# Questions tagged [polynomials]

For questions about solving and representing polynomials computationally.

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### Gradient descent for solving polynomial equations while encouraging variables to be nonzero

I would like to use gradient descent to "randomly sample" solutions to a set of homogeneous polynomial equations. Because the equations are homogeneous, setting all variables to 0 is a valid ...
• 123
97 views

### Solving a polynomial with NumPy

I'm trying to do something that I thought would be very straightforward but somehow I'm struggling. I have a time series and I want to extrapolate it, assuming a linear trend, to forecast when will it ...
96 views

### What is the point in non-intrusive Polynomial Chaos output moments?

So I recently learned about Polynomial Chaos Expansion (aka PCE), and it seemed to me that its purpose was to propagate uncertainty from the inputs to the outputs more efficiently (via closed-form ...
• 149
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### Solve bivariate polynomial system

Given a bivariate polynomial system with variables $(x, y, z)$ like (1) $f_1 = x * a_1 + y * a_2 + z * a_3 = 0$ (2) $f_2 = x * a_4 + y * a_5 + z * a_6 = 0$ (3) $f_3 = x^2 + y^2 - 1 = 0$ how do I ...
1 vote
72 views

### Strategies to solve an equation with a polynomial and a numeric function

I have to solve numerically an equation of the following form: $$\sum_{n=0}^m c_n x^n = f(x) x^k$$ Where the $c_n$ are real values, $k$ is an integer and $f$ can only be evaluated numerically. The ...
• 153
1 vote
130 views

### Explicit polynomial for quadratic elements? (FEM)

In this resource the linear (barycentric) elements are explicitly given: The geometry placement of higher order elements is also given but not expression for the polynomial of $P_2$ is given. I am ...
• 263
1 vote
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• 143
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### Find solution to Polynomial Sequences without going through variety in Sage

I'm computing the Groebner basis of an ideal defined over the QQ ring. Once I have this Groebner basis, I would like to obtain a set of values that satisfy the equations in the Groebner basis. I know ...
• 121
1 vote
43 views

### Minimizing a polynomial with millions of monomials

I need to minimize a single polynomial $P(x_1,x_2,...,x_n)$ with the constraint that for each $i$, $0\leq x_i \leq 1$. The number of variables in my practical problem is at most $50$. The degree is at ...
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### Fast evaluation functions given by straight-line programs

I have a simple but long function that takes a vector x[10], and outputs a vector y[100]. It is an automatically generated eval function for a multivariate polynomial, ie, there is only (complex) ...
• 129
1 vote