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Mathematical concept
modulo a prime p, there is an analogous theory to the classical theory of complex modular forms and the p-adic theory of modular forms. Modular forms
Modular_forms_modulo_p
Computation modulo a fixed integer
using modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. Modular arithmetic modulo m consists
Modular_arithmetic
Computational operation
same. Modulo (disambiguation) – many uses of the word modulo, all of which grew out of Carl F. Gauss' approach to modular arithmetic in 1801. Modulo (mathematics)
Modulo
Algorithm for fast modular multiplication
division and reduction modulo R are inexpensive, and the modulus is not useful for modular multiplication unless R > N. The Montgomery form of the residue class
Montgomery modular multiplication
Montgomery_modular_multiplication
Concept in modular arithmetic
calculation of modular multiplicative inverses. For a given positive integer m, two integers, a and b, are said to be congruent modulo m if m divides
Modular multiplicative inverse
Modular_multiplicative_inverse
Modular arithmetic concept
primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. In symbols, g is a primitive root modulo n if for every
Primitive_root_modulo_n
Word with multiple distinct meanings
cyclic shifts". Look up modulo in Wiktionary, the free dictionary. Essentially unique List of mathematical jargon Up to "Modular arithmetic". Encyclopedia
Modulo_(mathematics)
Exponentation in modular arithmetic
modulo m (for instance by using extended Euclidean algorithm). More precisely: c = be mod m = d−e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation
Modular_exponentiation
Orientation-preserving mapping class group of the torus
modular group has a trivial center, and thus the modular group is isomorphic to the quotient group of B3 modulo its center; equivalently, to the group of inner
Modular_group
Integer that is a perfect square modulo some integer
number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x such that
Quadratic_residue
Group of units of the ring of integers modulo n
of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements
Multiplicative group of integers modulo n
Multiplicative_group_of_integers_modulo_n
Special-purpose algorithm for factoring integers
preceding the factor, p − 1, is powersmooth; the essential observation is that, by working in the multiplicative group modulo a composite number N, we
Pollard's_p_−_1_algorithm
Algebraic variety
In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of
Modular_curve
Unsolved problem in mathematics
Boylan, Matthew (2005-01-01). "Coefficients of half-integral weight modular forms modulo ℓj". Mathematische Annalen. 331 (1): 219–239. doi:10.1007/s00208-004-0555-9
Newman's_conjecture
A prime p divides a^p–a for any integer a
states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In the notation of modular arithmetic, this
Fermat's_little_theorem
Number system extending the rational numbers
work can be interpreted as implicitly using p-adic numbers. Roughly speaking, modular arithmetic modulo a positive integer n consists of "approximating"
P-adic_number
Problem of inverting exponentiation in groups
cyclic group. A simple example is the group of integers modulo a prime number (such as 5) under modular multiplication of nonzero elements. For instance, take
Discrete_logarithm
Factorisation algorithm
the secret key are known and forms a base for Coppersmith's attack. Coppersmith's approach is a reduction of solving modular polynomial equations to solving
Coppersmith_method
Algorithm for public-key cryptography
Determine d as d ≡ e−1 (mod λ(n)); that is, d is the modular multiplicative inverse of e modulo λ(n). This means: solve for d the equation de ≡ 1 (mod
RSA_cryptosystem
Conjecture in number theory
finite field arises from a modular form. A stronger version of this conjecture specifies the weight and level of the modular form. The conjecture in the level
Serre's_modularity_conjecture
Relates rational elliptic curves to modular forms
number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way
Modularity_theorem
Mathematical group that can be generated as the set of powers of a single element
