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The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
The resulting algorithm for solving Pell's equation is more efficient than the continued fraction method, though it still takes more than polynomial time. Under the assumption of the generalized Riemann hypothesis , it can be shown to take time exp O ( log N ⋅ log log N ) , {\displaystyle \exp O\left({\sqrt {\log N\cdot \log ...
God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, [1] but which can also be applied to other combinatorial puzzles and mathematical games. [2] It refers to any algorithm which produces a solution having the fewest possible moves (i.e., the solver should not require any more than this number).
The fx-82ES introduced by Casio in 2004 was the first calculator to incorporate the Natural Textbook Display (or Natural Display) system. It allowed the display of expressions of fractions, exponents, logarithms, powers and square roots etc. as they are written in a standard textbook.
The user may estimate the location of the decimal point in the result by mentally interpolating between labeled graduations. Scientific notation is used to track the decimal point for more precise calculations. Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule.
The primitive unit cell for the body-centered cubic crystal structure contains several fractions taken from nine atoms (if the particles in the crystal are atoms): one on each corner of the cube and one atom in the center. Because the volume of each of the eight corner atoms is shared between eight adjacent cells, each BCC cell contains the ...
If this infinite continued fraction converges at all, it must converge to one of the roots of the monic polynomial x 2 + bx + c = 0. Unfortunately, this particular continued fraction does not converge to a finite number in every case. We can easily see that this is so by considering the quadratic formula and a monic polynomial with real ...
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.