Questions on the functionality operating on polynomials

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1
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1answer
55 views

Reducing a multi-variate polynomial to have terms upto certain degree

I have a polynomial in x and y. I want to keep all the terms with (combined) degree 4. Any pointers will be appreciated. Simple tricks for doing the same with univariate polynomial don't seem to work. ...
0
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1answer
172 views

Solve[polynomial, x, Reals] doesn't get all real roots or correct ones?

My main confusion is about the difference between the two code blocks at the end of this long spiel, but the spiel contains the code to create the polynomial if its coefficients are helpful for ...
7
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0answers
95 views

Apart may use Padé method: what's that?

How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
4
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0answers
92 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 ...
4
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0answers
178 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 ...
3
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0answers
210 views

Transform recursion for coefficients into differential equation for generating function

Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as a[i] == i a[i-1] I would like to convert this recursion ...
2
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0answers
173 views

Negative power instead of fraction

Solve returns a solution in the form {{x->y/a^2 + y^2/a^7}}. Since I want to process the input (with another program) in terms of Laurent polynomials, I would ...
1
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0answers
44 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
1
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0answers
108 views

Issue with Coefficient command

I'm trying to used the Coefficient command to extract the numerical values in front of a Chebyshev polynomial. I know that there is a numerical way to do this, presented in numerical recipes, which I ...
1
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0answers
94 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
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0answers
137 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
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0answers
95 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 ...
0
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0answers
44 views

Roots of characteristic equation of sixth order

I have problem how to localize the roots of the sixth order polynomial given in the form of determinant. Classical Solve gives the solution which are in the long form. Is there way how to present ...
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0answers
43 views

PolynomialReduce not working

I have a polynomial $f(x_1, x_2, \ldots , x_n)$ with coefficients in $Z[q,t]$, and I have a list of polynomials $g = g_1, g_2, \ldots , g_k$ where they are also polynomials in $(x_1, x_2, \ldots, ...
0
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0answers
65 views

Finding relations between polynomials

Suppose I have a multivariate polynomial ring $A=\mathbb{R}[x_1,\ldots,x_n]$ and a set of $S=\{p_1, \ldots,p_k\}$ polynomials in $A$. Using this code (which works great) Dimension of an algebraic ...
0
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0answers
69 views

How can I calculate all irreducible polynomials of 31 degree in $\mathbb Z_2[x]$?

How can I calculate all binary irreducible polynomials of degree 31? or how i calculate all irreducible $f$ in $\mathbb Z_2[x]$? (The irreducible polynomial in $\mathbb Z_2[x]$ and $\mathbb R$ are ...
0
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0answers
64 views

Parallelising the solving of polynomials

I'm working on finding solutions to a, not so very nice, system of equations. They are all polynomials of degree $4$ with $5$ parameters and all terms are of even order. I'll post the code on request, ...
0
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0answers
152 views

symbolic solution for a system of nonlinear equations in mathematica

Would appreciate any help on the following in mathematica I cant figure it out. I have a system of equations that I am trying to solve symbolically. I have 9 equations and 8 unknowns (I have also ...
0
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0answers
216 views

Generating various irreducible polynomials over finite fields

Mathematica offers the package FiniteFields, which supports generation of an irreducible polynomial in a finite field: IrreduciblePolynomial[s,p,d]: gives an ...