integer n, the set of integers modulo n, again with the operation of addition, forms a finite cyclic group, denoted Z/nZ. A modular integer i is a generator
Cyclic_group
Nonlinear differential operator used to study conformal mappings
of the complex projective line, and in particular, in the theory of modular forms and hypergeometric functions. It plays an important role in the theory
Schwarzian_derivative
Algorithm used in modular arithmetic
in modular arithmetic to solve for r in a congruence of the form r2 ≡ n (mod p), where p is a prime: that is, to find a square root of n modulo p. The
Tonelli–Shanks_algorithm
Method of exchanging cryptographic keys
protocol uses the multiplicative group of integers modulo p, where p is prime, and g is a primitive root modulo p. To guard against potential vulnerabilities
Diffie–Hellman_key_exchange
Mathematical identities related to integer partitions
function for partitions such that each part is congruent to either 1 or 4 modulo 5. q n 2 + n ( q ; q ) n {\displaystyle {\frac {q^{n^{2}+n}}{(q;q)_{n}}}}
Rogers–Ramanujan_identities
Result in modular arithmetic
Hensel, is a result in modular arithmetic, stating that if a univariate polynomial has a simple root modulo a prime number p, then this root can be lifted
Hensel's_lemma
Unique numeric book identifier since 1970
(11 minus the remainder of the sum of the products modulo 11) modulo 11. Taking the remainder modulo 11 a second time accounts for the possibility that
ISBN
Set of residue classes modulo n, relatively prime to n
integers modulo n Congruence relation Euler's totient function Greatest common divisor Modular arithmetic Number theory Residue number system Long (1972, p. 85)
Reduced_residue_system
Noncototient Nontotient Euler's theorem Wilson's theorem Primitive root modulo n Multiplicative order Discrete logarithm Quadratic residue Euler's criterion
List_of_number_theory_topics
17th-century conjecture proved by Andrew Wiles in 1994
Yutaka Taniyama suspected a link might exist between elliptic curves and modular forms, two completely different areas of mathematics. Known at the time as
Fermat's_Last_Theorem
range 0 ≤ a ≤ p − 1. This is a simple consequence of the laws of modular arithmetic; we are simply saying that we may first reduce a modulo p. This is consistent
Proofs of Fermat's little theorem
Proofs_of_Fermat's_little_theorem
Matrix group
fundamental objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence subgroups in more
Congruence_subgroup
Formula concerning prime numbers
quadratic residue modulo a prime. Precisely, Let p be an odd prime and a be an integer coprime to p. Then a p − 1 2 ≡ { 1 ( mod p ) if there is an integer
Euler's_criterion
Algorithm for integer factorization
taking the modular slope of a chord joining P {\displaystyle P} and Q {\displaystyle Q} , and thus division between residue classes modulo n {\displaystyle
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Mathematical function
mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex
Dedekind_eta_function
Method in number theory
over the field F p ≃ Z / p Z {\displaystyle \mathbb {F} _{p}\simeq \mathbb {Z} /p\mathbb {Z} } of remainders modulo p {\displaystyle p} . The algorithm
Berlekamp–Rabin_algorithm
1995 publication in mathematics
announced his proof on 23 June 1993 at a lecture in Cambridge entitled "Modular Forms, Elliptic Curves and Galois Representations". However, in September
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Quantum algorithm for integer factorization
Consider the abelian group Z p × Z p {\displaystyle \mathbb {Z} _{p}\times \mathbb {Z} _{p}} , where each factor corresponds to modular addition of values. Now
Shor's_algorithm
Unproved conjecture in mathematics
calculate the number N p {\displaystyle N_{p}} of points modulo p {\displaystyle p} for a large number of primes p {\displaystyle p} on elliptic curves whose
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Function studied by Ramanujan
Swinnerton-Dyer, H. P. F. (1973). "On ℓ {\displaystyle \ell } -adic representations and congruences for coefficients of modular forms". In Kuyk, Willem;
Ramanujan_tau_function
Representation of modular integers by "small" fractions
