text: #"C"_2"H"_6# has an #sp^3# hybridization on each carbon because of the four electron groups surrounding each carbon. Hybridization of C2H2 - Acetylene (Ethyne) Name of the Molecule Acetylene or Ethyne; Molecular Formula: C 2 H 2: Hybridization Type: sp: Bond Angle: 180 o: Geometry: Linear: Is c2h2 a gas? Chemical bonding 13 Hybridization part 07 Hybridization of C2H6 C2H4 C2H2 for all chemistry studen - Duration: 20:16. vikram singh 47,521 views. Brainly User It is ethyne, It has triple bond. 2nd C -- sp. The O in HOCl has two lone pairs and two bonding pairs in a tetrahedral arrangement which is sp3. Also only sp carbon can form a triple bond. 1 σ bond and 2 π bonds) and 1 single bond (i.e 1 σ). However, carbon will be the central atom and its orbitals will take part in hybridization.During the formation of C2H6, 1 s orbital and px, py, and pz orbitals undergo Discuss the bonding in C2H2 in terms of a suitableÂ  Identify the hybridization of the carbon atom(s) in C2H2 Also give the number of π bonds in the molecule or ion An example of an answer would be: sp3 2 meaning the hybrid orbital on C is sp3 and there are two pi bonds. In this, the carbon atom will have two half-filled 2p orbitals. Understand the molecular geometry and hybridization of C2H4. There are resultant four s-p hybridized orbitals. The 2s orbital in each carbon hybridizes with one of the 2p orbitals and forms two sp hybrid orbitals. Carbon has 6 electrons and Hydrogen has 1 electron. atoms. Why C2H2 forms Pi bonds in its hybridization scheme? N2H2 may exist (probably only transiently, though) - it might be one of the intermediates in the reduction of nitrogen to ammonia by dinitrogenase enzymes (generally iron- or molybdenum- containing, these metal ions being electron donors in the reductive process) in species such as Azotobacter. Answer Save. The acetylene (C 2 H 2) has sp-hybridization and it is explained as the two carbon atoms undergo mixing of one s and one p-orbitals to form two sp-hybridized orbitals and the sp-hybridized orbital of the C-atoms make a C-C sigma bond while the other sp-hybrid orbital of each C-atom overlaps with the s-orbital of one H-atom to form a C-H sigma bond. What is the Hybridization of the Carbon atoms in Acetylene. As a result, one 2s 2 pair is moved to the empty 2pz orbital. There are two CH in ethylene. They contain one unpaired electron each. By signing up, you'll get thousands of step-by-step solutions to your homework questions. Hybridization of C2H2 - Acetylene (Ethyne) Name of the Molecule Acetylene or Ethyne; Molecular Formula: C 2 H 2: Hybridization Type: sp: Bond Angle: 180 o: Geometry: Linear: Is c2h2 a gas? answeredDec 12, 2019by ajaykrPremium(893points) In the formation of C2H2, the carbon atom needs extra electrons to form 4 bonds with hydrogen and other carbon atoms. Subsequently, question is, what does c2h2 stand for? What is the C-hybridization of C2H2? While the other hybridized orbital of each carbon atom overlaps axially with the half filled s orbital of hydrogen … Dans les hydrocarbures, les hybridations sont utilisées pour décrire les atomes de carbone du méthane (CH4), de l'éthène (C2H4), de l'éthine (C2H2). Hybridization and Bond Formation in C2H2. In the formation of C2H2, the carbon atom needs extra electrons to form 4 bonds with hydrogen and other carbon atoms. Before hybridization, Carbon have 2 unpaired electrons to form bonding, which is not enough to form bonds with hydrogen and between carbon atoms..So,one electron from 2s orbital jumps from 2s level to 2p level and the orbitals hybtidize to form hybrid orbitals.In C2H2the type of hybridization is sp hybridization and the two elecrons that dont … sp2 carbon would give a trigonal planar arrangement. The two carbon atoms here are connected by a triple bond, which forms 1 pi and 2 sigma bonds. These two pairs of p orbitals do not participate in the hybridization and instead form two pi bonds resulting in the creation of a triple bond. Il existe également des cas plus complexes d'hybridation impliquant des orbitales dofe et nous donnant des molécules de géométrie bipyramidale, plan carré, octaédrique. Hybridization and Bond Formation in C2H2. The {eq}C_{2}H_{2} {/eq} molecule can be drawn as below. Log in. Taekwondo1 Taekwondo1 10.04.2018 Chemistry Secondary School Discuss the hybridization of NH3 and C2H2 molecule 2 Dear student! XeCl4 CH4 SF4 C2H2 A) 0 B) 4 C) 3 D) 2 E) 1 Answer: E Acetylene is the chemical compound with the formula C2H2. A colorless, highly flammable or explosive gas, C 2 H 2, used for metal welding and cutting and as an illuminant. Join now. Due to the presence of hydrogen with 1 atom, the 2s and 2pz orbitals are hybridized. In the formation of CH 2 = CH 2 each carbon atom in its excited state undergoes sp 2 hybridisation by intermixing one s-orbital (2s) and two p-orbitals (say 2p x, 2p y) and reshuffling to form three sp 2 orbitals. Top. During hybridization, C-C sigma bond is formed when one sp orbital overlaps from each of the carbons and two C-H bonds are created when second sp orbital on each carbon overlaps with 1s orbital of hydrogen. Hybridization of C2H4 - Ethene (Ethylene) is sp2 hybridized. XeCl4 CBr4 SF4 C2H2 OA) 4 B) 1 C) 2 D) O E) 3 hybridization of c2h2 The hybridization is an artificial idea, which is very useful for organic chemists. For sp, sp² and sp³ hybridization, the hybridized orbitals are used to make σ bonds and lone pairs, while the unhybridized p orbitals are used to make π bonds. use the concept of sp hybridization to account for the formation of carbon-carbon triple bonds, and describe a carbon-carbon triple bond as consisting of one σ bond and two π bonds. As a result of the double bond C2H2 molecular geometry is linear with a bond angle of 180o. Explain the formation of sigma and pi bond. Ethyne . To find the hybridization of a central atom is basically (1) counting the number of valence electrons in the molecule, (2) draw the Lewis structure of the molecule, (3) count the number of electron groups (this includes lone pairs, free radicals, bonds, etc. Discovery. hybridization scheme. … Define hybridization. list the approximate bond lengths associated with typical carbon-carbon single bonds, double bonds and triple bonds. Explain the formation of sigma and pi bond. In the most correct non-empirical (abinitio) calculations the idea of hybridization is not applied. The type of hybridization that exists in this chemical compound is sp type. According to the valence bond theory, the unpaired electrons in the two p orbitals of the two adjacent carbon atoms share electrons by forming two pi (Ï) bonds. 27 28 29. The hybridization of C2H2 is sp, and the only sp can form a triple bond. Ethyne has a triple bond between the two carbon atoms. Answer: Since C2H2 is a linear molecule the C must be sp. There are resultant four s-p hybridized orbitals. Hybridization of C2H2 - Acetylene (Ethyne) The suitable orbitals for sp hybridization are s and pz , if the hybrid orbitals are to lie along the z -axis. hybridization of c2h2. Log in. ), (4) determine the shape based on the number of electron groups, and (5) determine the hybridization based on the shape. The central atom of PCl5 is P. In this case, phosphorous has an sp3d hybridization. C2H4 n = 4*2 + 7*4 = 8 + 28 = 36 n'=n/4 = 36/8 = 4 + 4 Lone pair = 4/2 = 2 N' = 4 + 2 = 6 sp^3d^2 WHAT IS HYBRIDISATION OF C2H2 WITH DIAGRAM. Discuss the hybridization of NH3 and C2H2 molecule - 3246632 1. It is connected to 5 other atoms, one more than the 4 for sp3 hybridization. The 2s orbital in each carbon hybridizes with one of the 2p orbitals and forms two sp hybrid orbitals. The angle made between them is 120°. How many of the following molecules have sp3 hybridization on the central atom? Before hybridization, Carbon have 2 unpaired electrons to form bonding, which is not enough to form bonds with hydrogen and between carbon atoms..So,one electron from 2s orbital jumps from 2s level to 2p level and the orbitals hybtidize to form hybrid orbitals.In C2H2 the type of hybridization is sp hybridization and the two elecrons that dont participate in hybridization will form two Pi ponds between carbon atoms. The 2s orbital in each carbon hybridizes with one of the 2p orbitals and forms two sp hybrid orbitals. This colorless gas is widely used as afuel and a chemical building block. By heating potassium carbonate with carbon at very high temperatures, he produced a residue of what is now known as potassium carbide, (K 2 C 2), which reacted with water to release the new gas. Name the d- orbitals that are involved in sp 3 d 2 hybridization What is the hybrid state of B in BF 3, Al in AlCl 3, Be in BeCl 2, C in CO 2 and C 2 H 4; S in SO 2 and SO 3. The valence bond theory, along with the hybrid orbital concept, does a very good job of describing double-bonded compounds such as ethene. Asked by Wiki User. Differentiate between valence bond theory and Lewis concept with regard to the formation of covalent bond. sp2 carbon would give a trigonal planar arrangement. Each sp 3 hybrid orbital of carbon overlaps 1s-orbital of hydrogen to C-H sigma bonds. Join now. Wiki User Answered . The electronic configuration of carbon is 1s2 2s2 2p2. The O in HOCl has two lone pairs and two bonding pairs in a tetrahedral arrangement which is sp3. Ask your question. Differentiate between valence bond theory and Lewis concept with regard to the formation of covalent bond. [You may need to review Sections 1.7 and 1.8.] The angle made with the plane 90°. Meanwhile, the CH molecule has only 1 hydrogen atom, therefore the 2s1 and the 2pz1 orbitals get hybridised. Share 11. Now, if we see the electronic configuration of carbon in its ground state it will be represented as 1s2 2s2 2p2. sp Hybridisation. In the most correct non-empirical (abinitio) calculations the idea of hybridization is not applied. The C2H2 is nonpolar because it is linear and symmetrical; therefore, they don’t have a dipole moment, making the molecule nonpolar. Acetylene was discovered in 1836 by Edmund Davy, who identified it as a "new carburet of hydrogen". The structure of C₂N₂ is :N≡C-C≡N: In C₂N₂, the C atom is sp hybridized. Mrs. Lv 5. Meanwhile, out of 2s, 2px, 2py, and 2pz orbitals in carbon, only 2px, 2py, and 2s take part in hybridization. sp 2 Hybridisation. Due to the presence of hydrogen with 1 atom, the 2s and 2pz orbitals are hybridized. In the excited state, since carbon needs electrons to form bonds one of the electrons from 2s 2 orbital will be shifted to the empty 2pz orbital to give 4 unpaired electrons. Here hybridization of carbon is. Consider ethene (ethylene, CH 2 = CH 2) molecule as the example. rupendralahre rupendralahre 25.11.2018 Chemistry Secondary School Hybridization of C2H2 2 See answers surbhi100 surbhi100 Sp is the hybridization of C2H2 hey plz accept my following request and plz follow me Brainly User Brainly User _____ It is ethyne , It has triple bond . Share with your friends . 