^2



`mod`(Factor(polynomial), 7)






Hi everyone,


I have a question regarding the use of the applyrule function. I have an expression that contains a polynomial. The expression looks something like:


Y := (a0 + a_1*x + a_2*x^2 + ... a_n*x^n)*f(y) + b_0 + b_1*x + b_2*x^2 + ... b_n*x^n)*g(y):


I would like to express this as y(x) = P_1*f(y) + P_2*g(y).


So far I have tried applyrule([a0 + a_1*x + a_2*x^2 + ... a_n*x^n = P_1, b_0 + b_1*x + b_2*x^2 + ... b_n*x^n) = P_2],Y):


This doesn't seem to work. Any suggestions?





Hi everyone, I have been trying to plot the Taylor Polynomial approximation with the following code. However, my maple crushes everytime I run it. I indexed some of the variables to get the plot. The code works fine without the index. What did I do wrong?

y := array(1 .. 2);

Digits := 10;

n := 30;

h := .1;

T := 0;

X := 1; 

f := (x, t) -> 1/(3*x(t)-t-2); 

one := 1/(3*x(t)-t-2);

two := diff(f(x, t), t);

first := diff(x(t), t)


for k to n do

y[1] := subs(t = T(k), x(T(k)) = X(k), one);

y[2] := subs(first = y[1], t = T, x(T(k)) = X(k), two);

X[k+1] := X+sum(y[i]*h^i/factorial(i), i = 1 .. 2);

T[k+1] := T+h

end do;


data := [seq([T[n], X[n]], n = 0 .. 30)];

p[2] := plot(data, style = point, color = blue);

p[3] := plot(data, style = line, color = blue);
display(p[2],  p[3])


The code without Index (which works fine)

y := array(1 .. 2);

Digits := 10;

n := 30;

h := .1;

T := 1;

X := .1547196278;

f := (x, t) -> 1/(3*x(t)-t-2); 

one := x(t)^4*e^t-(1/3)*x(t);

two := diff(f(x, t), t);

first := diff(x(t), t);

for k to n do

y[1] := subs(t = T, x(T) = X, one);

y[2] := subs(first = y[1], t = T, x(T) = X, two);

X := X+sum(y[i]*h^i/factorial(i), i = 1 .. 2);

T := T+h

end do


Anyone knows how to define a ring of polynomials with variables x_1,...,x_n such that x_i*x_j = -x_j*x_i if i \neq j?

I tried using the Physics package and AntiCommutator but the problem is that in that case the variables anticommute with themselves so I have x_i^2=0.

If there is no direct way to this, I guess I could define a procedure that would look at the monomials of a polynomial and order them in lexicographic order and each time it switches two variables with different index it would multiply the monomial by -1.

I also don't know how to do that since I don't know how to look at a specific term in a monomial. For example, if my monomial is x_ix_jx_k, is there a way to find the first two variables and then switch them if LexOrder(variable1,variable2)= LexOrder(x_i,x_j)= false, i.e. if i>j?



Hi I am working on the following problem (See below the line) from the text A Introduction to the Mathematics of Biology (Ch 2 pgs.21-23). I am working in Maple 18 and the code for this problem is from Maple 11 I think. If you look at the last line of code, I ran into a snag. Can anyone help????? We are in a study Gourp and alll are stumped.


Problem # 2 - Find a fit for the cumulative US AIDS data as a polynomial function. Alsoo find an exponential fit for the data. (assume the Data I have inputed is correct if you don't have the book).

AIDS := [97, 206, 406, 700, 1289, 1654, 2576, 3392, 4922, 6343, 8359, 9968, 12990, 14397, 16604, 17124, 19585, 19707, 21392, 20846, 23690, 24610, 26228, 22768];
print(`output redirected...`); # input placeholder
[97, 206, 406, 700, 1289, 1654, 2576, 3392, 4922, 6343, 8359,

9968, 12990, 14397, 16604, 17124, 19585, 19707, 21392, 20846,

23690, 24610, 26228, 22768]

CAC := [seq(sum(AIDS[j]/(1000.0), j = 1 .. i), i = 1 .. 24)];
print(`output redirected...`); # input placeholder
[0.09700000000, 0.3030000000, 0.7090000000, 1.409000000,

2.698000000, 4.352000000, 6.928000000, 10.32000000,

15.24200000, 21.58500000, 29.94400000, 39.91200000,

52.90200000, 67.29900000, 83.90300000, 101.0270000,

120.6120000, 140.3190000, 161.7110000, 182.5570000,

206.2470000, 230.8570000, 257.0850000, 279.8530000]

Time := [seq(1981+(i-1)*(1/2), i = 1 .. 24)];
LnCAC := map(ln, CAC);
print(`output redirected...`); # input placeholder
[-2.333044300, -1.194022473, -0.3438997525, 0.3428802329,

0.9925107578, 1.470635510, 1.935571171, 2.334083760,

2.724054775, 3.071998629, 3.399328971, 3.686677031,

3.968441145, 4.209145378, 4.429661370, 4.615387808,

4.792578782, 4.943918402, 5.085810791, 5.207062453,

5.329074480, 5.441798471, 5.549406770, 5.634264465]
LnTime := map(ln, [seq((i+1)/(2*(1/10)), i = 1 .. 24)]);
print(`output redirected...`); # input placeholder
[ln(10), ln(15), ln(20), 2 ln(5), ln(30), ln(35), ln(40), ln(45),

ln(50), ln(55), ln(60), ln(65), ln(70), ln(75), ln(80), ln(85),

ln(90), ln(95), 2 ln(10), ln(105), ln(110), ln(115), ln(120),

3 ln(5)]
fit[leastsquare[[x, y], y = k*x+lnA]]([LnTime, LnCAC]);
print(`output redirected...`); # input placeholder
y = 3.293411005 x - 10.12289000
k := op(1, op(1, rhs(%))); LnA := op(2, rhs(`%%`)); A := exp(LnA);
print(`output redirected...`); # input placeholder
Error, invalid input: rhs received exp(LnA), which is not valid for its 1st argument, expr
Error, invalid input: rhs received exp(LnA), which is not valid for its 1st argument, expr

Hi all,

I have an expression of the form Sum(a[l]*x^l,l=0..n).

Is there a shorter way to obtain let's say the 5 lowest orders than add(coeff(expression,x,l)*x^l,l=0..4) ?




This is my code for the Extended Euclidean Algorthim which should return integer l, polynomials pi,ri,si,ti for 0<=i<=l+1. And polynomial qi for 1<=i<=l such that si(f)+ti(g) = ri and sl(f)+tl(g)=rl=GCD(f,g).
The problem is, I keep getting division by zero. Also it evaluates pi = lcoeff(ri-1 - qiri) to be zero, everytime. Even when I remove this it still says there is a division of zero, which must be coming from qi:=quo(ri-1,ri, x); however I do not know why considering the requirements for the loop are that r[i] not equal zero. I really could use a fresh pair of eyes to see what I've done wrong. Any help would be greatly appreciated!!

1 2 3 4 5 6 7 Last Page 1 of 10