# Tagged Questions

Questions on the functionality operating on polynomials

30 views

### Transforming Determinant to Polynomial Expression

I have determinant which equals zero. In determinant, i have x expressions. i want to transform the determinant to polynomial expression so i can solve that with mathematica. Note : Apologize for ...
50 views

### Finding Real Roots and Determining Range

I am interested in determining the minimum and maximum values of the real roots of polynomials of form $P(x)=\sum_{k=0}^n a_{k} x^k$ where $n$ will have a defined value (say 3,4,5...) and $a_k$ are ...
59 views

### Finding and plotting a parametric solution to a complicated equation (transcendental, log-polynomial)

I am trying (desperately) to find a way to solve a transcendental equation whose solution $x$ depends on non-numerical parameters $a$ and $b$. And then to produce a ...
220 views

277 views

80 views

MWE ...
57 views

### Solving for Polynomial roots

This simple Solve gives the roots of a quadratic: Solve[a x^2 + b x + c == 0, x] However, if I factor the polynomial in terms ...
129 views

### Expand power of a polynomial

I'm very new to Mathematica, so excuse my innocence. I have the following expression: $$\left( \sum_{n=0}^r \frac{(-1)^n}{n!} y^n \right)^f$$ I would like Mathematica to expand out the expression ...
135 views

Suppose I have a quadratic polynomial in two variables x and y in which the squares with respect to ...
61 views

### Crash after long GroebnerBasis calculation

I am running a long computation of a GröbnerBasis and after some hours the kernel crashes. The memory usage increases enormous, and it crashes, when it reaches somewhat 4 GB RES, however it is ...
427 views

### Easiest way to extract the coefficient of a polynomial

For a term in a polynomial, say 387 a1^4 a2^3 x^3 y^7 z^100 w^364 What is the most efficient way to extract the coefficient of this term, i.e. 387?
39 views

### Selecting terms on only one variable from a multiple-variable expression

Say I have a polynomial like $x y^2+15x^2 y+x+3y+10$ and I want to obtain, say, only the coefficient in $x$ alone, namely a 1. Using ...
250 views

### GroebnerBasis without specifying variables

All the examples in the Mathematica documentation specify that the syntax for the GroebnerBasis command is ...
34 views

### How can I quickly extract a specific coefficient in a Laurent polynomial?

Suppose we have a Laurent polynomial for the following: ...
34 views

### ApartSquareFree function

I have a doubt concerning the ApartSquareFree function in Mathematica. Roughly speaking, it is supposed to compute the partial fraction decomposition of a rational function $h/g$ with the denominators ...
97 views

### Symbolic calculation on roots of polynomial

Given a polynomial like $x^3 + a_2 x^2 + a_1 x + a_0$ with roots $r_i$, I would like to symbolically compute the coefficients of a polynomial whose roots are $r_i^3 + r_i + 1$. How can I do this in ...
87 views

### expressing a rising factorial as a polynomial

I have an equation in $x$ as follows: $f(x)=\prod\limits_{j=0}^{k}(j+x)=x(1+x)(2+x)\cdots(k+x)$ I want to express this as a polynomial in $x$, i.e., as $a_0x^0+a_1x^1+\cdots+a_kx^k$ I tried doing ...
248 views

### Get the coefficient matrix from a quadratic form

Suppose I have a quadratic form of qf = a x^2 + b y^2 + c z^2 + 2 d x y + 2 e x z + 2 f y z How can I easily to get the symmetric matrix A, such that $X^TAX=qf$?...
168 views

### Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
93 views

### How to efficiently find only the rational roots of a rational complex polynomial?

I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this? My best effort on an example polynomial: ...
104 views

### Does Solve[] find ALL the exact roots of rational polynomials?

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. But is the ...
113 views

### Factoring an arbitary variable in mathematica

Imagine we have a equation like this gf= 1 + (a3 - a1 x)^2 w1 + (b3 - b2 x)^2 w2 how can I reach the following equation ...
28 views

### PolynomialExtendedGCD in 2 variables

Consider a field $R$ and the ring $A=R[y]$. Consider two polynomials $g,h\in A[x]$. I want to obtain $d=\gcd(g,h)\in A[x]$ and two polynomials $s,t\in A[x]$ satisfying the Bézout relation: $sg+th=d$. ...
77 views

### Why are CoefficientRules and MonomialList so slow?

Why is CoefficientRules so slow in this example (v10.2 on OS X 10.11.4)? ...
135 views

### Alternative forms to Table for iterating over replacement rules

I have a multivariate polynomial x. I get coefficients of various monomials using CoefficientRules, which returns a list of ...