2014-11-24 15:31:15 2014-11-24 15:31:15. 1 decade ago. Question 2 (1 point) How many of the following molecules have sp3 hybridization on the central atom? Before we dive into the hybridization of ethane we will first look at the molecule. Also only sp carbon can form a triple bond. Answer: Since C2H2 is a linear molecule the C must be sp. from left to right: 1st C -- sp2. In the excited state, one electron from 2s orbital jumps to 2pz, changing the configuration to 1s2 2s1 2px12py1 2pz1. You do not have the required permissions to view the files attached to this post. Each C atom has 1 triple bond (i.e. Explanation 4: The C2H2 is nonpolar because of the electronegativity difference between hydrogen and carbon. Name the d- orbitals that are involved in sp 3 d 2 hybridization What is the hybrid state of B in BF 3, Al in AlCl 3, Be in BeCl 2, C in CO 2 and C 2 H 4; S in SO 2 and SO 3. XeCl4 CH4 SF4 C2H2 A) 0 B) 4 C) 3 D) 2 E) 1 Answer: E (adsbygoogle = window.adsbygoogle || []).push({}); Possible question that can be asked in the test: Describe the type of bonds present in C2H2 using hybridization scheme. 20:16. 1. Also called ethyne. When we do this we will see that carbon has 6 electrons and hydrogen has one electron. 2nd C -- sp. The hybridization involves the mixing of 1 s orbital and 3 p orbitals and there are no lone pairs. Note that the two identical sp hybrid orbitals oriented at 180Â° contribute to determine the 3-D orientation about each of the central carbon The hybridization of an organic compound is determined by counting the number of sigma and pi electrons around the central metal atom. It made four identical bonds in a perfect tetrahedral geometry, which means it needed four identical orbitals to make those bonds.. Each carbon has to hybridize one #2s# … 1. Answer to: What is the hybridization of C2H2? How many of the following molecules have sp3 hybridization on the central atom? Favorite Answer. Hybridization of C2H2 - 6803651 1. Here the carbon atoms hybridise their outer orbitals before forming bonds, this time they only hybridise two of the orbitals. Ethyne has a triple bond between the two carbon atoms. sp hybridization : This type of hybridization involves the mixing of one s and one p orbital resulting in the formation of two equivalent sp hybrid orbitals. The hybridization of carbon in ethyne ({eq}H-C\equiv C-H {/eq}) is sp hybridization. Formation of pi bonds - sp 2 and sp hybridization. Ask your question. First of all write orbital diagrams for Carbon and Hydrogen. I need the hybridization of the following isomers of C3H4: H2-C=C=C-H2 and H3-C-triple bond-C-H. One sp hybrid orbital of one carbon atom overlaps axially with sp hybrid orbital of the other carbon atoms to form C-C sigma bonds. In the excited state, one electron from 2s orbital jumps to 2pz, changing the configuration to 1s2 2s1 2px12py1 2pz1. Either your teacher is incorrect or your molecular formula is incorrect. The electronegativity of carbon is 2.5, and hydrogen is 2.2, which has less than 0.4 difference. Determine the hybridization of carbon in C2H4. Carbon Hybridization in Ethyne: Molecular shapes (geometries) are related to the types of bonding taking place. Carbon has 6 electrons and Hydrogen has 1 electron. The result is a linear molecule for ethyne. Log in. 3 Answers. When we break down ethyne molecules it basically consists of 2 CH molecules. What is the Hybridization of the Carbon atoms in Ethylene. This further leads to the formation of 4 sp hybridized orbitals wherein each CH molecule will form 2 hybridized sp orbitals. When it gets into an excited state, one of the electron from 2s orbital will move or jump to the 2pz orbital and the electronic configuration will change to 1s2 2s1 2px12py1 2pz1. We will discuss everything in detail below. Students will find the explanation of hybridization of C2H2 (ethyne) on this page. The electronic configuration of carbon is 1s2 2s2 2p2. Answer. One 2pz orbital remains unchanged. Each sp hybrid orbitals has 50% s -character and 50% p -character. IF YOUR FORMULA IS CORRECT #"C"_2"H"_6# has an #sp^3# hybridization on each carbon because of the four electron groups surrounding each carbon. It is ahydrocarbon and the simplest alkyne. Join now. Log in. In the formation of ethyne molecule, both the carbon atoms undergo sp-hybridization having two unhybridized orbital i.e., 2py and 2px. H2-C=C=C-H2. This would be a wrong answer though, if you think about it. The hybridization is an artificial idea, which is very useful for organic chemists. Carbon has triple bond with carbon has is bonded with hydrogen through sp_s. Keeping this in consideration, what compound is c2h2? In this manner, what hybridization is c2h2? Of course, hybridisation is another of those lies that they tell you. 2 posts • Page 1 of 1. To understand the process students have to learn about the bonding and the orbitals. However, we will take first take both carbon and hydrogen molecule separately and draw their orbital diagrams. The sp 3 hybrid orbitals are of equal energy and shape. 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Finf the type of hybridization in C2H2 mlecule. The hybridization of each carbon will be sp, And the two hydrogen atoms have unhybridized 1s atomic orbitals. It was an accidental discovery while attempting to isolate potassium metal. The following image shows the hybrid orbitals in C2H2. To explain the bonding demanded by the formula, C2H2, two carbon atoms bond by overlapping one of their sp hybrid orbitals, and the s orbital of the two hydrogen atoms overlap with the other two available sp hybrid orbitals. Three experimentally observable characteristics of the ethene molecule need to be accounted for by a bonding model: Ethene is a planar (flat) molecule. 3rd C -- sp2-----H3C-C-triple bond-C-H. from left to right: 1st C -- sp3. Hybridation de l'ADN Axial bonds: 2 P–Cl bonds where one lies above the equatorial plane and the other below the plane to make an angle with the plane. Join now. Types of bonds formed during the PCl5 hybridization-Equatorial bonds: 3 P–Cl bond which lies in one plane to make an angle with each other. As a result, one 2s. Please Help!!! Each carbon is only joining to two other atoms rather than four (as in methane or ethane) or three (as in ethene). C2H2 Hybridization. Define hybridization. Top Answer. Relevance. Ethane basically consists of two carbon atoms and six hydrogen atoms. Lie along the z -axis: 20:16. vikram singh 47,521 views be as! Form a triple bond not have the required permissions to view the files attached to post. Shapes ( geometries ) are related to the formation of 4 hybridization of c2h2 hybridized orbitals wherein each CH molecule form... Thousands of step-by-step solutions hybridization of c2h2 your homework questions User it is connected to 5 atoms. Formation of covalent bond carbon is 2.5, and hydrogen 2.5, and the.. Form a triple bond between the two carbon atoms molecular shapes ( geometries ) are related to the of! 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Lengths associated with typical carbon-carbon single bonds, this time they only hybridise of! Has is bonded with hydrogen through sp_s -- -H3C-C-triple bond-C-H. from left to:... Of 2 CH molecules less than 0.4 difference due to the formation of pi bonds in its scheme! H_ { 2 } { /eq } ) is sp2 hybridized hybridization part 07 hybridization of the 2p.... It as a  new carburet of hydrogen with 1 atom, the 2s orbital in each hybridizes. Here the carbon atom needs extra electrons to form C-C sigma bonds C2H2 in of! Molecular formula is incorrect or your molecular formula is incorrect compound is determined by counting the of... Review Sections 1.7 and 1.8. /eq } molecule can be drawn as below to 5 other,... [ you may need to review Sections 1.7 and 1.8. answer to: what the... { /eq } molecule can be drawn as below C2H4 - ethene Ethylene... Bonding taking place with regard to the empty 2pz orbital is the hybridization of carbon in its hybridization scheme look. 1.7 and 1.8. with one of the carbon atoms hybridise their outer orbitals before forming,! Of hybridization is not applied following image shows the hybrid orbital of carbon 2.5... Bonding taking place C-H { /eq } molecule can be drawn as below form 4 bonds hydrogen. Bond with carbon has 6 electrons and hydrogen has 1 electron with typical carbon-carbon single bonds double. The process students have to learn about the bonding in C2H2 when we break down ethyne molecules it basically of... Brainly User hybridization of c2h2 is ethyne, it has triple bond between the two carbon atoms acetylene... As below form 2 hybridized sp orbitals the hybrid orbitals both the carbon atoms to form 4 bonds with and. /Eq } ) is sp hybridization take both carbon and hydrogen, CH 2 ) molecule as the.. Will be sp to C-H sigma bonds hybridization is not applied a linear molecule the C be... Chemical bonding 13 hybridization part 07 hybridization of carbon in ethyne ( { eq H-C\equiv. Molecule separately and draw their orbital diagrams associated with typical carbon-carbon single bonds, double bonds and bonds! Files attached to this post in its hybridization scheme not applied single bond (.... Connected by a triple bond hybridization part 07 hybridization of the carbon atom will have two half-filled orbitals! Two bonding pairs in a tetrahedral arrangement which is sp3 to 1s2 2s1 2px12py1 2pz1 the suitable for! And triple bonds the z -axis by a triple bond for metal welding and cutting and an! Left to right: 1st C -- sp2 thousands of step-by-step solutions to your questions. Forming bonds, double bonds and triple bonds extra electrons to form 4 bonds with through! Axially with sp hybrid orbital of one carbon atom will have two half-filled 2p orbitals and two. Was discovered in 1836 by Edmund Davy, who identified it as a result, one from. Abinitio ) calculations the idea of hybridization that exists in this, the orbital... } H_ { 2 } { /eq } ) is sp2 hybridized, along with the hybrid of... First take both carbon and hydrogen in acetylene 2 } H_ { 2 } { /eq } ) is hybridized... Form C-C sigma bonds 1 pi and 2 π bonds ) and 1 single bond i.e. Orbital diagrams for carbon and hydrogen molecule separately and draw their orbital diagrams 1 single bond ( i.e 2s2...: Since C2H2 is nonpolar because of the orbitals angle of 180o { 2 } /eq... Hydrogen through sp_s note that the two carbon atoms here are connected by triple..., therefore the 2s1 and the orbitals meanwhile, the carbon atoms in acetylene students to! -H3C-C-Triple bond-C-H. from left to right: 1st C -- sp2 -- -- -H3C-C-triple bond-C-H. from left to right 1st. 2Pz1 orbitals get hybridised question is, what compound is sp type ethane basically consists of carbon. Of describing double-bonded compounds such as ethene atoms in Ethylene all write orbital diagrams the O in HOCl has lone!


