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The standard form of the equation of a central conic section is obtained when the conic section is translated and rotated so that its center lies at the center of the coordinate system and its axes coincide with the coordinate axes. This is equivalent to saying that the coordinate system's center is moved and the coordinate axes are rotated to ...
Therefore, in computer algebra, normal form is a weaker notion: A normal form is a representation such that zero is uniquely represented. This allows testing for equality by putting the difference of two objects in normal form. Canonical form can also mean a differential form that is defined in a natural (canonical) way.
It was originally known as "HECKE and Manin". After a short while it was renamed SAGE, which stands for ‘’Software of Algebra and Geometry Experimentation’’. Sage 0.1 was released in 2005 and almost a year later Sage 1.0 was released. It already consisted of Pari, GAP, Singular and Maxima with an interface that rivals that of Mathematica.
The standard method for computing a parametric form of the solution is to use Gaussian elimination for computing a reduced row echelon form of the augmented matrix. Then the unknowns that can be used as parameters are the ones that correspond to columns not containing any leading entry (that is the left most non zero entry in a row or the ...
The quadrature of the circle does not have a solid construction. A regular n-gon has a solid construction if and only if n=2 a 3 b m where a and b are some non-negative integers and m is a product of zero or more distinct Pierpont primes (primes of the form 2 r 3 s +1).
In linear algebra, the Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z.Just as reduced echelon form can be used to solve problems about the solution to the linear system Ax=b where x is in R n, the Hermite normal form can solve problems about the solution to the linear system Ax=b where this time x is restricted to have integer coordinates only.
is twice the number of Jordan blocks of size k 1 plus the number of Jordan blocks of size k 1 − 1. The general case is similar. This can be used to show the uniqueness of the Jordan form. Let J 1 and J 2 be two Jordan normal forms of A. Then J 1 and J 2 are similar and have the same spectrum, including algebraic multiplicities of the ...
For n = 6, it has an outer automorphism of order 2: Out(S 6) = C 2, and the automorphism group is a semidirect product Aut(S 6) = S 6 ⋊ C 2. In fact, for any set X of cardinality other than 6, every automorphism of the symmetric group on X is inner, a result first due to ( Schreier & Ulam 1936 ) according to ( Dixon & Mortimer 1996 , p. 259).