Download Shareware and Freeware Software for Windows, Linux, Macintosh, PDA

line Home  |  About Us  |  Link To Us  |  FAQ  |  Contact

Serving Software Downloads in 976 Categories, Downloaded 31.591.049 Times

GCD of Polynomials and Polynomials raised to some Power including Fractional Power 1.0

  Date Added: July 24, 2013  |  Visits: 164

GCD of Polynomials and Polynomials raised to some Power including Fractional Power

Report Broken Link
Printer Friendly Version

Product Homepage
Download (18 downloads)

15th July, 2005 : Poly_POWER.m is now corrected !So, for most reasonable cases of Multiple Roots including Multiple Real Roots, this Programme should now work.For eg, Poly_POWER works successfully for :{ x^6 + (-12+18j)*x^5 + (-75-180j)*x^4 + (920+180j)*x^3 + (-1785+1800j)*x^2 + (-732-3582j )*x + (2035+828j) } ^ 0.5The answer is "approx":{ ( x^3 + (-6 + 9j) * x^2 + (-15 - 36j) * x + (46 + 9j) }and for Liouville's Constant based Polys, like :( { x^6 - 75*x^3 - 190*x + 21 } ^ 3 } ^ 0.3333 ********************Functional Description of Poly_GCD :------------------------------------If we need to verify the fact that a Polynomial has multiple roots iff (if and only if) it has a common factor with it's derivative, we need two things :a) A function to compute the GCD of 2 Polynomials. Since I could not find a Standard Matlab function for this, I created this function : Poly_GCD.m :GCD = Poly_GCD ( sx_poly, rx_poly )For eg, if :sx_poly = x^9 - 3x^8 + 0x^7 + 2x^6 + 6x^5 + 0x^4 - 4x^3 - 6x^2 - 3x ? 1and rx_poly = 9x^8 - 24x^7 + 0x^6 + 12x^5 + 30x^4 + 0x^3 - 12x^2 - 12x ? 3,then their GCD = x^6 - 2x^5 - x^4 + 3x^2 + 2x + 1b) A function which can raise a Polynomial to some power in order to simulate an overall polynomial with multiple roots. Since I could not find a Standard Matlab function for this, I created Poly_POWER.m :P = Poly_POWER ( poly, n )In addition to computing the GCD of the 2 input Polynomials : sx_Poly and rx_Poly, Poly_GCD.m and Poly_GCD_Main.m also find suitable polynomials :Nx & nx and cx & dx such that :check_GCD_Orig = Nx * sx_Poly + nx * rx_Polycheck_GCD_Used = cx * sx_Poly_Used + dx * rx_Poly_Used (Internally used vars)While finding HCF of 2 Polynomials, as the degrees of the polynomials increase, the accumulated FP errors increase, and can only be "salvaged" to some extent. The trick lies in being able to devise a way to detect the correct Zero limit on the Remainder, and thereby, stop after the correct number of HCF divisions. This requires lots of experiments to find what limits to apply for the definition of 0 (zero) ; this has been done with some complex empirical logics obtained by trial and error.Convergence also depends upon whether we convert the input Polys to monic, or the intermediate computed Poly also to monic, or we do not convert at all. These 3 combinations create a whole lot of extra logics, almost 30 % of the development effort ! We choose the best combination.When compared to my very early submission of this zip file, the earlier Poly_GCD.m is now renamed as Poly_GCD_Main.m, and Poly_GCD.m is now a "top level" function.I think that all these functions : Poly_GCD, Poly_POWER, CMPLX_GCD, Ch_Rem_Thr_Poly.m, Ch_Rem_Thr_Int.m, Gen_Primes_Eq_2_Sqs etc are essential as commonly required functions, and can be placed in the dir : ...matlabspecfunShould generally work for R14, R13 and R12.

Requirements: No special requirements
Platforms: Matlab
Keyword: Apply Complex Definition Depends Divisions Empirical Experiments Limits Logics Requires
Users rating: 0/10