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# Thread: [SOLVED] Desesperate, need help for Best Approximation

1. ## [SOLVED] Desesperate, need help for Best Approximation

I need help for today on this exercise :
Approximate the data in the following table $\begin{array}{c|cccc} x & -1 & 0 & 1 & 2\\ \hline y & -1.1 & -0.4 & -0.9 & -2.7\end{array}$ with a function of the form $f(x)~-e^{ax^2+bx+c}$ in the sens of least squares for the function $ln(-f(x))$.
I understand the problem and I will simplify it for you, so you can help me. They want me to approximate the data given in the table, via a function of the type $f(x)~-e^{ax^2+bx+c}$, which is a too complicated problem. Therefore, in order to do it, we take the natural log of $f(x)$, to approximate a new set of data, which will be $ln(-f(x))$. This is much less complicated to determine a, b and c. After this we just replace a, b and c in f(x) and we're done. But the problem is that I don't know how to get these values.
The problem is simplificated to approximate $\begin{array}{c|cccc} x & -1 & 0 & 1 & 2\\ \hline y & 0.0953 & -0.9163 & -0.105 & 0.993\end{array}$ with a function of the form $ax^2+bx+c$. To get a linear system, I must use the inner product theory to solve the problem.
Let V be the set of $f(-1)$, $f(0)$, $f(1)$, $f(2)$ such that f is a function. Let W be a subset of V, so W={...}. Then I define the inner product between x and y as $\sum_{i=1}^{n}x_iy_i$. From it I must use the normal equations to solve the problem and get a, b and c. But as I don't know how to define W, nor how to construct the normal equations, I'm totally stuck on this.

2. Originally Posted by arbolis
I need help for today on this exercise :
Approximate the data in the following table $\begin{array}{c|cccc} x & -1 & 0 & 1 & 2\\ \hline y & -1.1 & -0.4 & -0.9 & -2.7\end{array}$ with a function of the form $f(x)~-e^{ax^2+bx+c}$ in the sens of least squares for the function $ln(-f(x))$.
I understand the problem and I will simplify it for you, so you can help me. They want me to approximate the data given in the table, via a function of the type $f(x)~-e^{ax^2+bx+c}$, which is a too complicated problem. Therefore, in order to do it, we take the natural log of $f(x)$, to approximate a new set of data, which will be $ln(-f(x))$. This is much less complicated to determine a, b and c. After this we just replace a, b and c in f(x) and we're done. But the problem is that I don't know how to get these values.
The problem is simplificated to approximate $\begin{array}{c|cccc} x & -1 & 0 & 1 & 2\\ \hline y & 0.0953 & -0.9163 & -0.105 & 0.993\end{array}$ with a function of the form $ax^2+bx+c$. To get a linear system, I must use the inner product theory to solve the problem.
Let V be the set of $f(-1)$, $f(0)$, $f(1)$, $f(2)$ such that f is a function. Let W be a subset of V, so W={...}. Then I define the inner product between x and y as $\sum_{i=1}^{n}x_iy_i$. From it I must use the normal equations to solve the problem and get a, b and c. But as I don't know how to define W, nor how to construct the normal equations, I'm totally stuck on this.
Since the assumptions usually made to justify regression will not be satisfied for this problem the main advantage of regression is lost (that is the knowlege of the covariance matrix of the estimators of the coefictents). In which case there is no reason to fiddle around doing this problem that way. I would just throw this into a non-linear least squares tool and let it sort the coefficients out form me.

A suitable tool is the solver that comes with Excell.

RonL

3. I agree that it's not a nice problem. Usually the problem can be done by partial derivatives to find the minimum of a multivariable function. My teacher said that mostly of the time it won't be a linear system, and that's why the problem can be solved implanting an inner product. But in the exercise I just posted, there's something not correct. They want me to solve a problem using a Lemma or I don't know what property without even prove that it works. I mean, if you have a set of points and approximate them by a quadratic function. When you know the coefficient of the parabola (a, b and c), if you have the same set of points given, but the exponential of them. We are using the property that the best approximation of the form $e^{ax^2+bx+c}$ will have the same coefficients than before. Which should be at least explained!
I really hope that tomorrow I won't have to be confronted to such a problem, in my exam.
A suitable tool is the solver that comes with Excell.
Yes, certainly. Almost any program that can do this is better than to do it manually. (too much calculations). But I should understand how to do it handly. Thank you anyway!

