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Another polynomial viewpoint is exploited by the Winograd algorithm, which factorizes into cyclotomic polynomials — these often have coefficients of 1, 0, or − 1, and therefore require few ( if any ) multiplications, so Winograd can be used to obtain minimal-multiplication FFTs and is often used to find efficient algorithms for small factors.
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Another and polynomial
Another method based on the Cayley – Hamilton theorem finds an identity using the matrices ' characteristic polynomial, producing a more effective equation for A < sup > k </ sup > in which a scalar is raised to the required power, rather than an entire matrix.
Another method with this style is the Dandelin – Gräffe method ( actually due to Lobachevsky ) which factors the polynomial.
Another characterization: A matrix or linear map is diagonalizable over the field F if and only if its minimal polynomial is a product of distinct linear factors over F. ( Put in another way, a matrix is diagonalizable if and only if all of its elementary divisors are linear.
Another example is an implicit function given by x − C ( y ) = 0 where C is a cubic polynomial having a " hump " in its graph.
Another example is that the maximum height ( maximum absolute value of coefficients ) of all the factors of x < sup > n </ sup > − 1 appears to be the same as height of nth cyclotomic polynomial.
Another paper by Hartmanis from 1977, with Leonard Berman, introduced the still-unsolved Berman – Hartmanis conjecture that all NP-complete languages are polynomial time isomorphic.
Another example: P being as above, a resolvent R for a group G is a polynomial whose coefficients are polynomials in the coefficients of p, which provides some information on the Galois group of P. More precisely, if R is separable and has a rational root then the Galois group of P is contained in G. For example, if D is the discriminant of P then is a resolvent for the alternating group.
Another possibility to transform a polynomial so as to satisfy the criterion, which may be combined with applying a shift, is reversing the order of its coefficients, provided its constant term is nonzero ( without which it would be divisible by x anyway ).
Another proof is that its Alexander polynomial does not satisfy the Fox-Milnor condition.
Another way is to find two factors of the polynomial and divide the original polynimial by them.
Another important basic class of examples are representations of polynomial algebras, the free commutative algebras – these form a central object of study in commutative algebra and its geometric counterpart, algebraic geometry.
Another polynomial associated with A is the Whitney-number polynomial w < sub > A </ sub >( x, y ), defined by
Another special case of an abelian integral is a hyperelliptic integral, where, in the formula above, is a polynomial of degree greater than 4.
Another well known example is the polynomial, whose roots are the golden ratio and its conjugate, showing that it is reducible over the field, although it is irreducible over the non-UFD which has as field of fractions.
Another and viewpoint
Another example is a strong operationalist viewpoint, which contends that reliance on operational definitions, as purported by the DSM, necessitates that intuitive concepts such as depression be replaced by specific measurable concepts before they are scientifically meaningful.
Another sports analyst wrote Limbaugh's viewpoint was shared by " many football fans and analysts " and " it is ... absurd to say that the sports media haven't overrated Donovan McNabb because he's black.
Another debate followed the appearance of The Bell Curve ( 1994 ), a book by Richard Herrnstein and Charles Murray, who argued in favor of the hereditarian viewpoint.
Another viewpoint on sex education, historically inspired by sexologists like Wilhelm Reich and psychologists like Sigmund Freud and James W. Prescott, holds that what is at stake in sex education is control over the body and liberation from social control.
Another viewpoint, most notably held by J. R. R.
Another traditional criticism of Orosius ’ s work relates to this dichotomy of pessimism / optimism, which often causes him to offer a narrative that in many ways lacks an objective viewpoint.
Another viewpoint on Richard's paradox relates to mathematical predicativism.
Another aspect of Trevor-Roper ’ s general outlook on history and on scholarly research that has inspired controversy is his viewpoint on historical experiences of pre-literate societies.
Another western historian, Rafe de Crespigny, is skeptical of the traditional viewpoint and questions Yuan Shao's supposed advantage over Cao Cao.
Another viewpoint is that while Mountbatten may have been too hasty he had no real options left and achieved the best he could under difficult circumstances.
Another typical view-looking north from the same viewpoint
Another definition-possibly reflecting a traditionalist's viewpoint with a certain moral dimension-refers to " the good humans ", or good people, meaning those who are on the right road / path given to them by the Creator or Gichi-Manidoo ( Great Spirit ).
Another 18th century writer, Richard Gough, concentrated on a contemporary viewpoint, noting that " Cornwall seems to be another Kingdom ", in his " Camden's Britannia ", 2nd ed.
Another viewpoint is that the gem does portray Augustus as a god, but the gem was cut specifically for a close friend or relative perhaps in Rome who would have been the only one to know of it.
Another similar technique is Z-culling, also known as occlusion culling, which attempts to skip the drawing of polygons which are covered from the viewpoint by other visible polygons.
Another popular viewpoint along the Seward Highway is Windy Corner at Mile 106.
Another and is
Another element to concern the choreographer is that of the visual devices of the theatre.
Another, more interesting explanation, is hinted at by Watson when he observes on several occasions that Holmes would have made a magnificent criminal.
Another beautiful building is the Propylaea, the entrance gate of the Acropolis.
Another recent achievement was the successful development of a method for the complete combustion in a bomb calorimeter of a metal in fluorine when the product is relatively non-volatile.
Another effect discovered is the large coefficient of thermal diffusion tending to separate nitrogen from the oxygen when temperature differences straddling the nitrogen dissociation region are present.
Another example is the recent cancellation of the F-108, a long-range interceptor with a speed three times as great as the speed of sound, which was designed for use against manned bombers in the period of the mid-1960's.
Another growth factor is increased consumer demand for better quality and larger quantities of fabrics that go with a rising standard of living.
Another thing that must be taken into consideration is the volume of the area between the top of the piston and the top of the cylinder block when the piston is in top dead center position.
Another boy's model is the
Another scenic spot in Tennessee is Chattanooga where the Rock City Gardens are not to be missed.
Another spot with an image-provoking name is the Black Hills where you can visit the old frontier mining town of Deadwood.
Another method of assuring a clean hole is to first drill a small pilot hole all the way through, then drill half way with the dimensional bit, turn the piece over, and finish from the other side.
Another reason gymnastic study is valuable is that it can be started very early in life.
Another factor that may hold hope is for parallel recognition is, as one man says it: `` that the fad for educating top people along managerial lines is yielding to the technically trained approach ''.
Another stock vaudeville gag ran: `` Mother is home sick in bed with the doctor ''.
Another specimen of such double-entendre is illustrated by a woman in a department store.
Another anode holder used in the experiments is shown in figure 3.
Another important source of evidence only recently receiving much attention is the analysis of atmospheric dust for a meteoritic component.
Another approach is to estimate from the rate of growth and the smallest size at maturity.
Another marked difference is noted here.
Another great danger is that the emerging middle class will feel itself increasingly alienated from the political leaders who still justify their dominance by reference to the struggle for independence or the early phase of nationalism.
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