Questions tagged [polynomials]

Questions on the functionality operating on polynomials

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Finding kernel of a set of polynomial functions

I have a list of polynomials fi[x_] and polynomial fractions qi[x_] (with i as an iterator) ...
342 views

PolynomialQ behaviour

I am crafting some functions on polynomials that must be in x. But I checked that it is always True whatever variable I use: ...
100 views

How to Collect where var is one expression?

Edit: Clear["Global`*"]; expr1 = (a + c - b + 1)^3 + (-b + a + c + 2)^4 // Expand For test case expr1, this is the ...
39 views

Extracting matrix coefficients from multivariate matrices

Suppose we have a multivariate polynomial matrix $P(\mathbf x) = \sum_\alpha A_\alpha\mathbf x^\alpha$ (in multi-index notation) where the $A_\alpha$ are constant coefficient matrices. I am looking ...
190 views

Finding a rational univariate representation (RUR) for a polynomial system

According to Wikipedia, a RUR of a zero-dimensional system consists in a linear combination of the variables, $x_0$ called ''separating variable'', and a system of equations : \begin{cases} h(x_0)=0\\...
79 views

Unstable work of PolynomialMod

I tried to use PolynomialMod for my calculation and i need some help on working with it, because i'll need to use it several hundred times. I made such a request ...
1 vote
97 views

How to sort the terms in a polynomial according to their degree?

I have the polynomial ...
125 views

How to execute this code? [closed]

I want to plot the following equation: ...
1 vote
56 views

Replacement rule runs for a long time [duplicate]

I have a simple expression that reads (some expression in b) q^(8/3): ...
1 vote
56 views

89 views

Finding the solution for the cubic formula over NonNegativeReals

The standard cubic polynomial is: $ax^3+bx^2+cx + d$. And when I used my function: ...
1 vote
157 views

How to factor a quartic equation whose coefficient has unknown parameters?

i'm trying to see if a quartic equation I obtained can be factored into simpler forms, such as the product of two quadratics. The problem is that their coefficients are some complex expressions in ...
46 views

How to factorize high-order polynomials that have only complex roots?

I have polynomials like this: ...
194 views

How to verify a solution of an ordinary differential equation?

Given an ordinary differential equation with initial conditions eq = u a[u] + (16 + u^2 + 2 u a[u] (12 + u a[u] (6 + u a[u]))) a'[u] == 0 ic = a[0] == -1/2 How can ...
178 views

Calculating the basis set of quotient spaces

Having a polynomial $f(x,y)$, I would like to compute the following quantity \begin{equation*} {\mathbb C}[X,Y,Z]/\langle f_{x}, f_{y}, f_{z} \rangle, \end{equation*} where $f_{x},f_{y},f_{z}$ are, ...
8k views

How to define a polynomial/function from an array of coefficients?

I have the coefficients of my desired polynomial in an array CoefArr (I'm new to mathematica, so I think of everything as arrays, it is actually a list I believe) starting with the constant at index 1....
1 vote
139 views

Elegant way to restrict PolynomialMod to non-negatives

Update at the bottom! PolynomialMod[4 + 10x, 1 + 2x] returns -1. Instead, I'd like to get 4, ...
1 vote
71 views

Expanding polynomials using valuation

I would like to expand the polynomial $p(\lambda) = \sum_{i=0}^{d} a_{i} \lambda^{i}$, as $F(p(\lambda), \lambda_{0})= \min_{j} [ val(a_{j}) + j \lambda_{0} ]$ with $\lambda_{0}$ being a real ...
490 views

How to generate a set of orthogonal polynomials with a special weight function?

Regarding to $e^{-ax-bx^2}$ as the weight function , how can I generate a set of orthogonal polynomials? I just know the Orthogonalize command in Mathematica which ...
1 vote
95 views

I have a polynomial of variables $x,y$, where $|x|<1$ and $|y|<1$. When I apply the Simplify function to this expression, I get an expression of the form $(x-... 0 votes 0 answers 54 views Solving polynomial roots of any degree only by Vieta's formula I have already wrote the code that solves it for quadratic formula and I'm curious if this is possible to make that function work with any kind of polynomial(higher degrees) and solving roots only ... 1 vote 2 answers 120 views How to extract coefficients of polynomial formatted like this? I want to extract coefficients. ... 16 votes 2 answers 666 views Does NRoots own an abstract counterpart? If not, can we write one? We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ... 4 votes 1 answer 316 views How to make a polynomial so that f(i) = 1/(2^i)? I know that, sequence has formula$f(n) = \dfrac{1}{2^n}$satifying the conditions$f(1)=\dfrac{1}{2}$,$f(2)=\dfrac{1}{4}$,$f(3)=\dfrac{1}{8}$,$f(4)=\dfrac{1}{16}$. Now I am trying to find a ... 0 votes 1 answer 41 views How to make MMA distinguish between symbolic coefficients and variables when doing factorization? [closed] I what to factor a polynomial with complicated symbolic coefficients Factor[p0^2 + k^2 r^2 \[Tau]^2 - 2 k p0 r \[Tau]^2 \[Omega] + p0^2 \[Tau]^2 \[Omega]^2] In ... 0 votes 1 answer 96 views Compute all bivariate polynomials over GF(2) of degree d or less and evaluate them at certain polynomial input 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^...
I'm trying to solve the following polynomial equation for $x$: $$(qx)^\alpha (1-qx)^{1-\alpha} = [(1-q)x]^\beta [1-(1-q)x]^{1-\beta}$$ where $\alpha, \beta, q, x$ are all strictly between 0 and 1. ...
Q1: Suppose I have an expression like this one: $(1+x+y+z)^3$ How can I transform it into the following expression: $$\{1,x+y+z,x^2+y^2+z^2,xy+xz+yz,x^3+y^3+z^3,x^2y+x^2z+xy^2+y^2z+xz^2+yz^2,xyz\}$$ ...