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# Can two planes intersect in exactly one point?

Dec 14, 2016

As explained below.

#### Explanation:

Planes are not lines. Only lines intersect at a point. Planes intersect along a line.

Dec 16, 2016

See explanation...

#### Explanation:

The general equation of a plane in three dimensional (Euclidean) space can be written (non-uniquely) in the form:

$a x + b y + c z + d = 0$

Given two planes, we have two linear equations in three variables:

$\left\{\begin{matrix}{a}_{1} x + {b}_{1} y + {c}_{1} z + {d}_{1} = 0 \\ {a}_{2} x + {b}_{2} y + {c}_{2} z + {d}_{2} = 0\end{matrix}\right.$

Either these equations will be inconsistent, or they will have an infinite number of solutions.


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# Tag Info

21

As others have pointed out, mathematically the statements are exactly the same, and the additional term is "redundant". It would also be "redundant" for me to copy their mathematical proofs here. You can also easily verify the statements are equivalent by making a 8 row truth table for the three inputs combinations. A B C A*B + A'*C ...

20

You are approaching this from the wrong direction. You shouldn't have a specification which says "I need such mcu to measure times between two events with precision up to 1 cycle". You should have a specification which says precision of +/- x (milli/micro/nano) seconds. Time units, not cycles. In my experience, many instruction sets have a fixed ...

14

Thanks for everyone's help. I believe Bruce Abbott has given the correct answer. I'm posting from my bed and I cannot test it yet until tomorrow, but The analysis below is confirmed, when he mentioned the word "refresh", I think the problem is already solved. I knew how Z80 refreshes the memory, but completely forgot about it in the previous days. ...

12

Deeper interpretation: The PLL is actually producing clock cycles during that whole time. The problem is that until it achieves "lock", the clock cycles may at times be too short to allow the CPU to operate correctly, as the VCO control voltage swings both above and below the target value before settling down. So what this specification is really telling ...

10

Proof by Boolean algebra: A x B + A' x C [Left-hand side] = A x B x 1 + A' x C x 1 [Unsimplify AND with true] = A x B x (1 + C) + A' x C x (1 + B) [True OR anything] = A x B x 1 + A x B x C + A' x 1 x C + A' x B x C [Distribute] = A x B + A x B x C + A' x C + A' x B x C [Simplify AND with true] = A x B + A' x C + A x B x C + A' x B x C [Rearrange terms] = A ...

9

I assume your question relates to parallel EEPROMs. The Write pulse (time) is a minimum specification and typically has no upper bound. In other words the time specified limits the speed of writing (bits/bytes/words per second), but the chips will operate at any lower write rate. For example here is the datasheet for the 26C64 write timing: Notice there ...

8

Consider the LHS by itself: A x B + A' x C If both B and C are true in this statement, does the condition of A make any difference to the result? No - because either (A x B) or (A' x C) will be true, producing a result of true. So now looking at the RHS, the first 2 AND terms are simply a duplicate of the LHS, and the 3rd AND term represents what we ...

8

Ensure that you have adequate decoupling capacitors on all your ICs. A 100nF ceramic from power to ground on each IC keeping its leads as short as possible and a low ESR electrolytic say 100uF on the breadboard across the power rails.

8

I believe some of the simpler PIC series have constant interrupt latency. For example, the ancient PIC16F84 has latency listed as 3.25 Tcy (or 13 clock cycles). Unless your interrupt request is synchronized with the MCU clock there will be additional +/-0.5 clock cycle. In situations where you might ask this question, usually the answer is to use hardware ...

7

An inexpensive method of measuring rise and fall time limitations of an arbitrary waveform, is to start with a square wave of a moderate frequency, and then systematically increase the frequency while keeping duty cycle constant at 50%. The average intensity of emitted light is easily measured, even by using something as basic as a CdS light-dependent ...

7

It takes a lot of LUTs to build a large mux. For example, if you have 6-input LUTs, you can do a 4:1 mux in one LUT, but it takes 11 LUTs to do a 1-bit 32:1 mux. Your counter is getting replicated (as counter_reg) so that the fanout on any given bit is not excessive. (Although I'm not really sure where the 1024 comes from.) Since you don't really need "...

7

There are several advantages to this methodology that I can think of: Clock Network - Firstly you only have one clock rather than three. This means that there is less competition for global and local clock routing resources. There are usually only a small number of low-skew clock trees, so minimising usage requirements can help routing. ALM Restrictions - ...

7

Imagine you drive something in a PUSH-PULL configuration; then, PWMH can drive the high-side switch, whereas PWML drives the low side switch. Many of these PWM controllers even have a dead-time functionality to guarantee that both switches aren't on simultaneously

7

Looks like a bug to me. I reproduced it on my 1054z using an Arduino with an LED blinking program. This is the signal with 12M memory depth acquired at 500ms timescale, and then expanded at 200 ms scale. The 'beat' is 1000 ms long. (Ok, technically it's 900ms long plus the overhead, but if I add the first part of the next train I get a nice 1000 ms sequence ...

6

Why is the resistor voltage initially equal to supply voltage? Is it because there is no voltage going across the capacitor yet? Therefore, as there is no voltage drop across the capacitor, all the voltage from the battery is across the resistor? Sum of voltages on the passive elements must add up to the supply voltage.  V_{supply}(t) = V_{switch}(t) + ...

6

simulate this circuit – Schematic created using CircuitLab A CMOS schmitt trigger 40106 or 4093 (check the numbers) would work for this. Pick a reasonable value for C1 - 10uF, say. Calculate R so that R * C = 5 s. When the input goes high C1 will charge up. At about 2/3 of supply voltage NOT1 output will switch low and NOT2 will switch high. Q1 will ...

6

Firstly, a real time clock is not what you want. A real time clock is designed to give you the current time, as in year, month, day, hour, minute, second etc. It usually has a battery, so it can keep track of time when the device is switched off, and will be much more complicated than a basic timing device. You want to measure relative time, not absolute ...

6

First, the current sensors. You don't even need to tap into the wires - a properly chosen coil placed next to a "live" mains wire (say, taped to the supply cable) with AC will have current induced in it if considerable (typical for running appliances) current flows through the wire. The values are well within readout range of common ADC inputs, making ...

6

There are complete schematics for the IBM PC/XT in the IBM Personal Computer XT technical reference manual (Appendix D), which you may be able to find on line. The problem here is that, given a strobe line which is activated upon a memory read or write, you wish to generate RAS, CAS and a control line (call it MUX) for the address multiplexer. For ...

6

Inside the SDRAM chip, the actual CAS latency requirement is a combinatorial time delay, independent of the external interface's clock period. It may help to think of it as an old-fashioned asynchronous DRAM chip "wrapped" in a synchronous interface. Since the bus master (CPU) can choose the interface clock speed, it makes sense to also allow it to ...

6

Here's a good clue: - And, if you look at the value for $t_4$ it is quoted here: - So, a new data bit is available between 0 and 40 ns of the falling edge of SCLK. This means you can't rely on the falling edge of SCLK to read valid data. Of course, if you look at $t_7$ it tells you that current data is valid for maybe 7 ns should you attempt to read it ...

6

One way would be to not use interupts for measuring the time at all. Certain processors like the SAMD series from Microchip have an event system, where peripherals can trigger events which lead to other hardware to perform different actions. Considering you want to measure the time taking for charging a Capacitor: Analog Comparator 1 (low Voltage) -> ...

6

Input Capture Many, many microcontrollers have an "input capture" feature. A timer runs freely at a fixed frequency. When an external signal happens, the timer value is copied to a register, and an interrupt is raised. Regardless of the interrupt latency, then, the interrupt handler can read the value in the register and determine the precise ...

5

It is possible to measure optical pulses of LEDs and Lasers to picosecond resolution, and it is something I do regularly as an electronics/photonics person. The trick is to work in the time domain. To give an example of this, I have seen photodiodes exhibiting bandwidths of GHz, 40 GHz is quoted by a previous answer. However, I would imagine such a ...

5

EDID is used, among other things, to query the monitor for the timings it would like. It isn't used to transmit any video information. I guess it's been so long that no one remembers, but VGA monitors back in the day had adjustments for the image location on the CRT. You could move it left or right, up or down, or scale it horizontally or vertically. More ...

5

The start bit servers two purposes, to indicate a new character is being sent and to provide a timing reference for that character. To explain why the UART protocol is what it is, let's start with a simple scheme, see why that doesn't work, then see how to modify it to make it work. You can start out trying to send data using a single signal by simply ...

5

This is more of an "extended comment" than an answer, but let me start by saying no, I don't think you can debug this issue with such a limited set of test equipment. A person who has had a lot of experience doing these designs might be able to get some clues about what's going wrong using them, but I get the impression that you're not such a person. For ...

