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Given an original knot K, the knots produced by mutations together with K itself are called mutant knots. Mutant knots are often difficult to distinguish. For instance, ...

The only linear associative algebra in which the coordinates are real numbers and products vanish only if one factor is zero are the field of real numbers, the field of ...

The breaking up of self-intersecting polygons into simple polygons (illustrated above) is also called tessellation (Woo et al. 1999).

Lachlan's terms for a collection of n points.

A positive measure is a measure which is a function from the measurable sets of a measure space to the nonnegative real numbers. Sometimes, this is what is meant by measure, ...

A primary ideal is an ideal I such that if ab in I, then either a in I or b^m in I for some m>0. Prime ideals are always primary. A primary decomposition expresses any ideal ...

A ring for which the product of any pair of ideals is zero only if one of the two ideals is zero. All simple rings are prime.

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

To compute an integral of the form int(dx)/(a+bx+cx^2), (1) complete the square in the denominator to obtain int(dx)/(a+bx+cx^2)=1/cint(dx)/((x+b/(2c))^2+(a/c-(b^2)/(4c^2))). ...

The inverse curve of a right strophoid with parametric equations x = (1-t^2)/(t^2+1) (1) y = (t(t^2-1))/(t^2+1) (2) for an inversion circle with radius 1 and center (1,0) is ...