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331
The sum and product of finite sequences of real numbers.
- Formalized Mathematics,
, 1990
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Many sorted algebras
- Journal of Formalized Mathematics
, 1994
"... Summary. The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between ..."
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Cited by 123 (14 self)
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Summary. The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between (1 sorted) universal algebras [8] and many sorted algebras with one sort only is described by introducing two functors mapping one into the other. The construction is done this way that the composition of both functors is the identity on universal algebras.
Combining of Circuits
, 2002
"... this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S ..."
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Cited by 93 (25 self)
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this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S
Factorial and Newton coefficients
- Journal of Formalized Mathematics
, 1990
"... Summary. We define the following functions: exponential function (for natural exponent), factorial function and Newton coefficients. We prove some basic properties of notions introduced. There is also a proof of binominal formula. We prove also that ∑ n �n � k=0 k = 2n. ..."
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Cited by 85 (0 self)
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Summary. We define the following functions: exponential function (for natural exponent), factorial function and Newton coefficients. We prove some basic properties of notions introduced. There is also a proof of binominal formula. We prove also that ∑ n �n � k=0 k = 2n.
The Euclidean Space
, 1991
"... this paper. In this paper k, n are natural numbers and r is a real number. Let us consider n. The functor R ..."
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Cited by 83 (0 self)
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this paper. In this paper k, n are natural numbers and r is a real number. Let us consider n. The functor R
Binary operations applied to finite sequences.
- Formalized Mathematics,
, 1990
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Cartesian product of functions
- Journal of Formalized Mathematics
, 1991
"... Summary. A supplement of [3] and [2], i.e. some useful and explanatory properties of the product and also the curried and uncurried functions are shown. Besides, the functions yielding functions are considered: two different products and other operation of such functions are introduced. Finally, two ..."
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Cited by 64 (22 self)
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Summary. A supplement of [3] and [2], i.e. some useful and explanatory properties of the product and also the curried and uncurried functions are shown. Besides, the functions yielding functions are considered: two different products and other operation of such functions are introduced. Finally, two facts are presented: quasi-distributivity of the power of the set to other one w.r.t. the union (X � x f (x) ≈ ∏x X f (x) ) and quasi-distributivity of the product w.r.t. the raising to the power (∏x f (x) X ≈ (∏x f (x)) X).
