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Algebraic sum

Sum Sum, n. [OE. summe, somme, OF. sume, some, F. somme, L. summa, fr. summus highest, a superlative from sub under. See Sub-, and cf. Supreme.] 1. The aggregate of two or more numbers, magnitudes, quantities, or particulars; the amount or whole of any number of individuals or particulars added together; as, the sum of 5 and 7 is 12. Take ye the sum of all the congregation. --Num. i. 2. Note: Sum is now commonly applied to an aggregate of numbers, and number to an aggregate of persons or things. 2. A quantity of money or currency; any amount, indefinitely; as, a sum of money; a small sum, or a large sum. ``The sum of forty pound.' --Chaucer. With a great sum obtained I this freedom. --Acts xxii. 28. 3. The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections. 4. Height; completion; utmost degree. Thus have I told thee all my state, and brought My story to the sum of earthly bliss. --Milton. 5. (Arith.) A problem to be solved, or an example to be wrought out. --Macaulay. A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole. --Gladstone. A large sheet of paper . . . covered with long sums. --Dickens. Algebraic sum, as distinguished from arithmetical sum, the aggregate of two or more numbers or quantities taken with regard to their signs, as + or -, according to the rules of addition in algebra; thus, the algebraic sum of -2, 8, and -1 is 5. In sum, in short; in brief. [Obs.] ``In sum, the gospel . . . prescribes every virtue to our conduct, and forbids every sin.' --Rogers.

Sum Sum, n. [OE. summe, somme, OF. sume, some, F. somme, L. summa, fr. summus highest, a superlative from sub under. See Sub-, and cf. Supreme.] 1. The aggregate of two or more numbers, magnitudes, quantities, or particulars; the amount or whole of any number of individuals or particulars added together; as, the sum of 5 and 7 is 12. Take ye the sum of all the congregation. --Num. i. 2. Note: Sum is now commonly applied to an aggregate of numbers, and number to an aggregate of persons or things. 2. A quantity of money or currency; any amount, indefinitely; as, a sum of money; a small sum, or a large sum. ``The sum of forty pound.' --Chaucer. With a great sum obtained I this freedom. --Acts xxii. 28. 3. The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections. 4. Height; completion; utmost degree. Thus have I told thee all my state, and brought My story to the sum of earthly bliss. --Milton. 5. (Arith.) A problem to be solved, or an example to be wrought out. --Macaulay. A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole. --Gladstone. A large sheet of paper . . . covered with long sums. --Dickens. Algebraic sum, as distinguished from arithmetical sum, the aggregate of two or more numbers or quantities taken with regard to their signs, as + or -, according to the rules of addition in algebra; thus, the algebraic sum of -2, 8, and -1 is 5. In sum, in short; in brief. [Obs.] ``In sum, the gospel . . . prescribes every virtue to our conduct, and forbids every sin.' --Rogers.

- addends or summands; the result is their sum or total. Besides numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials...

- used to form the direct sum of any two algebraic structures, such as rings, modules, and vector spaces. We can also form direct sums with any finite number...

- In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest...

- Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word...

- theory, an algebraic data type is a kind of composite type, i.e., a type formed by combining other types. Two common cl****es of algebraic types are product...

- In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are 3 x...

- theory Direct sum, a combination of algebraic objects Direct sum of groups Direct sum of modules Direct sum of permutations Direct sum of topological...

- resultant of two concurrent forces about any point is equal to the algebraic sum of the torques of its components about the same point. In other words...

- is algebraic if and only if both a and b are algebraic. The sum, difference, product and quotient (if the denominator is nonzero) of two algebraic numbers...

- bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where...

- used to form the direct sum of any two algebraic structures, such as rings, modules, and vector spaces. We can also form direct sums with any finite number...

- In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest...

- Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word...

- theory, an algebraic data type is a kind of composite type, i.e., a type formed by combining other types. Two common cl****es of algebraic types are product...

- In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are 3 x...

- theory Direct sum, a combination of algebraic objects Direct sum of groups Direct sum of modules Direct sum of permutations Direct sum of topological...

- resultant of two concurrent forces about any point is equal to the algebraic sum of the torques of its components about the same point. In other words...

- is algebraic if and only if both a and b are algebraic. The sum, difference, product and quotient (if the denominator is nonzero) of two algebraic numbers...

- bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where...

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