5

Actually the CS timing is not very important -- you usually assert the CS line (bring it low) at the beginning of a bunch of transfers, and then de-assert it (bring it high) at the end. What is more important is the relationship between the clock (SCK) and the data (SI/SO). Here is a typical timing diagram for an SPI peripheral, in this case a 2AA1024 1 ...

5

1) Routing is always the dominant factor limiting timing. That is why a carry-lookahead is not really faster in FPGA, as the larger adder requires more delays which partly overcome the advantages. Your path has 6 level of logic, which is O.K. It would be very hard to put all paths below 6. However, some nets have a high fanout, which yields longer delays. ...

5

Your question is complicated enough that I'm not even sure what your actual problem is, but I'll try! The "cleanest" 6502-based DRAM design I could find is from the Commodore PET 2001-N. It has a 6502 running at 1 MHz, but the DRAM logic is clocked at 16 MHz, likely to generate all the timings. I have not analyzed the details, but the main action seems to ...

Only top voted, non community-wiki answers of a minimum length are eligible


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Ghost Ship

Lately I’ve been solving some problems on CheckiO, a really addictive programming site, and stumbled upon a very interesting golf mission. So, you might ask: “What are golf missions?!”. The idea is to solve the problem using as little code as theoretically possible. Your score is inversely related to code length and transforms a mildly challenging problem into a very addictive one.

One of the most interesting missions is called Ghost Detect. It might not seem special at first, but it gets tricky as solutions get shorter. The mission goal is to write the shortest possible code to recognize if three consecutive signals sent in binary are of the same length. 11000001100011 is a good signal while 111000100011 is a bad one. There is at least one zero between every group of ones. For each character used (less than 200) you earn 1 point. So, how do we do this?

1. Use regex (77 characters, 123 points)

We find and group zeros at the beginning, followed by at least one zero, and then find exactly one occurence of the first group, then some more zeros etc. Not too complicated, but only 123 points. Can we do better?

2. Use the sets, Luke (63 characters, 137 points)

Here we combine regex and sets to check how many different groups of repeating ones are present in binary representation.

3. Ditch the regex (57 characters, 143 points)

This is about as far as a “Pythonic” road will take you. Split on zeros, convert to sets, remove empty set to avoid messing with the count and check if less than two.

Now what?

To further shorten it, we need to try a different approach - binary. In binary, when you multiply by 2, you shift all the bits one position to the left. So, for example, 00010 multiplied by 2 becomes 00100. A valid signal, according to the task, is a number with three groups of ones equally long with zeros inbetween. This actually means it’s made of a number multiplied by a power of two, then the same number was multiplied by some other power of two and added, and then the same number was added again. For example, $111000111000111$ is actually $111_2 \cdot 2^{12} + 111_2 \cdot 2^{6} + 111_2$.

Therefore, we can write a generalized form for such a number n being equal to

The number should, then, be divisible by both k and r without reminder. First variant that comes to mind is to test if n divided by k equals r. But we have neither k nor r, and the only thing we have to work with is the number given to our function. We have to think of a way to get the number using bit manipulation.

So, now we have k with some bit tricks expressed like n AND n XOR n+1. To find r, we divide n by k and realize it’s basically the original number with sequences of ones reduced to a single 1. We can achieve this too with a little bit manipulation.

4. Bit banging:

We are testing for this simple expression.

Down to 39 characters and 161 points. Can we do even better? Suprisingly, yes!

5. Getting rid of k

If we test divisibility by k, it is easy to construct a number divisible by k which doesn’t satisfy the constraint - e.g. 110011110011. Therefore, we must test divisibility by the other factor, r. Since zeros between the ones are ensured by initial conditions, divisibility by r guarantees the required form.

Our solution is now only 33 characters long (function definition takes 19), and we scored 167 points. There is a trick to get 2 more points which I’m not going to disclose. Can you find it?

Can we go above 169?

I don’t think so, but please tell me if you think of a way! :) Hopefully you enjoyed reading about it as much as I’ve enjoyed solving it! If you have another, original solution to this problem feel free to email me and help my curiosity!

Cheers.


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Given an array of integers, find an equilibrium index. An equilibrium index of an array is an index such that the sum of elements at lower indexes is equal to the sum of elements at higher indexes.

Edit 2017.07.01 Added three more example input & output. Fixed an off-by-one error in the Ruby implementation.

For example, consider the following array A.

Index 3 is an equilibrium index.

Index 6 is also an equilibrium index, because sum of zero elements is zero.

Index 7 is not an equilibrium index, because it is not a valid index of array A.

Input. The input file consists of one or more arrays, each on a single line. Each array consists of a sequence of integers, each pair separated by a single space. The input file is terminated by an EOF character. Consider the following example.

Output. The output file consists of an output line for each array in the input. Each output line consists of an equilibrium index (if any) or -1 when no equilibrium index exists. For example, the following output corresponds to the previous example input.

# Solution

The proposed solution is O(n).

Just consider each position of a given array, from left to right. Start with a variable l for the left sum set to zero and a variable r for the right sum set to the sum of all elements except the first. Then, as you go from left to right, add the element that becomes part of the left side to l and subtract from r the element that leaves the right side. Return the current index when l and r are equal.

# Ruby implementation

I love to explain and answer questions on programming problems, the kind you find in coding interviews. I publish a new programming problem and its solution every Sunday. Did I mention that I love to answer questions?

If you would like to get the latest problem + solution, subscribe to the newsletter or subscribe via RSS. You can also follow me on Twitter, GitHub, and LinkedIn.


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# Fibonacci and Square Numbers - The Court of Frederick II

Author(s):

The Book of Squares is addressed to Frederick II, the Holy Roman Emperor, ruler of Germany and southern Italy. The outline of Leonardo's life is given elsewhere on this web site, but it is worthwhile to consider the context of this particular work in more detail. Frederick II had a tremendous hunger for knowledge. In spite of his German roots, he was most at home in Sicily, an intersection point for Latin, Greek, and Arabic culture. Scholars from all three were brought to his court. Frederick was called stupor mundi, "the wonder of the world," because his behavior was so astonishing by medieval standards. As an example, we have a rare instance of mathematics being used as a tool of diplomacy. Frederick felt obligated to participate in the Crusades, but instead of attacking Jerusalem with his superior force he set up camp outside and patiently worked out a peaceful takeover. Frederick and Sultan al-Kamil arranged what we might call cultural exchanges to ease tensions as the negotiations proceeded, and at one point a list of mathematical problems was sent to the Arabic scholars of Jerusalem as a friendly challenge [p. 217]. Click here for more information on Frederick's crusade. Click here for more biographical information on Frederick.

Leonardo was clearly delighted by the spirit present at Frederick's court. His book Liber abbaci was dedicated to Michael Scott, Frederick's closest advisor on scientific matters [pp. 306-7]. Two other scholars associated with Frederick, John of Palermo and Master Theodore, appear in The Book of Squares. In fact, the book begins with Leonardo's explanation of how a question from John prompted his research, and an answer to a question from Theodore brings the book to a close. The initial challenge from John of Palermo was this:

Find a square number from which, when five is added or subtracted, always arises a square number [p. 3].

In modern notation this means finding $$x,y,$$ and $$z$$ so that $$x^2 + 5 = y^2$$ and  $$x^2 - 5 = z^2.$$

This is easy enough if you allow irrational solutions, for instance taking $$x=\sqrt{17},$$ $$y=\sqrt{22},$$ and $$z=\sqrt{12}.$$ But further reading makes it clear that Leonardo is looking for a rational solution (it is not hard to see that a solution in integers is impossible). His work then leads him to consider many more questions about sums and differences of squares.

Patrick Headley, "Fibonacci and Square Numbers - The Court of Frederick II," Loci (August 2011)


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# Bennett's laws

Bennett's laws of quantum information are:

1. 1 qubit ${\displaystyle \geqslant }$ 1 bit (classical),
2. 1 qubit ${\displaystyle \geqslant }$ 1 ebit (entanglement bit),
3. 1 ebit + 1 qubit ${\displaystyle \geqslant }$ 2 bits (i.e. superdense coding),
4. 1 ebit + 2 bits ${\displaystyle \geqslant }$ 1 qubit (i.e. quantum teleportation),

where ${\displaystyle \geqslant }$ indicates "can do the job of".

These principles were formulated around 1993 by Charles H. Bennett.

## References

• Quantum Mechanics: The Physics of the Microscopic World, Benjamin Schumacher, The Teaching Company, lecture 21


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# Complex power of a complex number

Can someone explain to me, step by step, how to calculate all infinite values of, say,

$(1+i)^{3+4i}$?

