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NC
View this contact
Paul McCarthy
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NC
View this contact
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Math & Computer Science stuff – Math & Computer Science stuff | paul-mccarthy.us Reviews
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Math & Computer Science stuff
paul-mccarthy.us
Tonelli Shanks
http://paul-mccarthy.us/Algebra/Tonelli-Shanks.htm
This page links to six demonstrations of the Tonelli-Shanks modular square root algorithm applied to prime factorizations over Z[i], Z[w], and Z[2i]. First, this is an excerpt from Henri Cohen's A Course in Computational Algebraic Number Theory. Springer-Verlag, 1993, that explains the Tonelli-Shanks algorithm and the Algorithm of Cornacchia:.
Norm Problems
http://paul-mccarthy.us/Misc/Norm_problems.htm
Having some trouble finding representations for given norms with the integers in the complex quadratic fields in 1 (mod 4). This started to show itself in. The problem is now evident That is, the equation. Has no solution in integers, yet the equation. Does have solutions in integers I believe the problem may be that. Covers all the points in the maximal integral domain of. I’m not sure yet. First of all, one needs to see the relationship between. So, in general, we want to find solutions to this equation.
Simple Continued Fractions
http://paul-mccarthy.us/Cfrac/index.htm
Trivial Redundancy in Simple Continued Fractions. Transforming between N- and Z-fractions. Simple Periodic Continued Fractions. Transformations of Simple Periodic Continued Fractions. Convergents of Continued Fractions. Do all Continued Fractions converge? Flowchart of Simple Continued Fraction Algorithm. Interval Analysis of the Continued Fraction dissection of the continuum. Mobius Transformations and their relation to Continued Fractions. Vector and Matrix representation of Continued Fractions.
Infinite carry chains
http://paul-mccarthy.us/Algebra/neg_radix/Infinite%20carry%20chains.htm
You may have noticed that repetends can have carries across repetend boundaries I’ve developed methods for dealing with this, which is the subject of this paper. First, a few quick notes on terminology. I’ve been using the Euler Phi function, , inconsistently and inappropriately. As I’ve now recalled, . Although not appropriate, until I can find, or someone can show me, better terminology, for this paper I’m going to redefine . The standard Phi function would then be . This is an interesting case.
Inner Product proof of the Law of Cosines
http://paul-mccarthy.us/Misc/Inner_Product_proof_L_of_Cos.htm
This paper is adapted from a post I made to the Math Message Board). You can easily see both the little dot inner product and the outer product here. If we take the two complex numbers depicted in the graph above,. And multiply on the left by. We get the mapping of these two complex numbers to vectors I mentioned in my previous post. That is, the vectors representing the complex numbers are. From the two complex numbers here, their inner and outer product is:. Which can be easily seen from the graph above.
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Mot de passe :. J'ai oublié mon mot de passe. The beatles,the rock,and me. Mise à jour :. Abonne-toi à mon blog! Qui pourra jamais rivaliser avec les Beatles? Depuis leur premier tube Love Me Do en 1962 jusqu'à leur séparation de 1970, et aujourd'hui encore, les Fab Four ont pulvérisé tous les records. Lennon, Mc Cartney, Harrison et Ringo Starr sont à ce jour les musiciens les plus populaires de l'histoire de la musique. Ou poster avec :. Posté le samedi 15 septembre 2007 13:11. Love love me do. N'oubli...
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Math & Computer Science stuff – Math & Computer Science stuff
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Would you like to make this site your homepage? It's fast and easy. Yes, Please make this my home page! Don't show this to me again. Musician, Singer, Composer. June 18, 1942. Liverpool, England, U.K. Wife: Linda Eastman (dead '98); kids: James, Mary, Stella, Heather. 584 Broadway St. Suite 1201 New York City, NY 10012 USA. The History of Paul McCartney. Paul McCartney was born at 18th. Of June 1942 in Liverpool. He had a little brother, a father and a mother. But in spring '70 the Beatles disintegrated.
