# Questions tagged [polynomials]

Questions on the functionality operating on polynomials

955 questions
Filter by
Sorted by
Tagged with
1 vote
47 views

78 views

### Relation between coefficients of polynomial to get real roots

I am trying to find a relation between coefficients $a$ and $b$ of the equation $a x^3 + b x^2 - x + 2 =0$ so that I get positive real roots of the equation (i.e. $x\geq0$). Any help on how to do this ...
1 vote
33 views

### How can I transform an expression with radicals to RootSum?

I am working with the integrals like these: ...
141 views

### Factorization of 5th polynomial with Wolfram-Mathematica

I have a very complicated 5th-degree polynomial form. Using the factor function in Wolfram is impossible to make it because of the high degree. I just want to know that is it possible to factor as I ...
85 views

### How can I compute the $n$-th complete Bell polynomial?

I'm interested in computing the n-th complete Bell polynomial $B_n(x_1,..., x_n)$ using the formula given as the last equation in the "Exponential Bell polynomials" section here (I tried ...
67 views

### Comparing two power series and extracting their coefficients

I have a standard mathematical problem that I was wondering how to solve efficiently by mathematica. Here is the problem. I have two power series expansions of a function ...
40 views

### Poles of filter transfer function, fifth order equation [duplicate]

I am just trying to find the roots of the fifth-order equation. But I could get enough result from Wolfram. Could anyone help to me about this issue? ...
120 views

### Looking for a recurrence relation for these specific polynomials?

Trying to answer this question related to the calculation of $$I_k=\int_1^\infty x^ke^{-x}\ln(x+a)\,dx$$ which, at least to me, looks problematic. What is missing for a complete answer is to ...
1 vote
74 views

### Taylor series loop

I'm a beginner not only in Mathematica but also in programming in general, and so I'm not really sure where my problem lies exactly and I'd be glad to receive any guidance. Using the Taylor series for ...
87 views

### How to get the coefficient list of their product from the coefficient list of two polynomials?

If I have the coefficient list of two polynomials ...
1 vote
103 views

### Finding negative powers of polynomial expressions

Suppose I have the following expressions ...
252 views

### Extract monomials with a certain structure from a given polynomial

I have a long polynomial such as a x^2+ bx^2y+cx^2y^2 +d x^3y^4+e x^4y^3+f y^2+g xy^2 Consider an example problem as follows: I want to output the monomials (along ...
1 vote
83 views

### Solving a complicated equation of order 5. completely parametrically

I have this equation and it takes so much time to solve. i would appreciate some guidance how to solve it. 0<l<1 and 0<gamma<1 and -Pi/2<theta<Pi/2 and w is real and positive. other ...
1 vote
66 views

### Reducing roots of power sums

Often I encounter expressions like for example Root[ 1 - # + #^2 - #^3 + #^4 - #^5 + #^6 &, 3 ] or ...
1 vote
39 views

### Collect with rational powers

I need a function, which will collect terms next to the same rational power of a given variable. For the input RCollect[3xy^(3/2)+2/y+zx/y-y/x+2*x^z y^(3/2),y] the ...
271 views

273 views

### Basis for multivariable polynomials

I have a bunch of two-variable polynomials and as part of a larger algorithm need to find a basis for them and express them in terms of this basis. As an illustrative example, for one case my ...
96 views

### Guessing patterns of symbolic series

I have a system of 2s+1 equations, where s can take integer values of {1,2,3,....,n}. Here ...
52 views

### How to solve Equation for different variable in Mathematica?

I want to solve the given equation for $(n=m=3)$ and I want the output variable $q_{1,1}, q_{1,2}, q_{2,1}, q_{2,2}$ Given Equation Given Equation-2 The output should be required Output Here is my ...
31 views

### Expanding a large dynamic expression involving roots of a degree 4 polynomial

I am trying to find the eigenvalues of a 4x4 Matrix symbolically. Below is the code I am using, ...
76 views

### How to arrange the obtained results according to the descending power of x?

The function of the code is to obtain a univariate quadratic equation about x by simultaneous equation the code is this： ...
1 vote
186 views

### Stepped Infinite Square Well [closed]

Here is the link for making the above graph for the Stepped infinite square well. The problem here is, all the eigenfunctions and energy eigenvalues are previously defined. Whereas, I want to use this ...
81 views

I want to compute all $<=d$ degree bivariate polynomials of form $f_1(x)g_1(y) + f_2(x)g_2(y)$, over field $GF(2)$, and evaluate them at a certain polynomial input for eg $d = 1$, evaluation at $(p^... 0 votes 1 answer 72 views ### How can I verify that the function$f$and its simplified version are same? I have the function$f=f(x,y,z)$and rewrite it in the PolynomialForm and TraditionalOrder ; then, I try to verify the result by ... 0 votes 0 answers 107 views ### How to calculate Intermediate fields of Galois group in Hasse diagram? I can easily calculate the Hasse diagram of an equation in maple, for example for the equation$x^4 + 8x + 12$(It's Galois group is$A4$): ... 1 vote 3 answers 328 views ### Drawing the roots of polynomials on the complex plane [duplicate] I have a polynomial$f(x)=x^2(x + 1)^{2n} + 2x^{n + 1}(x + 1)^n + x^{2n}$. Then I want to show the roots of$f(x)$from$2\leq n\leq 30\$ in the complex plane. I have tried lots of methods but don't ...
I have some inequality ,like this $$\left\{\begin{array}{l} x+y+z \geqslant 1 \\ 2 x+6 y+3 z \geqslant 6 \\ a x+b y+c z \geqslant d \end{array}\right.$$ I want to put all the y's in this inequality ...