# What is Primitive: Definition and 152 Discussions

The Primitive Methodist Church is a body of Holiness Christians within the Methodist tradition, which began in England in the early 19th century, with the influence of American evangelist Lorenzo Dow (1777–1834).
In the United States, the Primitive Methodist Church had eighty-three parishes and 8,487 members in 1996. In Great Britain and Australia, the Primitive Methodist Church merged with other denominations, to form the Methodist Church of Great Britain in 1932 and the Methodist Church of Australasia in 1901. The latter subsequently merged into the Uniting Church in Australia in 1977.

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1. ### I Questions Regarding Primitive Unit Cell

Questions regarding Primitive Unit Cell (and what I think the answer are, correct me if I am wrong) 1. Can there be more than one Primitive Unit cells for the same crystal? yes, Wigner Seitz cell always will exist. There can be other primitive Unit cells along with Wigner Seitz too. But...
2. ### A Mapping High Symmetry Points from Primitive to Conventional Cell

We usually plot electronic bands with the help of high symmetry points of the irreducible zone of primitive cell of particular material. But if we want to plot bands with conventional cell, we have to map the high symmetry points from primitive cell to conventional cell. so how can we map the...
3. ### MHB Number of natural numbers that have primitive roots

Hey! :giggle: How can we calculate the number of natural numbers between $2$ and $n$ that have primitive roots? Let $m$ be a positive integer. Then $g$ is a primitive root modulo $m$, with $(g,m)=1$, if the modulo of $g\in (Z/m)^{\star}$ is a generator of the group. We have that $g$ is a...
4. ### MHB Proving Primitive Symbols with Axioms

Given : A) primitive symbols : (1, *) and B) The axioms: 1) \forall x\forall y[x*=y*\Longrightarrow x=y] 2) \forall x[x*\neq 1] 3) [P(1)\wedge\forall x(P(x)\Longrightarrow P(x*))]\Longrightarrow\forall xP(x) Then prove: \forall x[x=1\vee \exists y(y*=x)]
5. ### I Primitive unit cell (Diamond)

Hi guys , I want to construct a primitive unit cell for diamond, which is made of a fcc lattice and a basis of 2 carbons atoms. I know that a primitive unit cell isn't unique but the two variants I get are drastically different . As far as I can see they both include 2 whole atoms/points in the...
6. ### PE 75 primitive Pythagorean triples

The question simply asks primitive pythagorean triples ##(a,b,c)## such that ##S = a + b + c <15\times 10^{5}## import time import math start = time.perf_counter() pythagorean_triples = {(3, 4, 5) : 12} for m in range(0, 10**3, 2): for n in range(1, m, 2): if math.gcd(m, n) == 1...

8. ### B A primitive function graphing tool

Recently I found this online: https://www.html5canvastutorials.com/labs/html5-canvas-graphing-an-equation/ It is a html page using the <canvas> element and it can graph functions. Although much better versions of this is already everywhere(like desmos), it should still be useful considering...
9. ### I Primitive Elements and Free Modules .... ....

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by Bland we read...
10. ### MHB Understanding Bland's Proof of Proposition 4.3.14: Primitive Elements of Modules

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need yet further help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by...
11. ### MHB Help Understanding Bland's Proposition 4.3.14 in Rings and Their Modules

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some further help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by...
12. ### MHB Primitive Elements and Free Modules .... ....

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help in order to fully understand the proof of Proposition 4.3.14 ... ... Proposition 4.3.14 reads as follows: In the above proof by Bland we...
13. ### MHB Modules over Principal Idea Domains .... and Primitive Elements .... Bland, Lemma 4.3.10 .... ....

I am reading Paul E. Bland's book, "Rings and Their Modules". I am focused on Section 4.3: Modules Over Principal Ideal Domains ... and I need some help to fully understand the proof of Lemma 4.3.10 ... ... Lemma 4.3.10 and its proof read as...
14. ### Are there any resources for questions on primitive roots?

Does anyone know of any resources on questions on primitive roots and order of a modulo n? They need to be suitable for elementary number theory course. (These could be interesting results and challenging ones).
15. ### I What is the most motivating way to introduce primitive roots

I am teaching elementary number theory to first year undergraduate students. How do introduce the order of an integer modulo n and primitive roots? How do I make this a motivating topic and are there any applications of this area? I am looking at something which will have an impact.
16. ### MHB What is the most motivating way to introduce primitive roots?