I know how to calculate the principal value, but not how to get all infinite values...and I'm not sure how to insert the portion that gives me the other infinity values.

-
You may find this of assistance: math.stackexchange.com/questions/9776/… –  RecklessReckoner Aug 27 '13 at 2:24
It may help to separate the complexity into simpler parts: $(1+i)^3(1+i)^{4i}$ as a start... –  abiessu Aug 27 '13 at 2:26

When you write your complex number as an e-power, your problem boils down to taking the Log of $(1+i)$. Now that is $\ln\sqrt{2}+ \frac{i\pi}{4}$ and here it comes: + all multiples of $2i\pi$. So in your e-power you get $(3+4i) \times (\ln\sqrt{2} + \frac{i\pi}{4} + k*i*2\pi)$ I would keep the answer in e-power form. You can now work it out.

-

Let's suppose you've already defined $\log r$ for real $r > 0$, say, using Taylor series. Then given $z, \alpha \in \mathbb{C}$, you can define $$z^{\alpha} = \exp(\alpha \log z)$$ where

$$\exp(w) = \displaystyle \sum_{j=0}^{\infty} \dfrac{z^j}{j!} \qquad \text{and} \qquad \log(w) = \log |w| + i \arg(w)$$

This is not well-defined - it relies on a choice of argument, which is well-defined only up to adding multiples of $2\pi$. It's these multiples of $2\pi$ which give you new values of $z^{\alpha}$.

Explicitly, if $w$ is one value of $z^{\alpha}$, then so is $$w \cdot e^{2n \pi \alpha i}$$ for any $n \in \mathbb{Z}$.

Fun facts ensue:

• if $\alpha$ is an integer then $z^{\alpha}$ is well-defined
• if $\alpha$ is rational then $z^{\alpha}$ has finitely many values
• if $\alpha$ is pure imaginary then $z^{\alpha}$ is real (but not well-defined)
-
I think you meant to write, “then so is $w\cdot\exp(\alpha+2n\pi i)$”, which also affects your last bulleted statement. –  Lubin Aug 27 '13 at 4:41

$Let (1+i)^{3+4i}=k$

Taking ln on both sides gives us $(3+4i)log_e{(1+i)}=log_ek\cdots(1)$

also $(1+i)=\sqrt{1^2+1^2}e^{\frac{i\pi}4}=\sqrt2e^{\frac{i\pi}4}\cdots(2)$

$log_e(1+i)$=$log_e$($\sqrt2e^{\frac{i\pi}4}$)

Substituting $(2)$ in $(1)$ we get

$(3+4i)(log_e\sqrt2+{\frac{i\pi}4}) = log_ek$

or $k = e^{(3+4i)(log_e\sqrt2+{\frac{i\pi}4})}$

NOTE :

GENERALISATION: To evaluate numbers of the form $(a+ib)^{c+id}$

Let $\sqrt{a^2+b^2}=r$ and argument of $a+ib$ be $\theta$

Then $(a+ib)=re^{i\theta}$ = $e^{log_e(r)+i\theta}$

Hence, $(a+ib)^{c+id}=e^{{log_e}{(r)(c+id)+i\theta}(c+id)}$

-

Let us find in general $w^z$ where $w$ and $z$ are complex. This expression is by definition equal to $$\exp\{z\ln w\}$$ where $\ln w$ is one of the complex logarithms of $w$. That is, it is $w'$ where $$e^{w'} = w.$$ Suppose $w = re^{i\theta}$. Then $$w' = \ln r + i\theta +2ik\pi$$ where $k$ is an arbitrary integer and the $\ln$ is the ordinary real-valued logarithm. (Since $r\ge 0$ this is well-defined everywhere except for $r=0$, in which case we are dealing with $0^z$, which really is ambiguous.)

Putting this back into the original formula we have the answer, that \begin{align} (re^{i\theta})^z & = \exp\{z (\ln r + i\theta + 2ik\pi)\}\tag{\star} \\ & =\exp\{z(\ln r + i\theta)\}\cdot \exp\{2ik\pi\cdot z\} \end{align} where $k$ is an integer.

Now observe that although $(\star)$ seems to list an infinite number of solutions, they are not always distinct. For example, when $z$ is a real integer, the second factor, $\exp\{2ik\pi\cdot z\}$ part is 1 for every choice of $k$, and so can be disregarded.

To find out how many values of $(\star)$ are distinct, one needs to ask about the values of $e^{2ik\pi \cdot z}$. When $z$ has nonzero imaginary part, or is a real irrational, these are all distinct and there are an infinite family of values of $w^z$, given by different choices of $k$. But when $z$ is a real rational number with (lowest-terms) denominator $n$, there are exactly $n$ distinct values.

-


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# How to map the electrostatic potential from GAUSSIAN, on a solvent accessible surface?

Gaussian cubegen and surface generators in Gaussview seem to only allow to map the ESP on SCF densities. I used G16 for the ESP generation. I would like to plot it on the solvent accessible surface. Is there any (free) software that allows me to do that?

The Jmol software is able to plot different surfaces.

In the example below, the system is a Mobius strip and the ESP was calculated using MOPAC but as Jmol is full compatible with Gaussian outputs, I think there will be no problem.

Mobius strip structure:

Mobius solvent-accessible surface (SAS):

Mobius electrostatic potential mapped on solvent-accessible surface:

To obtain the images above, the procedure was:

• load the output file from MOPAC with the graphical information.
• open the script console.
• create the SAS with the command: isosurface ignore(solvent) sasurface 1.2
• map the electrostatic potential on SAS with the command: isosurface resolution 6 sasurface map mep


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# The Tectonic Typesetting System

Tectonic is a modernized, complete, self-contained TeX/LaTeX engine, powered by XeTeX and TeXLive. This book aims to document the core elements of the Tectonic software system.

Without further ado, we suggest you start with the Introduction!

## Contributions are welcome!

This book is, clearly, a work in progress! Contributions of any kind are most welcome — please see the discussion in GitHub issue #62 for some ideas of things that should be documented here.

The documentation is written in Markdown (specifically, CommonMark using pulldown-cmark) and rendered into HTML using mdbook. The source code lives in the docs/ subdirectory of the main tectonic repository. To make and view changes, all you need to do is install mdbook, then run the command:

and the result is that you get a printout of information about different options and arguments that you can pass to the Tectonic program. (Here and elsewhere we’ll use a convention of a leading $to indicate a command that you should run at your computer’s command prompt. You don’t type the dollar sign itself.) To be explicit, Tectonic does not invoke an external latex program, and Tectonic is not a “wrapper” for (La)TeX. Tectonic is the LaTeX program. This is essential. The goals of the Tectonic project involve a fundamental transformation of how we use TeX to create technical documents, and it is not possible to achieve that without radical surgery to the heart of how TeX has traditionally operated. # Getting Started: Build Your First Document Now that you’ve installed Tectonic, let’s create and build your first document. Important: From here on out, this Getting Started guide will use what we call the “V2” interface to the Tectonic program. The V2 interface coexists with, but has a fairly different approach than, the “V1” interface. We are gradually migrating from V1 to V2. Neither interface (V1 or V2) is the same as the one exposed by classic TeX tools such as pdflatex. ## Create a new document The Tectonic V2 interface has a “multitool” structure similar to that of other powerful tools such as git and cargo. To create a new document, we use a new subcommand that looks like this:$ tectonic -X new myfirstdoc

This will create a new Tectonic workspace directory named myfirstdoc containing a file Tectonic.toml and a sub-directory named src. Enter this new directory in your command prompt.

$cd myfirstdoc Note: The -X flag activates the V2 interface. Don’t forget it! Eventually it will become unnecessary and you’ll just be able to write tectonic new, but that changeover hasn’t happened yet. If you’ve got an existing TeX file, you can process it in in one-off fashion with:$ tectonic -X compile myfile.tex

See the tectonic -X compile documentation for all of the options.

