Absolute polynomial factorization in two variables and the knapsack
... dition attached to each factor Pk of P . In fact this condition is, with a genericity hypothesis, sufficient as stated in the: Theorem 1.3 (Galligo-Rupprecht’s theorem). Let P be an irreducible polynomial in Q[X, Y ], monic in Y of total degree n. Consider Q(x, y, λ) = P (x + λy, y). Then for P almo ...
... dition attached to each factor Pk of P . In fact this condition is, with a genericity hypothesis, sufficient as stated in the: Theorem 1.3 (Galligo-Rupprecht’s theorem). Let P be an irreducible polynomial in Q[X, Y ], monic in Y of total degree n. Consider Q(x, y, λ) = P (x + λy, y). Then for P almo ...
Pascal
... Fibonacci’s Question A pair of newly born rabbits, male and female, were placed in a hutch. In two months, these rabbits began their breeding cycle and produced one pair of rabbits, one male and one female. The original rabbits and their offspring continued to breed in this manner, that is the firs ...
... Fibonacci’s Question A pair of newly born rabbits, male and female, were placed in a hutch. In two months, these rabbits began their breeding cycle and produced one pair of rabbits, one male and one female. The original rabbits and their offspring continued to breed in this manner, that is the firs ...
Least Common Denominator
... Like and Unlike Fractions Fractions that have the same or common denominator are called like fractions. Fractions that have different denominators are called unlike fractions. Like Fractions ...
... Like and Unlike Fractions Fractions that have the same or common denominator are called like fractions. Fractions that have different denominators are called unlike fractions. Like Fractions ...
Mixed numbers
... Merry have breakfast at different times. Each one takes a quarter of the porridge in the pan, thinking that the other three have not yet eaten. What fraction of the porridge is left after all four hobbits had their breakfast? ...
... Merry have breakfast at different times. Each one takes a quarter of the porridge in the pan, thinking that the other three have not yet eaten. What fraction of the porridge is left after all four hobbits had their breakfast? ...
9.2 Multiplication Properties of Radicals y x
... calls for a positive (non√ is the fact that negative√if you want to√include the case 0) square root. In both of the errors above, namely x2 = ±x and x2 = x, the left-hand side is calling for a nonnegative response, but nothing has been done to insure that the right-hand side is also nonnegative. Doe ...
... calls for a positive (non√ is the fact that negative√if you want to√include the case 0) square root. In both of the errors above, namely x2 = ±x and x2 = x, the left-hand side is calling for a nonnegative response, but nothing has been done to insure that the right-hand side is also nonnegative. Doe ...
MaWi 1 Skript
... It is obvious: Even for the most simple examples, there is no end of questions you can ask concerning possible arrangements of your elements. Some answers to possible questions are rather obvious, some certainly are not. For some, you might feel that given enough time you would eventually find the a ...
... It is obvious: Even for the most simple examples, there is no end of questions you can ask concerning possible arrangements of your elements. Some answers to possible questions are rather obvious, some certainly are not. For some, you might feel that given enough time you would eventually find the a ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.