multiplication of points

USAGE SUMMARY

The phrase "multiplication of points" is correct and usable in written English.
It can be used in contexts related to mathematics, geometry, or discussions involving the increase or replication of specific items or concepts. Example: "In this geometry lesson, we will explore the multiplication of points on a graph to understand how they interact with each other."

✓ Grammatically correct

Science

Computers & Electrical Engineering

City, Territory and Architecture

Human-verified examples from authoritative sources

Exact Expressions

5 human-written examples

All elliptic curve cryptographic schemes are based on scalar multiplication of points, and hence its faster computation signifies faster operation.

Computers & Electrical Engineering

It proceeds in two ways: the multiplication of points of concentration and the increase in size of individual concentrations".

City, Territory and Architecture

In this paper, we define addition and multiplication of points on the line O U = [ 0, 1, 0 ] geometrically, also we give the algebraic correspondences of them.

Journal of Inequalities and Applications

In this paper, our aim is to construct a relation between algebraic and geometric definitions of addition and multiplication of points in projective Klingenberg planes which seem to be a generalization of ordinary projective planes.

Journal of Inequalities and Applications

A + B = B + A and A + Z = Z + A ; A + O = A and O + Z = Z ; A + Y ∼ A ; A ⋅ B ≠ B ⋅ A ; O ⋅ A = A ⋅ O = O ; 1 ⋅ A = A = A ⋅ 1 and 1 ⋅ Z = Z = Z ⋅ 1 ; A ⋅ Y ∼ Y and Y ⋅ A ∼ Y. Now we give a theorem which interprets the relation between the geometric addition and multiplication of points and the collineations S a, L a which are given in last section.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

55 human-written examples

Calculation of the cumulative index characterizing the intensity of contacts as a sum of multiplications of points to the number of the firms indicates that Moscow and Saint-Petersburg leads with large advantage from others 277 and 195.

Triple Helix

In this paper, we determine the addition and multiplication of the points on the line [ 0, 1, 0 ] of P K 2 ( Q as the image of some collineations of the plane P K 2 ( Q.

Journal of Inequalities and Applications

A natural way to represent multidimensional data is using quaternions, a four-dimensional associative normed division algebra over the real numbers that allows for the multiplication and division of points in three-dimensional space.

Information Sciences

To do this, we give the collineations S a and L a. Later we show that the addition and multiplication of the nonneighbor points on the line [ 0, 1, 0 ] can be obtained as the images under that S a and L a. MSC 51C05, 51J10, 12E15.

Journal of Inequalities and Applications

For W-OFDM, the complexity of point-to-point multiplication of CP-OFDM signal and windowing at the transmitter and receiver is 2Lβ tx and 2Lβ rx, respectively, which are relatively small.

EURASIP Journal on Wireless Communications and Networking

This method has the advantages of reducing the order of the ordinary transfer equation systems and minimizing the propagation of round-off errors occurring in recursive multiplication of transfer and point matrices.

Journal of Sound and Vibration

Expert writing Tips

Best practice

When using the phrase "multiplication of points" in technical writing, ensure that the context clearly defines what constitutes a 'point' to avoid ambiguity. For example, in urban planning, 'points' might refer to population concentration, while in cryptography, it could refer to scalar multiplication on elliptic curves.

Common error

Avoid using "multiplication of points" in contexts where a simpler term like "increase" or "growth" would suffice. The phrase is more appropriate when describing a complex or technical process involving specific points and their interactions.

Linguistic Context

The phrase "multiplication of points" primarily functions as a noun phrase, typically used to describe a process or result involving an increase or transformation of points in a specific context. As evidenced by Ludwig, this often involves mathematical or geometrical concepts.

Expression frequency: Rare

Frequent in

Science

75%

Computers & Electrical Engineering

12%

Academia

12%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

The phrase "multiplication of points" is a technical term primarily used in scientific and mathematical contexts, particularly in fields like cryptography, geometry, and urban planning. While grammatically correct, its usage is relatively rare and specialized. As Ludwig AI confirms, the phrase describes the increase, replication, or transformation of points within a specific system or framework. If you’re aiming for broader understanding, simpler alternatives such as “increase in points” or “growth of points” may be more suitable. However, in technical or mathematical writing, "multiplication of points" precisely conveys specific operations or phenomena related to points within defined structures, so it should be used.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

point multiplication

Reverses the order of the words, creating a compound noun.

increase in number of points

Uses a more descriptive phrase to convey the growth in the amount of points.

growth of points

Replaces "multiplication" with "growth", focusing on the increase in quantity.

proliferation of points

Substitutes "multiplication" with "proliferation", suggesting a rapid increase.

expansion of points

Uses "expansion" to indicate an increase in the number of points.

replication of points

Replaces multiplication with replication, highlighting the duplication aspect.

augmentation of points

Uses "augmentation" to suggest an increase or enhancement of the points.

accumulation of points

Suggests a gradual increase or gathering of points over time.

generation of points

Focuses on the creation or production of new points.

amplification of points

Indicates an increase in the effect or significance of the points.

FAQs

How is "multiplication of points" used in mathematics?

In mathematics, "multiplication of points" often refers to operations performed on points within specific mathematical structures, such as elliptic curves in cryptography, where scalar multiplication is a fundamental operation. It's not simply about increasing the quantity of points, but rather performing a mathematical operation on those points.

What fields commonly use the term "multiplication of points"?

The term "multiplication of points" is most frequently used in fields like cryptography (particularly elliptic curve cryptography), geometry, and urban planning. The meaning varies by field, so context is crucial.

What's a simpler alternative to "multiplication of points" in non-technical contexts?

In less technical contexts, you could use phrases like "increase in points", "growth of points", or simply "more points" depending on the specific meaning you want to convey. See also: "increase in number of points".

Is "multiplication of points" the same as multiplying coordinates?

While related, "multiplication of points" is often a higher-level concept than simply multiplying coordinates. In elliptic curve cryptography, for example, point multiplication involves a series of complex operations, not just scalar multiplication of x and y coordinates.