Questions on the functionality operating on polynomials

learn more… | top users | synonyms (1)

2
votes
1answer
38 views

How to gather terms into Elementary Symmetric Polynomials?

I would like to gather the terms of this polynomial (and much higher order ones): $$q = 1-3 c+c^2+p[1]-2 c p[1]+p[2]-2 c p[2]+p[1] p[2]-c p[1] p[2]+p[3]-2 c p[3]+p[1] p[3]-c p[1] p[3]+p[2] p[3]-c ...
2
votes
2answers
51 views

How do I find a polynomial in a field?

If I have a polynomial: $$f(x) = c_0 x^0 + c_1 x^1 + c_2 x^2 + \dots + c_n x^n$$ How can I find the polynomial, modulo a prime number $p$? In other words, I want to take all of the coefficients ...
8
votes
2answers
189 views

How can I get the solutions of $x^n-x-t=0$ in hypergeometric form?

$x^3-x-t=0$ has three roots that can be expressed in hypergeometric form, for example $$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} ...
4
votes
1answer
73 views

How to equate coefficient of two polynomials? [on hold]

Given two polynomials, How can I equate coefficients of them in Mathematica? For instance a + b x + (c+d) x^2 + (e+f)x^3 == 0
3
votes
3answers
114 views

General function for the expansion of a polynomial of operators

This question is motivated by a Quantum mechanical problem - but in explaining the problem - I assume no knowledge of quantum mechanics. I want to define a function that can expand and simplify the ...
1
vote
2answers
74 views

What's the easiest way to remove overall factors from polynomials?

I have code that outputs polynomials (in #1) such as the ones below (note that the trailing Function character ...
2
votes
1answer
86 views

How do I find the analytical roots of this polynomial? [closed]

I want to find the analytical roots of this polynomial - x - a^3*x*(a^2*x*(a*x*(x - 1) + 1)*(x - 1) + 1)*(a*x*(x - 1) + 1)*(x - 1) ...
0
votes
1answer
94 views
2
votes
3answers
75 views

How to set/adjust Precision for an iterative calculation?

How should I restructure this code? I generate a high-order polynomial poly with integer coefficients, then find roots and divide them out of poly one at a time. ...
0
votes
2answers
76 views

Finding all complex polynomial roots in a specified range efficiently

I need to find the roots of a rational polynomial that are near i. In the following code, I try that two different ways. First, I use a constraint to only find roots in the right region. Second, I ...
8
votes
3answers
353 views

Bug: Wrong results from NSolve on coupled polynomials. WorkingPrecision->Automatic fails

OP UPDATE: I received an email from WR on 1-18-2016: "...It does appear that the NSolve function is not behaving properly in this case and I have forwarded an incident report to our developers with ...
3
votes
1answer
73 views

How to prevent fractions in polynomial quotients?

(This was a hard question to give a succinct title to, so feel free to edit it.) When I divide polynomials, I would like Mathematica to NOT create negative powers of variables. For example: ...
7
votes
3answers
234 views

Write a function that returns the coefficient of x^n

Write a function C[p_, x_, n_] that returns the coefficient of $x^n$ in the polynomial equation. C[p_, x_, n_] := ... If we ...
1
vote
2answers
122 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 ...
3
votes
2answers
182 views

Convert polynomial to Chebyshev

I want to convert a polynomial in "standard form" to Chebyshev form. Here's one way to do it: ...
3
votes
6answers
288 views

Avoiding a For-loop when finding the solution to a set of polynomial equations

There are several examples and questions regarding Map, but I couldn't find what I need. This is a minimal working example. I have two functions $\qquad ...
3
votes
2answers
73 views

Workaround for issues with Coefficient in 10.0.2

Coefficient is Mathematica 10.0.x seems to be affected by a bug. While in 10.3.1 the following ...
3
votes
4answers
503 views

NSolve didn't get the answer for my equations within 24 hours

I have two polynomials as function of $wa$ and $wb$ , I am going to show those polynomials. This is the expression for $GS65$: ...
1
vote
2answers
59 views

Complex polynomial variable transformation

I have two real polynomials that depend in variables (xi1, xi2) and parameters (eps, e2). I apply the following ...
3
votes
0answers
295 views

Negative power instead of fraction [duplicate]

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 ...
3
votes
1answer
126 views

Factor fraction, where variable occurring in both, numerator and denominator, only appears once

I have an expression like $$\frac{1+a^2+2 a \cos\left(p\right)}{\left(1+b^2\right)z-1-a^2-2 \left(a+b z\right)\cos\left(p\right)}\text{.}\tag{1}$$ Is there a combination of Mathematica functions to ...
3
votes
1answer
101 views

How to solve coupled multi-variable polynomials?

