Questions on the functionality operating on polynomials

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2
votes
2answers
76 views

Expanding rational functions with minimal denominator

I'm working with rational functions and I want to be able to put them in a specific form and then get a list of terms in which the numerators are monomials. Take for example ...
0
votes
1answer
57 views

Expand a complicated polynomial

I am entirely new to Mathematica. I am wondering whether Mathematica can help me to expand expression like the following $$f(x_1,\dots, x_n) = \left(\sum_i x_i\sum_j x_ix_j^2\right)^3\left(\sum_{i,...
0
votes
1answer
48 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 ...
6
votes
0answers
75 views

What is the underlying algorithm to simplify sums of reciprocals of polynomials?

Flipping through Wolfram's blog entry on Leibniz, W noted Huygens' interview test for the young Leibniz, namely to determine: $$ \sum_{n\ge2} \frac{1}{{n \choose 2}} $$ It's one thing to do this by ...
5
votes
0answers
97 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
5
votes
0answers
239 views

Discriminant of Characteristic Polynomial

I'm doing a calculation which finds the characteristic polynomial of a matrix with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 ...
5
votes
0answers
338 views

Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
4
votes
0answers
48 views

Using Mathematica to find an alternative continued fraction for $\zeta(5)$

Given the Riemann zeta function $\zeta(n)$. I. $x=\zeta(3)$ Using Euler's continued fraction formula, we can form $\zeta(3)$'s cfrac as, $$Ax+B = \cfrac{1}{v_1 - \cfrac{1^6}{v_2 - \cfrac{2^6}{...
3
votes
0answers
79 views

Change of basis of polynomials

Suppose I have a favourite basis for polynomials in $x_1,\dotsc,x_n$, say non-symmetric Macdonald polynomials to be specific. I can easily compute these, and thus the change-of-basis matrix that takes ...
3
votes
0answers
176 views

Extracting an equation from an interpolated function

Im trying to use LibraryLink to do some calculations in C but part of the expression i want to calculate is an Interpolating Function. C cant use that obviously so I'm trying to shift it to a data ...
2
votes
0answers
114 views

Check Zagier theorem about Mahler's measure

I want to check the following theorem by using Mathematica: (from Heights of Polynomials and Entropy in Algebraic Dynamics, page 22) $\textbf{Theorem}.$ Let $\omega$ denote a primitive $6th$ ...
2
votes
0answers
64 views

Crash on use of CoefficientList

The Kernel of my Mathematica 10.4 seems to crash on certain use of the CoefficientList command. The line CoefficientList[x + y^2, {x, y}] Produces the matrix $$ ...
2
votes
0answers
33 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
2
votes
0answers
147 views

Puiseux series for algebraic curves

Has anyone implemented a function in Mathematica that computes Puiseux expansions of algebraic curves? Using something like ...
1
vote
0answers
47 views

Find interpolation polynomial using newtons formula

I found this program for calculating the interpolation polynomial using Newtons formula. This function takes as input data points and returns a polynomial. For example: I want to find the ...
1
vote
0answers
45 views

Coppersmith's algorithm like Pari's zncoppersmith?

Is there some Mathematica package (or built-in that I missed) available, more or less equivalent to Pari's zncoppersmith function? Paraphrasing that source: given ...
1
vote
0answers
59 views

FindFit with a sophisticated function (2), with corrected question and code

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simplier functions. In particular, I observe T(x) (this ...
1
vote
0answers
87 views

Working with rational polynomials

I work a lot with transfer functions (Laplace transform) and I often need to convert them into different forms: rational transfer functions pole/zero representation pole/zero/gain representation ...
1
vote
0answers
41 views

Error in NullSpace, with AlgebraicNumber entries

Consider the following 14x14 matrix, with typical entry ...
1
vote
0answers
67 views

Finding related roots to a polynomial

I posted this in math.stackexchange, but this might be a better place. Assume that $f(X,Y,Z,V,W)\in \mathbb{Z}[X,Y,Z,V,W]$ is some polynomial and assume that $f(x,y,z,v,w)=0$. I would like to know if ...
1
vote
0answers
226 views

Best way to determine polynomial coefficients in series expansion

I would like to solve the equation $$h'(\boldsymbol{x}_1)\left[B_1\boldsymbol{x}_1+g_1(\boldsymbol{x_1},h(\boldsymbol{x}_1))\right]=B_2h(\boldsymbol{x}_1)+g_2(\boldsymbol{x}_1,h(\boldsymbol{x}_1))$$ ...
1
vote
0answers
281 views

Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
1
vote
0answers
400 views

Polynomial factorization over finite fields with non-prime order

One can easily factor a polynomial over finite fields of prime order, using Factor command: ...
1
vote
0answers
113 views

Know the degree of the equation with the radicals expanded

I have an equation with radicals. I would like to know what would be the degree of the polynomials if I'd move the terms and square the equation a number of times sufficient to remove all the radicals....
0
votes
0answers
40 views

expand[] without multiplying binomial coefficients

I'd like to expand an expression of the form (ax+b)^5 without the binomial coefficents being multiplied out. I would like to see Binomial[5,0], Binomial[5,1] , etc... that intermediate step for ...
0
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0answers
84 views
0
votes
0answers
34 views

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

Suppose we have a Laurent polynomial for the following: ...
0
votes
0answers
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 ...
0
votes
0answers
29 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: $sg+th=d$. ...
0
votes
0answers
28 views

Obtain a SymmetricReduction of a bivariate (symmetric) function given in Piecewise form

I would like to re-express the following bivariate (symmetric) function (defined over the unit square) ...
0
votes
0answers
49 views

Multivariate remainder of polynomial in respect to a set of polynomials

I would like to have a really fast routine that computes the so called Normal Form of a multivariate polynomial f in respect to a set of other multivariate ...
0
votes
0answers
85 views

Ideals in Mathematica

I am having trouble finding the commands for ideals and basic manipulation of them, such as: (1) how to designate my field, (2) how to create a polynomial ring over this field in several variables, (...
0
votes
0answers
44 views

Timing of associated Legendre polynomials

I encountered a strange issue with the associated Legendre polynomials implemented with LegendreP[l,m,z]. Quite simply, the time used for the numerical computation of those quantities depends on ...
0
votes
0answers
66 views

Extracting coefficients of very large polynomials (perhaps by improving Expand or ExpandAll)

Is there a way to improve or bypass Expand (or ExpandAll) for extremely large polynomials? I have a polynomial system of the form $$ 0 = \sum_n a_n d_{i_1,i_2} \cdots d_{i_{p-1},i_p},$$ in which ...
0
votes
0answers
100 views

Applying the square root of operator on polynomial functions

I am trying to apply an "operation" on polynomial functions: apply the operator $(\frac{\partial f}{\partial x}-y\frac{\partial f}{\partial z})^2+(\frac{\partial f}{\partial y}+x\frac{\partial f}{\...