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PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series , algebraic numbers, and transcendental functions . [ 3 ]
Macaulay2 is built around fast implementations of algorithms useful for computation in commutative algebra and algebraic geometry. This core functionality includes arithmetic on rings, modules, and matrices, as well as algorithms for Gröbner bases, free resolutions, Hilbert series, determinants and Pfaffians, factoring, and similar.
Ultra Fractal – proprietary fractal generator for Windows and Mac OS X; Wolfram Mathematica – can be used specifically to create fractal images; XaoS – cross platform open source fractal zooming program; Most of the above programs make two-dimensional fractals, with a few creating three-dimensional fractal objects, such as mandelbulbs and ...
This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether. [36] Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: [14] group theory; field theory
Worksheets, online bulletin boards, and threaded discussions are examples of tools for e-tivities. An e-tivity may be an effective learning tool if it has an illustrative title, a stimulus or challenge, involves invitations to learners to post messages, is carefully timed, has postings to which others can add, and summaries, critiques or ...
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
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