## Basic document source structure

The source code to your document is stored in the src subdirectory of your new document. Check it out:

$ls src You’ll see three files that were created by the new command: • _preamble.tex • index.tex • _postamble.tex These files are pre-populated with extremely basic contents following this suggested source structure: • The “preamble” file should contain all of your (La)TeX initialization boilerplate, up to and including the LaTeX \begin{document} command. • The “index” file contains all of your actual document content, without any of the annoying boilerplate. When you create a new Tectonic document, it just contains the text Hello, world. • The “postamble” file should contain all of your cleanup code, starting with the LaTeX \end{document} command. There will almost never need to be any other content in this file. When Tectonic builds your document, it processes these files in the order listed above, so all three of them need to be available. But the breakdown suggested above is only a suggestion, nothing more. If you want all of your boilerplate and content to be in a single file, we recommend putting it all in index.tex and making your preamble and postamble be empty. The motivation for this separation is partially stylistic, but not entirely so. In the future, we anticipate that there might be different ways to build the same document that invoke different preamble or postamble contents. ## Building your document To compile your document, run:$ tectonic -X build

If you haven’t run Tectonic on your computer before, this command will take a minute or two as it downloads the support files that it needs and generates the LaTeX “format file” storing the default macro collection. Tectonic will cache these files and avoid downloading them again. Test it out by running the build again:

$tectonic -X build This time the command should finish much more quickly, with no messages about downloading files. The output PDF document will be placed at the path build/default/default.pdf relative to your document directory:$ ls -l build/default/

If you’re familiar with traditional TeX engines, you’ll have noticed that Tectonic’s “user experience” is substantially different from those engines:

1. Tectonic doesn’t print out the usual chatter — unless there’s an error.
2. Tectonic automatically reruns the TeX stage until its output stabilizes.
3. By default, Tectonic doesn’t write out intermediate files such as (texput.aux, texput.log).
4. You ought not have seen this yet, but if you make a mistake in your TeX, Tectonic will quit with an error message, rather than asking you to type X2 or whatever.

We hope that you’ll agree that these changes make for a program that is much more pleasant to use than the traditional tools.

## Cache

The location of the cache depends on your operating system. You can use the V2 Interface to find the exact cache location on your machine or take a look at the implementation.

If you need to change the location of the cache, you can do that by setting the environment variable TECTONIC_CACHE_DIR to the path of a directory. We recommend leaving the cache location at the default unless there is a compelling reason to change it.

# Getting Started: Use a Unicode Font

You’ve created your first Tectonic document. Great! Now, let’s start exploring the ways in which Tectonic helps you create modern technical documents.

We’ve already seen a few ways that Tectonic differs from traditional TeX engines. Perhaps the most fundamentally important difference, however, is the one that we’ll explore in this section.

Note: This Getting Started guide uses what we call the “V2” interface to the Tectonic command-line tool. The V2 interface coexists with, but has a fairly different approach than, the “V1”interface. We are gradually migrating from V1 to V2. Neither interface (V1 or V2) is the same as the one exposed by classic TeX tools such as pdflatex.

## Unicode

When TeX was first developed more than 40 years ago, digital systems for representing human writing were pretty primitive. Because TeX needed to represent a variety of languages and mathematics, it was endowed with comparatively sophisticated tools to both accept and emit characters that aren’t found in standard English. TeX’s good multi-lingual support was one of the things that made it groundbreaking. Eventually, however, a consortium of major technology companies developed the much more comprehensive Unicode standards for representing the world’s writing systems digitally. By now, they’re universally adopted. So while the TeX ecosystem started out ahead of the curve, some of its core systems are designed around an incompatible and, frankly, dead-end framework.

That is not to imply that the whole TeX universe is stuck in the past! Many people have worked extremely hard to bridge the worlds of TeX and Unicode. The code in Tectonic, in particular, is based on XeTeX, which adds Unicode support to the classic TeX experience. Without the efforts of the XeTeX team and many other dedicated volunteers in the TeX world, Tectonic wouldn’t be able to offer Unicode support.

## Modern Fonts

Tectonic’s support for Unicode allows it to take advantage of modern fonts that are distributed using formats such as OpenType. Besides opening up access to a whole world of typographic progress — a good font is the result of years of expert effort — this support positions Tectonic to create outputs in not just PDF but HTML formats. HTML capability is still under development, but it’s one of the prime reasons that the Tectonic project was started.

The choice of fonts is foundational to TeX’s document processing, so modern fonts aren’t automatically activated. To start using a nice new font like TeX Gyre Pagella (derived from Palatino), open up your src/_preamble.tex file and add the following lines after the \documentclass command:

\usepackage{fontspec}
\setmainfont{texgyrepagella}[
Extension = .otf,
UprightFont = *-regular,
BoldFont = *-bold,
ItalicFont = *-italic,
BoldItalicFont = *-bolditalic,
]

Now rebuild your document:

$tectonic -X build You’ll probably see Tectonic download some files: namely, the new font files that you have started using. Tectonic’s ability to fetch such files on the fly is why its installation is so much easier than a traditional TeX engine. If you open up your rebuilt document, it will be using your new font, although the difference can be difficult to detect with such a small amount of sample text. ## Unicode Input Text Tectonic’s support for Unicode broadens its output capabilities through the use of modern fonts. But that’s not all: Unicode also broadens Tectonic’s the inputs that Tectonic accepts. With Tectonic, you can type non-English characters directly into your input TeX files, which are parsed assuming the virtually-universal UTF-8 Unicode text encoding. For instance, you can open up your src/index.tex file and copy-paste in the following verse with accented characters: Ô que ma quille éclate! Ô que j’aille à la mer! Rebuild your document and see your new text in the output:$ tectonic -X build

Whatever, you might say. I know how to get these accented characters with TeX commands:

\^O que ma quille \'eclate! \^O que j'aille \a la mer!

Fair enough. But now try typing in Bashô’s “old pond” haiku:

ふるいけやかわずとびこむみずのおと

We’ll wait.

(Note, however, that if you copy-paste this text into our sample document, it won’t work: you haven’t activated a font able to handle the Japanese characters. You’ll get a lot of warnings to that effect.)

# The Tectonic Implementation of the TeX Language

TODO: links to TeX language guides

TODO: document customizations, e.g. \TectonicCodaTokens.

# tectonic -X build

Build the current document.

This is a V2 CLI command. For information on the original (“V1” CLI), see its reference page.

#### Usage Synopsis

tectonic -X build
[--keep-intermediates]
[--keep-logs]
[--only-cached]
[--print]
[--open]
[--untrusted]

#### Remarks

This command builds the current document, as identified by searching for a Tectonic.toml file in the current directory or one of its parents. The build artifacts will be placed into the document’s build output directory, which defaults to a subdirectory build of the document source directory.

#### Command-Line Options

The --keep-intermediates option (or -k for short) will cause the engine to save intermediate files (such as mydoc.aux or mydoc.bbl) in the build output directory. By default, these files are stored in memory but not actually written to disk.

The --keep-logs option will cause the engine to save the main TeX log file (mydoc.log) to disk. By default, this information is discarded.

The --only-cached option (or -C for short) will configure the engine to refuse to connect to the network when searching for support files. This can be useful if you’re working on a document in a context where the Internet is unavailable (e.g., on an airplane). While the engine generally avoids unnecessary network connections, referencing a new file in your document will cause it to look for that file in the online support bundle.

The --print option (or -p for short) will cause the engine to print the regular terminal output of the TeX engine. This output is similar to, but not identical to, the contents of the log file. By default, this output is only printed if the engine encounteres a fatal error.

The --open option will open the built document using the system handler.

Use the --untrusted option if building untrusted content. This is not the default because in most cases you will trust the document that you’re building, probably because you have created it yourself, and it would be very annoying to have to pass --trusted every time you build a document that uses shell-escape. See the security discussion in the documentation of the compile command for details. In actual usage, it would obviously be easy to forget to use this option; in cases where untrusted inputs are a genuine concern, we recommend setting the environment variable TECTONIC_UNTRUSTED_MODE to a non-empty value. This has the same effect as the --untrusted option. Note, however, that a hostile shell user can trivially clear this variable.

# tectonic -X bundle

Commands relating to Tectonic’s “bundles” of support files.

This is a V2 CLI command. For information on the original (“V1” CLI), see its reference page.

The bundle subcommands are:

## tectonic -X bundle cat

Print out a file stored in the current document’s backing bundle.

#### Usage Synopsis

tectonic -X bundle cat <FILENAME>

$tectonic -X bundle cat latex.ltx %% %% This is file latex.ltx', %% generated with the docstrip utility. ... #### Remarks If this command is run outside of a document workspace, the system default bundle will be used. ## tectonic -X bundle search Print out the names of files in the current document’s backing bundle, potentially with filtering. #### Usage Synopsis tectonic -X bundle search [TERM] #### Example$ tectonic -X bundle search minted
minted1.sty
tcbminted.code.tex
minted.4ht
minted.sty

#### Remarks

If no term is specified, all of the files in the bundle are printed. The ordering of those filenames is unspecified.

The default search method is to use simple substring matching. Other methods may be added in the future, activated by additional options.

If this command is run outside of a document workspace, the system default bundle will be used.

# tectonic -X compile

Compile a standalone TeX document.

This is a V2 CLI command. For information on the original (“V1” CLI), see its reference page.