I am teaching elementary number theory to first year undergraduate students. How do introduce the order of an integer modulo n and primitive roots? How do I make this a motivating topic and are there any applications of this area? I am looking at something which will have an impact.
17. ### Number theory, primitive pythagorean triples

Homework Statement Find the known pythagorean triangles with sides of integers lengths, given the area of the pythagorean triangle is 60. Homework Equations Pythagorean triangles are right angled triangles. a primitive pythagorean triple is of the form: x=2mn y=m^2-n^2 z=m^2+n^2 gcd(m,n)=1...
18. ### Complex logarithm as primitive

The problem I am trying to calculate the integral $$\int_{\gamma} \frac{z}{z^2+4} \ dz$$ Where ## \gamma ## is the line segment from ## z=2+2i ## to ## z=-2-2i ##. The attempt I would like to solve this problem using substitution and a primitive function to ## \frac{1}{u} ##. I am not...
19. ### I Feynman Diagram-Momentum conservation in primitive vertex

In the first Feynman diagram, an electron comes in, emits a photon and then leaves. Is this an allowed process? Because if you rotate the diagram by 90o, the diagram should be just as valid, but it doesn't seem to be since it would violate the law of conservation of momentum. So is the...
20. ### Proving 2 as a Primitive Root of Z_83: A Step-by-Step Approach

Homework Statement Prove that 2 is a primitive root of ##\mathbb{Z}/83\mathbb{Z}## by hand. Hint: Think hard about ##2^{41}##. Homework Equations Euler's theorem, Euler's Totient function, Chinese remainder theorem(not sure if its relevant). We don't really have anything else. The Attempt at...
21. ### Primitive of a definite integral

Homework Statement I need find the function ##F(x)## . Homework Equations ##\int_0^r F(x)dx = \frac{r^3}{(r^2+A)^{3/2}}+N## where ##A,N## are constants. The Attempt at a Solution I tried using some function of test, for instance the derivative of the right function evaluated in x. But , i...
22. ### B The Most Primitive Star-Forming Galaxy Ever Found

Lying 620 million light-years away, this galaxy has the lowest oxygen abundance ever seen in a star-forming galaxy. Link: New Scientist
23. L

### 2D lattice, primitive cell choice

Homework Statement When calculating the Fourier coefficients of the potential of the following lattice (the potential is a sum of deltas at the atom sites): I get the wrong coefficients if I choose the following primitve cell, with primitve vectors a1,a2: And the right coefficients if I...
24. ### Primitive function - smart substitution

The problem $$\int \frac{x}{\sqrt{x^2+2x+10}} \ dx$$ The attempt ## \int \frac{x}{\sqrt{x^2+2x+10}} \ dx = \int \frac{x}{\sqrt{(x+1)^2+9}} \ dx## Is there any smart substitution I can make here to make this a bit easier to solve?
25. ### Finding anitderivative using complex numbers and Euler

I have to find a primitive function below using the Euler formulas for ##\sin x## and ## \cos x## The problem $$\int e^{2x} \sin 3x \ dx$$ Relevant equations ## \cos x = \frac{e^{ix}+e^{-ix}}{2} \\ \sin x = \frac{e^{ix}-e^{-ix}}{2i} \\ \\ \int e^{ix} \ dx = \frac{e^{ix}}{i} ## The attempt...

28. ### Proving Primitive Roots of Odd Numbers Modulo pm

Hello friends from afar. I ran into what I felt to be somewhat of an odd question: Prove that some odd numbers are primitive roots modulo pm for each odd prime p and each positive integer m. It feels dodgy given that any odd number n = p1p2 ⋅⋅⋅ ps cannot be a primitive root of a prime number...
29. ### Extending a field by a 16th primitive root of unity

Homework Statement let c be a primitive 16th root of unity. How many subfields M<Q(c) are there such that [M:Q] = 2 Homework EquationsThe Attempt at a Solution I think the only subfield M of Q(c) such that [M:Q] = 2 is Q(c^8). Then M = {a+b(c^8) such that a,b are elements of Q}. I'm thinking...
30. ### A Tools to transform primitive cell orientation

In case the orientation of a primitive cell is not what I want, is there tools to do a user-supplied 3D rotation to bring the primitive cell to the preferential orientation and output the new coordinates? Thanks,
31. ### A Primitive cell parameter given chemical unit cell info

Experimentalists usually provide chemical unit cell information including full symmetry (space group) information of the crystal together with coordinates of independent atoms. But this cannot be directly used by ab initio packages, which requires either primitive cell or unit cell information...
32. ### Finding the minimal polynomial of primitive 15th root of 1

Homework Statement So I need the find the minimal polynomial of the primitive 15th root of unity. Let's call this minimal polynomial m(x) Homework EquationsThe Attempt at a Solution I know that m(x) is an irreducible factor of x^15 - 1 and also that the degree of m(x) is equal to the Euler...
33. ### B What is a Primitive Cell in Material Science?

