 About 31,700 results  books.google.com As such, the form in which a polynomial is written might matter a lot for numerical
issues. Let us compare the results of NRoots for the factored and expanded forms
ofH1 + xL12 = 0. In[12]:= poly = (x  1)^12; NRoots[poly == 0, x] Out[13]=x1. 

 books.google.com Subroutine ROOTJO is listed below: C. C. C. C. C. C. C. C. C.
c. c. c. c. c. c. c. c. c. c. c. c. c. c. c. c. c. c. c. c. SUBROUTINE ROOTJ0 ( NROOTS ,
ROOTS , BF J 1 ) SUBROUTINE ROOTJ0 COMPUTES THE ROOTS OF J0(X),
AND EVALUATES ... 

 books.google.com Some of these commands include FindRoot and NRoots. NRoots numerically
approximates the roots of any polynomial equation. The command NRoots [poly1
==poly 2, x] approximates the solutions of the polynomial equation poly1==poly2,
... 

 books.google.com 3.7.1 Finding Zeros to the Right of a Specified Point The userdefined function
NZeros finds n roots of f(x) = 0 to the right of the specified initial point x0 by
incrementing x and inspecting the sign of the corresponding f(x). A root is
detected when ... 

 books.google.com For the inverse problem, namely determining the curve from its 28 bitangents,
see [302]. b) Using NRoots, we can calculate a dense set of curve points. We
recognize 12 selfintersections. In[1]:= eq[q_, z_] = 2 z^6  q^3  q; pic = With[{R =
0.9, ... 

 books.google.com ... dx = 0.01; nroots = 0; while 1 [x1,x2] = rootsearch(func,a,b,dx); if isnan(x1)
break else a = x2; x = bisect(func,x1,x2,1); if ~isnan(x) nroots = nroots + 1; root(
nroots) = x; end end end I'OOt Running the program resulted in the output >> root
= 0 ... 

 books.google.com A polynomial of degree n over the field F has at most n roots in F. Proof. The proof
is by induction on n. To start the induction, we note that a polynomial of degree 0
is a (nonzero) constant and has no roots. Now suppose the proposition is true ... 

 books.google.com if (nroots == 1) { printf("\n1 distinct real root at x = %f\n", roots [0]); } else { printf("\n
?id distinct real roots for x: ", nroots); for (i = 0; i ! = n roots; iH+) printf("%f ", roots [
i]); printf("\n"); /* * Sturm. C x x the functions to build and evaluate the Sturm ... 

 books.google.com 
 books.google.com We, therefore, simulate the amount of water available on a given day (AVWh), in
a given horizon (h) as a function of the number of roots (Nroots) in that horizon (
strictly, the total root length), the radius of influence of the roots (Rr), and the total
... 

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