LYCOS RETRIEVER 
Monoid
built 276 days ago
A Monoid is borne into central control, lying very still. Humans and Monoids gather round as Zentos relays their report. A strange disease-fever is spreading among the Monoids. Everyone looks to the Commander, but he too is looking very ill. He collapses, complaining that it is very hot in the control centre. The Doctor, Steven, and Dodo surround the Commander as Zentos and Mellium tend to him. The Commander has the same fever as the Monoids, and it was brought by the strangers.
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A Monoid is a concept that describes a simple kind of algebraic system. A monoid consists of a set of elements S, a binary operation, and an identity element. The C++ representation of a monoid consists of a function object that implements the binary operation, a set of objects that represent the elements of S, and an object that represents the identity element.
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In the first form, Monoid returns the monoid generated by the arguments gen1, gen2 ..., that is, the closure of these elements under multiplication and taking the 0-th power. In the second form, Monoid returns the monoid generated by the elements in the homogeneous list gens; a square matrix as only argument is treated as one generator, not as a list of generators. In the third form, Monoid returns the monoid generated by the elements in the homogeneous list gens, with identity id.
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In the central chamber, another Monoid signals to Deputy Commander Zentos. He in turn relays to the Commander that three intruders have been spotted. The Commander is more curious than upset, although Zentos reacts angrily. On a scanner screen, they see the Doctor, Steven, and Dodo as well as the blue box that must be their spaceship. They appear to be human, but that seems impossible. Zentos wants them arrested immediately.
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With the Commander suffering from the same fever that has killed a Monoid, Zentos demands that the strangers be made to suffer for the crime that they have committed. If the Guardians die now, it will have been pointless them leaving the Earth in the first place.
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Monoid of natural numbers (0,1,2,3,...) is generated by the arrow 1, since every positive integer is a finite sum of 1's. Number zero is a composition of zero generators, that is sum of zero 1's.
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Monoid