In modular arithmetic, Thue's lemma roughly states that every modular integer may be represented by a "modular fraction" such that the numerator and the
Thue's_lemma
Number of partitions of an integer
-Pochhammer symbol and is similar to the product formulation of many modular forms, and specifically the Dedekind eta function. The same sequence of pentagonal
Partition function (number theory)
Partition_function_(number_theory)
Space of complex matrices with positive definite imaginary part
Bowman, Joshua P. "Some Elementary Results on the Siegel Half-plane" (PDF).. van der Geer, Gerard (2008), "Siegel modular forms and their applications"
Siegel_upper_half-space
Method for computing the relation of two integers with their greatest common divisor
that provision, x is the modular multiplicative inverse of a modulo b, and y is the modular multiplicative inverse of b modulo a. Similarly, the polynomial
Extended_Euclidean_algorithm
Theorem on prime numbers
assume p {\displaystyle p} is an odd prime, p ≥ 3 {\displaystyle p\geq 3} . Since the residue classes modulo p {\displaystyle p} form a field, every non-zero
Wilson's_theorem
Efficient algorithm to count points on elliptic curves
or Atkin. In order to do so, we make use of modular polynomials, which come from the study of modular forms and an interpretation of elliptic curves over
Schoof's_algorithm
Period of the Fibonacci sequence modulo an integer
π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known
Pisano_period
Some remarkable congruences for the partition function
Zbl 0984.11050. Ono, Ken (2004). The web of modularity: arithmetic of the coefficients of modular forms and q-series. CBMS Regional Conference Series
Ramanujan's_congruences
Algebraic structure
number p {\displaystyle p} , the prime field of order p {\displaystyle p} may be constructed as the integers modulo p {\displaystyle p} , Z / p Z {\displaystyle
Finite_field
Complex-valued smooth functions of the upper half plane (harmonic analysis topic)
fundamental domain of Γ {\displaystyle \Gamma } . In contrast to modular forms, Maass forms need not be holomorphic. They were studied first by Hans Maass
Maass_wave_form
Particular kind of exponential sum
x modulo m. The Kloosterman sums are a finite ring analogue of Bessel functions. They occur (for example) in the Fourier expansion of modular forms. There
Kloosterman_sum
Result concerning properties of Galois representations associated with modular forms
level descent modulo p strips all odd primes from the conductor. However, no newforms of level 2 remain because the genus of the modular curve X0(2) is
Ribet's_theorem
On unit fractions adding to 4/n
not 1 modulo 4, so the searches only need to test values that are 1 modulo 4. One way to make progress on this problem is to collect more modular identities
Erdős–Straus_conjecture
Probabilistic primality test
a prime, then the only square roots of 1 modulo n are 1 and −1. Proof Certainly 1 and −1, when squared modulo n, always yield 1. It remains to show that
Miller–Rabin_primality_test
Multiplication algorithm
by recursively applying fast Fourier transform (FFT) over the integers modulo 2 n + 1 {\displaystyle 2^{n}+1} . The run-time bit complexity to multiply
Schönhage–Strassen_algorithm
Algorithm for determining whether a number is prime
requires about p {\displaystyle p} modular multiplications, rendering it impractical, theorems about primes and modular residues form the basis of many
Primality_test
One over a whole number
This conversion can be used to perform modular division: dividing by a number x {\displaystyle x} , modulo y {\displaystyle y} , can be performed by
Unit_fraction
Number divisible only by 1 and itself
algebra, the ability to perform division means that modular arithmetic modulo a prime number forms a field or, more specifically, a finite field, while
Prime_number
Function in number theory
{\displaystyle a} and p {\displaystyle p} defined as ( a p ) = { 1 if a is a quadratic residue modulo p and a ≢ 0 ( mod p ) , − 1 if a is a quadratic
Legendre_symbol
Methods to test or prove primality
P p {\displaystyle P_{p}} be the point P evaluated modulo p. Thus, on E p {\displaystyle E_{p}} we have ( m / q ) P p = u q ( m / q ) P p = u m P p =
Elliptic_curve_primality
Arithmetic in a field with a finite number of elements