The following code generates two polynomials $q_1$ and $q_2$ in complex variables p and c: ...
14
votes
1answer
171 views

What's going on here? Some kind of rationalization “under the covers”?

Observe: eq = (.25 a + .5 b + .25 c); CoefficientRules[eq^2] CoefficientRules[eq^2 // Expand] results in {{2, 0, 0} -> 1/16, {1, 1, 0} -> 1/4, {1, 0, 1} ...
5
votes
0answers
66 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 ...
3
votes
1answer
50 views

Using the InterpolatingPolynomial function

How can I find the interpolation polynomial for the function $f(x) = \frac{1}{1+2x^2}$ with interpolation knots $x_k = 1 + 0.2k , k=0,1,...,6$ using the ...
1
vote
0answers
35 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
35 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 ...
2
votes
1answer
71 views

Improving working precision of LegendreP[n,x]? [duplicate]

I was trying to evaluate N[LegendreP[5,0.1]] The cell gives me: N[LegendreP[5,0.1]]=0.178829 However I wanted more ...
0
votes
0answers
95 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 ...
11
votes
1answer
336 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: ...
0
votes
1answer
43 views

Why is monomial list failing here? [closed]

I've tried to use MonomialList here but it seems to be failing: ...
0
votes
1answer
114 views

Conditions for real roots of a cubic polynomial with complicated, yet constant, parameter values

Can anyone find conditions on the following parameters $\sigma_{\ell}$, $\mu_{\ell}$, $d_{\ell}$ and $\sigma_M$ such that the cubic: $$ (d_{\ell}-d_{\ell}\sigma_M)\ell^3 + ...
4
votes
1answer
113 views

Solving for the roots of a trilinear system of polynomials

I have been trying to solve for the roots of the following system of trilinear polynomials: ...
1
vote
2answers
39 views

Inserting numbers or polynomials into a polynomial

Essentially my issue is that, in the algorithm im working on, I construct a polynomial by taking factors out of a list and multiplying them. For example, i have ...
0
votes
0answers
35 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
1answer
60 views

How to compare two polynomial and keep one of them

I created a automatisation that assign different values to the coefficient of Poly1 (a,b,c,d,e,f), this can be 0, eliminated some expression and in that moment I ...
0
votes
0answers
78 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, ...
5
votes
0answers
91 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 ...
3
votes
3answers
174 views

FindFit with a sophisticated function (integral)

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 simpler functions (two polynomials), that is the model. ...
7
votes
3answers
217 views

Interval calculations in wolfram mathematica

If x = Interval[-100,100], then obviously x^2 + x = Interval[-0.25,10100], because as we know, ...
1
vote
0answers
55 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
1answer
111 views

Polynomial decomposition algorithm with a hint

If $p,f,g$ are polynomials of degree 2 or higher and $p(x)=f(g(x))$ we have a polynomial decomposition of $p$. When Mathematica (as noted below this was actually on Wolfram Alpha) says ``decomposition ...
6
votes
6answers
375 views

Rewrite a real polynomial in real (but only linear and quadratic) factors

According to my calculus book: "Every real polynomial can be factored into a product of real (possibly repeated) linear factors and real (also possibly repeated) quadratic factors having no real ...
0
votes
2answers
119 views

Rearranging a simple algebraic equation

Suppose I have a simple algebraic equation like: ChebyshevT[4, p] == 0 1 - 8 p^2 + 8 p^4 == 0 and I want to solve for the ...
1
vote
1answer
67 views

Graph of second order polynomials [closed]

As I mentioned before, I want to write a notebook for teaching graphs of second order polynomials that shows discriminant and the conditions when a>0, a<0, having real roots, having no real roots. ...
7
votes
1answer
184 views

Trouble with polynomial multiplication

Bug introduced in 10.1.0 and persisting through 10.3.0 or later ...
1
vote
2answers
76 views

Creating a random complex univariate polynomial

I am a newbie in Mathematica, but I need to create a random univariate polynomial of degree d with complex coefficients whose entries are random complex variables with real and imaginary parts being ...
0
votes
2answers
69 views

Fit a polynomial/curve to an NIntegrate result

I want to NIntegrate a function which also contains some parameter. In the end, I would like to plot the result as a function of one of these parameters. The thing ...