Questions on the functionality operating on polynomials

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4
votes
1answer
69 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
1
vote
2answers
72 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
85 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) ...
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 ...
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: ...
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 ...
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
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 $GS65$: ...
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
100 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: ...
-1
votes
0answers
32 views

How to calculate the pseudo-remainder and pseudo-quotient of one multivariable polynomial withrespect to one mutivariable polynomias set [duplicate]

Here is some code, but it produce error results, who can tell me the right code? ...
0
votes
1answer
94 views

How to calculate the pseudo-remainder and pseudo-quotient of two multivariate polynomials

I have fixed some code, but it always gives me errors. Can anybody tell me its right code? ...
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 ...
14
votes
1answer
170 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} ...
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
34 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 ...
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: ...
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
59 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, ...
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 + ...
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 ...
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 ...
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
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
1
vote
2answers
47 views

How to reorder and combine terms in a polynomial with multi-variables?

I have a polynomial with the coefficients of {a1, b1, b2} ...
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. ...
4
votes
1answer
410 views
0
votes
2answers
125 views

Don't understand results from solving easy polynomial equations

I am alarmed by the behavior of Mathematica (9.0) when given the following simple set of equations to solve: ...
2
votes
1answer
98 views

Cannot get plot of polynomial (x^2 + y^2 + z^2 - 4)^2 == 0 from ContourPlot3D [closed]

I'm trying to make a 3D contour plot the polynomial equation $$(x^2 + y^2 + z^2 - 4)^2 == 0, \quad \quad (1)$$ Without power 2 $$ (x^2 + y^2 + z^2 - 4) == 0, \quad \quad (2)$$ it plots a ...
1
vote
1answer
92 views

Is Factor reliable to find factorization? [closed]

I have two polynomials given by: ...
0
votes
0answers
52 views

Numerically finding a single root of a polynomial system

I may be off base, but from the documentation, it sounds like NSolve is specifically tailored to finding (all) roots of a polynomial system. On the other hand, ...
4
votes
1answer
95 views

Points on discriminant variety?

I am trying to find a way in Mathematica to compute points on discriminant variety for modest size systems, but I couldn't find one. The system is something like: ...
2
votes
1answer
62 views

RootReduce-Part of Solve

I have given the following expression in $M$ and $z$: \begin{equation} a = \frac{-4 M^2+M (-3 z-5)+\frac{1.1875 z}{\sqrt{\frac{0.015625 z}{M+1}-1.5625} \sqrt{\frac{0.765625 ...
3
votes
4answers
85 views

CoefficientList with multivariable [closed]

Consider: t = (1 + x)^3 (1 - y - x)^2 Expand[t] Now: CoefficientList[t, {x, y}] The output is: {{1, -2, 1}, {1, -4, 3}, ...
4
votes
1answer
187 views

Counting the number of terms in a polynomial using Length command

I have the following polynomial which depends on $n$: poly = (Sum[(i - 1) y[i], {i, 1, n, 1}])^2 - Sum[(i - 1)^2 y[i]^2, {i, 2, n, 1}] // Expand; The ...
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 ...
2
votes
1answer
62 views

Efficient way to apply linear function to multivariate polynomial [closed]

Suppose I start with an expression that is a multivariate polynomial in $x_k$'s, $$W = a + b \cdot x_1^{n_1} x_2^{n_2} x_3^{n_3} x_4^{n_4} + c \cdot x_1^{m_1} x_2^{m_2} x_3^{m_3} x_4^{m_4}$$ where ...
0
votes
1answer
59 views

Primitive polynomials of a field [closed]

I would like to know how I can get the primitive polynomials to generate the points of the fields GF(7) and GF(9) using Mathematica. Any help is appreciated.