finite field theory, Évariste Galois. GF(p), where p is a prime number, is simply the ring of integers modulo p. That is, one can perform operations (addition
Finite_field_arithmetic
Type of group in group theory
another direction the classical topic of modular forms has blossomed into the modern theory of automorphic forms. The driving force behind this effort is
Arithmetic_group
American mathematician
on Hilbert modular surfaces. Hirzebruch and Zagier coauthored Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
Don_Zagier
Gives conditions for the solvability of quadratic equations modulo prime numbers
reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety
Quadratic_reciprocity
Multiplication table in Indian mathematics
{Z} } is the set of positive integers partitioned by the residue classes modulo nine. (the operator ∘ {\displaystyle \circ } refers to the abstract "multiplication"
Vedic_square
Mathematical functions
Functions. Cambridge. Reinhardt, William P.; Walker, Peter L. (2010b). "23. Weierstrass Elliptic and Modular Functions". In Olver, Frank; et al. (eds
Lemniscate_elliptic_functions
Boolean polynomials as sums of monomials
1927, they are the polynomial ring over the integers modulo 2. The resulting degeneracies of modular arithmetic result in Zhegalkin polynomials being simpler
Algebraic_normal_form
is a prime number one less than a power of 2. modular form Modular form modularity theorem The modularity theorem (which used to be called the Taniyama–Shimura
Glossary_of_number_theory
coefficients of modular forms. More specifically, it gives the modularity of certain two-dimensional Galois representations. In one common form, it states
Langlands–Tunnell_theorem
Approach to public-key cryptography
keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in finite fields, such as the RSA cryptosystem and ElGamal
Elliptic-curve_cryptography
Algorithm to multiply two numbers
S2CID 8437794. De, A.; Saha, C.; Kurur, P.; Saptharishi, R. (2008). "Fast integer multiplication using modular arithmetic". Proceedings of the 40th annual
Multiplication_algorithm
Primality test for certain numbers
necessary. The starting value u0 will be the Lucas sequence term Vk(P,1) taken modulo N. This process of selection takes very little time compared to the
Lucas–Lehmer–Riesel_test
Numbers obtained by adding the two previous ones
3 modulo 5, then, p divides Fp+1. The remaining case is that p = 5, and in this case p divides Fp. { p = 5 ⇒ p ∣ F p , p ≡ ± 1 ( mod 5 ) ⇒ p ∣ F p − 1
Fibonacci_sequence
}=(-1)^{(p-1)(q-1)/4}.} For an even integer u in the range 1 ≤ u ≤ p−1, denote by r(u) the least positive residue of au modulo p. (For example, for p = 11
Proofs of quadratic reciprocity
Proofs_of_quadratic_reciprocity
Primality test for numbers of a certain form
working, and if p is not prime, then no chosen a will work. Furthermore, since the calculation is modulo p, only values of a smaller than p have to be considered
Proth's_theorem
American mathematician
Polymath project on bounded gaps between primes, the L-functions and Modular Forms Database, the sums of three cubes project, and the computation and classification
Andrew Sutherland (mathematician)
Andrew_Sutherland_(mathematician)
About simultaneous modular congruences
When this condition is satisfied, the set of solutions forms a single congruence class modulo N = lcm ( n 1 , … , n k ) . {\displaystyle N={\text{lcm}}(n_{1}
Chinese_remainder_theorem
Shorthand way of determining whether a given number is divisible by a fixed divisor
Reducing modulo 7: N ≡ a0 − a1 + a2 − a3 + ... (mod 7) Thus, the alternating sum of the three-digit groups is congruent to the original number modulo 7. Therefore
Divisibility_rule
Mathematical concept
Frobenius endomorphism is congruent to zero modulo p {\displaystyle p} . When q = p > 3 {\displaystyle q=p>3} this is equivalent to having the trace of
Supersingular_elliptic_curve
Chinese gambling game using tiles
total number of pips on both tiles in a hand are added using modular arithmetic (modulo 10), equivalent to how a hand in baccarat is scored. The name
Pai_gow
Test if a Mersenne number is prime
3 M p − 1 2 ≡ − 1 ( mod M p ) . {\displaystyle 3^{\frac {M_{p}-1}{2}}\equiv -1{\pmod {M_{p}}}.} In contrast, 2 is a quadratic residue modulo M p {\displaystyle