License: Shareware Size: 92.16 KB
Photo & Video  -  SmartEditor
Developed by Ahmad ALMughrabi Smart Editor V.2.0: ------------------------------------------------------------------------- - Is an image Processing Program that helps the User to apply: + Complex Operation. +Simple operation...
1024 KB  
Video Editors  -  FastCut RT 3.0.6
FastCut offers video editing in real-time. Experience outstanding performance. FastCut uses the power of the GPU (graphic processing unit) for accelerated graphical calculations.FastCut is a full-featured video editor. It brings 3D motion &...
Business  -  pptXTREME Effects library for PowerPoint 1.5
Never re-create custom animations in PowerPoint again. Save complex animation settings, then reuse them at any time with the click of a button!! Do you like to spend time on your custom animations, but find it's not worth it because you...
3.02 MB  
Libraries  -  HTTP::Browscap 0.02
HTTP::Browscap is a Perl module that can parse and search browscap.ini files. SYNOPSIS use HTTP::Browscap; my $capable = browscap(); if( $capable->{wap} ) { output_WAP(); } if( $capable->{css} > 1 ) { # Browser can handle CSS2 } #...
9.22 KB  
Utilities  -  SPList Manager for SharePoint 2007 1.2
SPList Manager for SharePoint 2007 (SPListM) is a powerful application to import & manage metadata for list items in SharePoint. SPListM can import / update / delete list items (including folders and file attachments) in SharePoint lists. SPListM...
3.14 MB  
Utilities  -  Document Import Kit for SharePoint 2007 3.9
Document Import Kit for SharePoint 2007 (DocKIT) is a powerful, easy-to-use tool to import documents from file systems & network shares into Microsoft Office SharePoint Server 2007 (MOSS 2007) and Microsoft Windows SharePoint Services v3.0 (WSS...
5.58 MB  
Science  -  PhyloPattern 1.05
PhyloPattern is a Java/Prolog API, helpful to simulate human reading of phylogenetic trees. Bioinformatician can: annotate trees, apply complex patterns to a tree to search specific architectures or extract information, compare trees with...
987.45 KB  
Education  -  Buoyancy 1.05
When will objects float and when will they sink? Learn how buoyancy works with blocks. Arrows show the applied forces, and you can modify the properties of the blocks and the fluid. Sample Learning Goals: * Predict whether...
1.04 MB  
Text Role Playing Games  -  3D SurfBlocks 1.0
3D SurfBlocks is a puzzle type game with playing field spread upon a 3D surface. It will give you opportunity to apply both your intelligence and reaction speed. The game requires groups of three or more adjacent blocks to be cleared making the...
4.25 MB  
Modules  -  Filefield download tracker 6.x-1.0-beta3
Description:The filefield_tracker module allows you to track the download of private filefields.This module depends on the Filefield module and requires the private download method to be set.Features: * Provides new CCK field formatter that lists...
10 KB  
Scripts  -  Freelancer Script 5.05
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Post projects. Featured projects. Private projects. Sealed projects. Edit/delete projects. Select freelancers....
5.49 MB  
Scripts  -  B2B Script 4.20
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Sign-up Account (Registration of account). Lead generation tools (for the sellers). Email verification to...
5.49 MB  
Scripts  -  B2C Script 5.06
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). The script comes with totally editable site colors, icons and graphics Multilevel categories allows extensive browsing Admin can change Category ordering or...
5.49 MB  
Scripts  -  Social Networking Script 2.86
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Registration with name, email, password, date of birth etc. User can add multiple school, college, university with start...
5.49 MB  
Scripts  -  Business Networking Script 8.04
Main Features: 100% Secured. Email Support (3 Years). FREE Updates (3 Years). Ajax based interface. Profile creation. Different types of profile. Profile for jobseekers, employers and employed...
5.49 MB  
Development Tools  -  VMP Viewer 1.0
This is a very rudimentary tool to visualize the VMP files generated by BrainVoyager. Useful to share files with people who do not have BV.
10 KB  
Development Tools  -  Sending reports and timestamped file by emailing 1.0
main executing reference usage:[1] usage_send_mail.mIllustrates email sending with multiple separate files or single timestamped tar file. Attachment failure is properly handled, with continuation of report emailing without the attachment.[2]...
768 KB  
Development Tools  -  IrisMVC 2.0 rc1
IrisMVC is an OOP PHP framework that developers can use as a strong and secure foundation to build on various web applications following the Model-View-Controller (MVC) pattern. It provides the basic functionality developers need, without...
51.2 KB  
Development Tools  -  7-Zip for Script 4.42
7-Zip is a file archiver with a high compression ratio.Features:- High compression ratio in new 7z format with LZMA compression- Supported formats:- Packing / unpacking: 7z, ZIP, GZIP, BZIP2 and TAR- Unpacking only: RAR, CAB, ISO, ARJ, LZH, CHM,...
624.64 KB  
Development Tools  -  Barnardextest 1.0
This file, as the Fisher's exact test, performs the exact probability test for a table of frequency data cross-classified according to two categorical variables, each of which has two levels or subcategories (2x2). It is a non-parametric...
10 KB