In Material Science, what is a primitive cell when speaking crystals.
34. ### Determine all primitive functions

Homework Statement Determine all primitive functions for the function: 2x(x^2+3)^4 2. The attempt at a solution When i expanded i got the primitive to be: 2(x^9/9)+3x^8+18x^6+54x^4+81x^2But this was wrong. I am not sure I have understood the question. Help?
35. ### Creating technology from primitive conditions

So this is kind of a speculative question but it is something I have long wondered about. I know that if I were to suddenly find myself transported backward in time, say 5000 years, or transported to a primitive Earth like planet, chances are that I would probably die in no time at all. I...
36. ### I Don't understand lemma about primitive polynomial product

I was reading about Gauss's Lemma here: https://cims.nyu.edu/~kiryl/Algebra/Section_3.10--Polynomials_Over_The_Rational_Field.pdf Unfortunately, I am stuck on Lemma 3.10.1 that concludes that the product of a pair of primitive polynomials is itself primitive. I understand about how there is...
37. ### MHB Principle Ideal in F[x] & Primitive nth root of unity

Let ζ5 be e2πi/5. Find a monic polynomial of degree two in K(ζ + ζ−1) So, if E/F is a field extension, with α∈E then K(α) = {f(x)∈F[x] | f(α)=0} and m(x) is the minimal polynomial of α over F such that K(α) = [m(x)] where [m(x)] is the ideal generated by m(x). I was thinking maybe (x- ζ -...

Prove that for any primitive Pythagorean triple (a, b, c), exactly one of a and b must be a multiple of 3, and c cannot be a multiple of 3. My attempt: Let a and b be relatively prime positive integers. If $a\equiv \pm1 \pmod{3}$ and $b\equiv \pm1 \pmod{3}$, $c^2=a^2+b^2\equiv 1+1\equiv 2... 39. ### How are the direction of primitive vectors determined in BCC crystal structures? hello i have browsed this forum for topics about this, and i found them very enlightening and helped a lot in terms of finding the length of the primitive vectors , the problem that i have is with the direction of said primitive vectors , while in fcc they are more or less easy to visualize in... 40. ### 3D object represent with primitive shapes Hi, Given a 3D object in R3 space can we represent it using three basic primitive shapes like Sphere, Cone and Cylinder? Would this claim be valid? 41. ### FInd non-zero elements are primitive in a field Homework Statement Construct$\mathbb{F}_{16}$as a quotient of$\mathbb{Z}_2[X]$. How many non-zero elements are primitive in this field? Calculate$|GL2_(\mathbb{F}_16)|$. Homework Equations Primitive Theorem The Attempt at a Solution For the first question, I don't know how to construct... 42. ### Distribution function primitive Homework Statement the distribution function: f(x)= x + 1 when -1 < x ≤ 0 -x + 1 when 0 ≤ x < 1 0 otherwiseHomework Equations The Attempt at a Solution on the first interval i found (1/2)x2 +x + c on the second interval -(1/2)x2 + x + c and when integrating the c's will cancel each... 43. ### Figuring out Bravais lattice from primitive basis vectors Homework Statement Given that the primitive basis vectors of a lattice are ##\mathbf{a} = \frac{a}{2}(\mathbf{i}+\mathbf{j})##, ##\mathbf{b} = \frac{a}{2}(\mathbf{j}+\mathbf{k})##, ##\mathbf{c} = \frac{a}{2}(\mathbf{k}+\mathbf{i})##, where ##\mathbf{i}##, ##\mathbf{j}##, and ##\mathbf{k}## are... 44. ### MHB Primitive recursive functions Hey! :o Can we enumerate the primitive recursive functions? 45. ### MHB Recursive and Primitive recursive functions Hey! :o According to the book that I'm reading, we can define the$\mu-$recursive functions inductively, as follows: The constant, projection, and successor functions are all$\mu-$recursive. If$g_1, \dots , g_m$are$n-$variable$\mu-$recursive functions and$h$is an$m-$variable... 46. ### MHB Find Min Polynomial of$\alpha$Over$\mathbb{Q} | Solution Included

I started by setting $\alpha= e^{2\pi i/3} + \sqrt[3]{2}.$ Then I obtained $f(x) = x^9 - 9x^6 - 27x^3 - 27$ has $\alpha$ as a root. How can I proceed to find the minimal polynomial of $\alpha$ over $\mathbb{Q},$ and identify its other roots?
47. ### MHB Primitive recursive functions/sets

Hey! :o I have to show that the following functions and sets are primitive recursive: $$f(x,y)=x+y$$ $$f(x,y)=x \cdot y$$ $$sign (x)=\left\{\begin{matrix} 1 &\text{ if } x=0\\ 0 &\text{ if } x>0 \end{matrix}\right.$$ x \dot - y=\left\{\begin{matrix} x-y &\text{ if } x \geq y\\...
48. ### Primitive Flow Table: C1 & C2 Logic Conditions

Homework Statement Following the amount of C1 front, the output Z be 1 . Following an amount of C2 front, the output Z must be 0 . Otherwise, the output remains unchanged. Homework EquationsThe Attempt at a Solution in Attached file. This is the answer but I really do not understand the...
49. ### How number of primitive cells in a material = number of K-States ?

Dear All, 1) I am not able to understand the statement given by one of the professor. i,e., Number of primitive cells in a material = Number of K-States. 2) Additionally, if one atom is per primitive cell then why do we have NUMBER of k-states equivalent to number of atoms in this case ? 3)...
50. ### MHB Primitive Roots Modulo $p$: The $(p-1)/2$ Rule

Is it true that $g$ is a primitive root modulo $p$ if and only if $g^{(p-1)/2} \equiv -1 \pmod p$?