Lucas–Lehmer_primality_test
Mathematical concept
ISBN 3-540-33068-2 Kato, Kazuya (2004), "p-adic Hodge theory and values of zeta functions of modular forms", in Pierre Berthelot; Jean-Marc Fontaine;
Euler_system
Error detection for identification numbers
check digit method would be to take the sum of all digits (digital sum) modulo 10. This would catch any single-digit error, as such an error would always
Check_digit
Mathematical function associated to algebraic varieties
reducing modulo each prime number p. It is a global L-function defined as an Euler product of local zeta functions. Hasse–Weil L-functions form one of the
Hasse–Weil_zeta_function
Result on the class group of certain number fields, strengthening Ernst Kummer's theorem
prime to p, ω(n) be congruent to n modulo p. The p part of the class group is a Z p {\displaystyle \mathbb {Z} _{p}} -module (since it is p-primary),
Herbrand–Ribet_theorem
Algorithm checking for prime numbers
EulerPhi[x]; PolyModulo[f_] := PolynomialMod[PolynomialRemainder[f, xr-1, x], n]; max = Floor[Log[2, n]√φ[r]]; For (a = 1; a ≤ max; a++) { If (PolyModulo[(x+a)n
AKS_primality_test
Algorithm for generating prime numbers
L. Atkin and Daniel J. Bernstein. In the algorithm: All remainders are modulo-sixty remainders (divide the number by 60 and return the remainder). All
Sieve_of_Atkin
Standard representation of a mathematical object
with equivalence classes more effective. For example, in modular arithmetic, the canonical form for a residue class is usually taken as the least non-negative
Canonical_form
Counting from "0" instead of "1" first
convention is in the use of modular arithmetic as implemented in modern computers. Usually, the modulo function maps any integer modulo N to one of the numbers
Zero-based_numbering
Result of partitioning the elements of an algebraic structure using a congruence relation
the equivalence class of x ∈ A {\displaystyle x\in A} generated by E ("x modulo E"). For an algebra A = ( A , ( f i A ) i ∈ I ) {\displaystyle {\mathcal
Quotient_(universal_algebra)
Algorithm for generating pseudo-randomized numbers
of the integers modulo m. The initial state must be chosen between 1 and m−1. One disadvantage of a prime modulus is that the modular reduction requires
Linear_congruential_generator
Algorithm for computing greatest common divisors
modular arithmetic. In this field, the results of any mathematical operation (addition, subtraction, multiplication, or division) is reduced modulo 13;
Euclidean_algorithm
Number in {..., –2, –1, 0, 1, 2, ...}
\mathbb {Z} } ). Additionally, Z p {\displaystyle \mathbb {Z} _{p}} is used to denote either the set of integers modulo p (i.e., the set of congruence classes
Integer
Solving integer equations from all modular solutions
equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the
Hasse_principle
Factorization method based on the difference of two squares
all the values for a. Squares are always congruent to 0, 1, 4, 5, 9, 16 modulo 20, because these are the quadratic residues of 20. The values repeat with
Fermat's_factorization_method
Attack applicable to block and stream ciphers
is a form of partitioning cryptanalysis that exploits unevenness in how the cipher operates over equivalence classes (congruence classes) modulo n. The
Mod_n_cryptanalysis
Integer factorization algorithm
linear sieve. The algorithm attempts to set up a congruence of squares modulo n (the integer to be factorized), which often leads to a factorization of
Quadratic_sieve
Algorithm in computational number theory
the discrete logarithm problem in the multiplicative group of units modulo a prime p, it is in fact a generic discrete logarithm algorithm—it will work
Pollard's_kangaroo_algorithm
Function in mathematical number theory
algebraic terms, λ(n) is the exponent of the multiplicative group of integers modulo n. As this is a finite abelian group, there must exist an element whose
Carmichael_function
MODULAR FORMS-MODULO-P
MODULAR FORMS-MODULO-P
Boy/Male
Hindu
Popular, Renown
Girl/Female
African, Australian, Nigerian
I am Grateful; Gratefulness
Female
English
Variant spelling of Middle English Mauld, MOULD means "mighty in battle."
Girl/Female
Hindu, Indian, Marathi
Sacred Thread; Mother
Surname or Lastname
English
English : from the Middle English female personal name Mau(l)d, a reduced form of the Norman name Mathilde, Matilda, composed of the Germanic elements maht ‘might’, ‘strength’ + hild ‘strife’, ‘battle’. The learned form Matilda was much less common in the Middle Ages than the vernacular forms Mahalt, Maud and the reduced pet form Till. The name was borne by the daughter of Henry I of England, who disputed the throne of England with her cousin Stephen for a number of years (1137–48). In Germany the popularity of the name in the Middle Ages was augmented by its being borne by a 10th-century saint, wife of Henry the Fowler and mother of Otto the Great.
Boy/Male
Hindu
Name of Lord Shiva
Boy/Male
Muslim
Sample, Model, Paragon
Boy/Male
Arabic, Muslim
Sample; Model; Paragon
Boy/Male
Hindu, Indian, Telugu
Lord Shiva; Wearing
Girl/Female
Indian
Popular
Surname or Lastname
English
English : variant spelling of Ormes.
Boy/Male
Arabic, Assamese, Indian, Muslim
Main; New
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Enjoyment
Boy/Male
Tamil
Parishrut | பரீஷà¯à®°à¯à®¤
Popular, Renown
Parishrut | பரீஷà¯à®°à¯à®¤
Boy/Male
Indian
Love
Surname or Lastname
English
English : variant of Mule.
Male
Spanish
Spanish form of Latin Theodulus, TEÓDULO means "god-slave."
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Attractive
Surname or Lastname
Americanized form of French Petitjean.English
Americanized form of French Petitjean.English : variant spelling of Pettyjohn.
Boy/Male
French, German, Teutonic
Rich
MODULAR FORMS-MODULO-P
MODULAR FORMS-MODULO-P
Boy/Male
Australian, Danish, Finnish, German, Greek, Irish, Swedish
People of Victory; Victorious Person
Boy/Male
Tamil
Lord Brahma
Girl/Female
Hindu, Indian
Beautiful Eyes
Boy/Male
Tamil
The Moon
Girl/Female
Muslim
Pure
Male
German
Variant form of German Landoberct, LAMPRECHT means "land-bright."
Boy/Male
Australian, Dutch, Greek
Follower of Dionysius; Greek God of Wine
Boy/Male
Muslim
Servant of the one, Servant of God
Boy/Male
Tamil
Wind, Divine
Boy/Male
Tamil
Balaraj | பாலாராஜ
Strong, King
MODULAR FORMS-MODULO-P
MODULAR FORMS-MODULO-P
MODULAR FORMS-MODULO-P
MODULAR FORMS-MODULO-P
MODULAR FORMS-MODULO-P
a.
Given to jesting; jocose; as, a jocular person.
n.
The size of some one part, as the diameter of semi-diameter of the base of a shaft, taken as a unit of measure by which the proportions of the other parts of the composition are regulated. Generally, for columns, the semi-diameter is taken, and divided into a certain number of parts, called minutes (see Minute), though often the diameter is taken, and any dimension is said to be so many modules and minutes in height, breadth, or projection.
n.
To model; also, to modulate.
n.
A fixed part of a module. See Module.
a.
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.
a.
Of, pertaining to, or in the form of, a nodule or knot.
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
n.
One who models; hence, a worker in plastic art.
a.
Beloved or approved by the people; pleasing to people in general, or to many people; as, a popular preacher; a popular law; a popular administration.
v. t.
To form into a particular shape; to shape; to model; to fashion.
pl.
of Modulus
n.
The sphere or globular mass of cells (blastomeres), formed by the clevage of the ovum or egg in the first stages of its development; -- called also mulberry mass, segmentation sphere, and blastosphere. See Segmentation.
a.
Adapted to the means of the common people; possessed or obtainable by the many; hence, cheap; common; ordinary; inferior; as, popular prices; popular amusements.
v. i.
To make a copy or a pattern; to design or imitate forms; as, to model in wax.
n.
A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength, efficiency, etc.; a parameter.
a.
Of or pertaining to the common people, or to the whole body of the people, as distinguished from a select portion; as, the popular voice; popular elections.
n.
A model or measure.
a.
Prevailing among the people; epidemic; as, a popular disease.
a.
Pertaining to the medula oblongata.
pl.
of Morula