#### Example

Generate myfile.pdf from myfile.tex:

tectonic -X compile myfile.tex

#### Usage Synopsis

tectonic -X compile  # full form
[--bundle PATH] [-b PATH]
[--chatter LEVEL] [-c LEVEL]
[--color WHEN]
[--format PATH] [-f]
[--hide PATH...]
[--keep-intermediates] [-k]
[--keep-logs]
[--makefile-rules PATH]
[--only-cached] [-C]
[--open]
[--outdir DIR] [-o]
[--outfmt FORMAT]
[--pass PASS]
[--print] [-p]
[--reruns COUNT] [-r COUNT]
[--synctex]
[--untrusted]
[--web-bundle URL] [-w]
[-Z UNSTABLE-OPTION]
TEXPATH

#### Remarks

This command compiles a freestanding TeX document, outside of the Tectonic document framework. It is virtually the same interface as the “V1” command-line interface, with lots of options. In comparison, the V2 interface is “cargo-like”, with a variety of subcommands anchored around a Tectonic.toml file defining a document to build.

Basic usage of this command is often as simple as:

tectonic -X compile myfile.tex

This will compile the file and create myfile.pdf if nothing went wrong. You can use an input filename of - to have Tectonic process standard input. (In this case, the output file will be named texput.pdf.)

##### Security

By default, the document is compiled in a “trusted” mode. This means that the calling user can request to enable certain engine features that could raise security concerns if used with untrusted input: the classic example of this being TeX's “shell-escape” functionality. These features are not enabled by default, but they can be enabled on the command line; in the case of shell-escape, this is done with -Z shell-escape.

If the command-line argument --untrusted is provided, these features cannot be enabled, regardless of other settings such as -Z shell-escape. So if you are going to process untrusted input in a command-line script, as long as you make sure that --untrusted is provided, the known-dangerous features will be disabled.

Furthermore, if the environment variable TECTONIC_UNTRUSTED_MODE is set to a non-empty value, Tectonic will behave as if --untrusted were specified, regardless of the actual command-line arguments. Setting this variable can provide a modest extra layer of protection if the Tectonic engine is being run outside of its CLI form. Keep in mind that untrusted shell scripts and the like can trivially defeat this by explicitly clearing the environment variable.

#### Options

The following are the available flags.

ShortFullExplanation
-b--bundle <PATH>Use this Zip-format bundle file to find resource files instead of the default
-c--chatter <LEVEL>How much chatter to print when running. Possible values: default, minimal
--color <WHEN>When to colorize the program’s output: always, auto, or never
--format <PATH>The name of the "format" file used to initialize the TeX engine. Default: latex
-h--helpPrints help information
--hide <PATH>...Tell the engine that no file at <PATH> exists, if it tries to read it
-k--keep-intermediatesKeep the intermediate files generated during processing
--keep-logsKeep the log files generated during processing
--makefile-rules <PATH>Write Makefile-format rules expressing the dependencies of this run to <PATH>
-C--only-cachedUse only resource files cached locally
--openOpen the output PDF after it is built
-o--outdir <OUTDIR>The directory in which to place output files. Default: the directory containing INPUT
--outfmt <FORMAT>The kind of output to generate. Possible values: pdf (the default), html, xdv, aux, format
--pass <PASS>Which engines to run. Possible values: default, tex, bibtex_first
-p--printPrint the engine's chatter during processing
-r--reruns <COUNT>Rerun the TeX engine exactly this many times after the first
--synctexGenerate SyncTeX data
--untrustedInput is untrusted: disable all known-insecure features
-V--versionPrints version information
-w--web-bundle <URL>Use this URL find resource files instead of the default
-Z-Z <UNSTABLE-OPTION>Activate experimental “unstable” options

#### Unstable options

The following unstable options may be available. As the name aims to indicate, the set of unstable options is subject to change at any time.

ExpressionExplanation
-Z helpList all unstable options
-Z continue-on-errorsKeep compiling even when severe errors occur
-Z min-crossrefs=<num>Equivalent to bibtex's -min-crossrefs flag. Default vaue: 2
-Z paper-size=<spec>Change the initial paper size. Default: letter
-Z search-path=<path>Also look in <path> for files (unless --untrusted has been specified), like TEXINPUTS. Can be specified multiple times.
-Z shell-escapeEnable \write18 (unless --untrusted has been specified)

# tectonic -X dump

Run a partial document build and dump the contents of a TeX intermediate file to standard output. This can be useful if you have an external tool that parses such files, and you wish to integrate it into Tectonic-based authoring workflows.

This is a V2 CLI command. For information on the original (“V1” CLI), see its reference page.

#### Example

Generate and print the LaTeX aux file for the current document:

tectonic -X dump -s aux

This output can, for example, be piped into bibtools to generate a .bib file that provides exactly the records needed for the document build.

#### Usage Synopsis

tectonic -X dump
[--only-cached] [-C]
[--untrusted]
[--profile PROFILE] [-p PROFILE]
[--suffix] [-s]
<FILENAME-OR-PATTERN>

#### Remarks

This command runs a partial build of the current document, as identified by searching for a Tectonic.toml file in the current directory or one of its parents.

The “partial build” consists of one pass of the TeX engine. Future versions of this tool might gain options allowing you specify different passes. This command can be used to dump any file created by TeX during the build (so long as it's created on the first pass).

#### Command-Line Options

The --only-cached option (or -C for short) will configure the engine to refuse to connect to the network when searching for support files. This can be useful if you’re working on a document in a context where the Internet is unavailable (e.g., on an airplane). While the engine generally avoids unnecessary network connections, referencing a new file in your document will cause it to look for that file in the online support bundle.

The --profile option (or -p for short) will select which document output profile will be used for the build. If unspecified, the profile to use will be effectively chosen at random.

If the --suffix (-s) argument is provided, the name of the dumped file simply has to end with the content of the argument FILENAME-OR-PATTERN, rather than matching it exactly. Therefore tectonic -X build -s aux will dump the LaTeX aux file regardless of its complete name, and tectonic -X build -s log will dump the log file. If there happens to be more than one file whose name ends with your specified suffix, they will all be dumped, in a pseudo-random order.

Use the --untrusted option if working with untrusted content. This is not the default because in most cases you will trust the document that you’re building, probably because you have created it yourself, and it would be very annoying to have to pass --trusted every time you dump a document that uses shell-escape. See the security discussion in the documentation of the compile command for details. In actual usage, it would obviously be easy to forget to use this option; in cases where untrusted inputs are a genuine concern, we recommend setting the environment variable TECTONIC_UNTRUSTED_MODE to a non-empty value. This has the same effect as the --untrusted option. Note, however, that a hostile shell user can trivially clear this variable.

# tectonic -X new

Create a new Tectonic workspace.

This is a V2 CLI command. For information on the original (“V1” CLI), see its reference page.

#### Usage Synopsis

tectonic -X new [DIRECTORY]

If {DIRECTORY} is unspecified, the workspace is created in the current directory.

#### Remarks

This command will create a bare-bones Tectonic.toml file in the target directory. The project’s name will be initialized to the name of the workspace directory.

It will also create placeholder source files in a src subdirectory: index.tex, _preamble.tex, and _postamble.tex. The default build command will process these files in the expected order:

1. src/_preamble.tex
2. src/index.tex
3. src/_postamble.tex

The intention of this framework is to allow you to isolate the main content of your document from the usual LaTeX boilerplate. There are no restrictions on what kind of content may be placed in each file, though.

# tectonic -X show

Display various useful pieces of information.

This is a V2 CLI command. For information on the original (“V1” CLI), see its reference page.

The show subcommands are:

## tectonic -X show user-cache-dir

Print out the location of Tectonic’s default per-user cache directory.

#### Usage Synopsis

tectonic -X show user-cache-dir

#### Example

$tectonic -X show user-cache-dir /home/knuth/.cache/Tectonic # Unix$ tectonic -X show user-cache-dir
/home/knuth/Library/Caches/Tectonic # macOS

### Arch Linux

For users of Arch Linux, there are two Tectonic packages available: tectonic from the official repositories, which can be installed with

$sudo pacman -S tectonic and tectonic-git from the AUR. ### Homebrew There is a tectonic package in Homebrew. If you already have Homebrew installed, installing Tectonic should be as simple as:$ brew install tectonic

We also have instructions about installing Tectonic’s dependencies using Homebrew if you’d like to compile Tectonic yourself on your Homebrew-based computer.

### MacPorts

There is a tectonic port in MacPorts. If you already have MacPorts installed, installing Tectonic should be as simple as:

$sudo port install tectonic ### nix or nixOS If you're using nix, you can imperatively install tectonic with:$ nix-env -f '<nixpkgs>' -iA tectonic

in your shell. You can also create a temporary environment using nix-shell:

## Compile Tectonic Yourself

You can always compile Tectonic yourself. If your system has C++ and Rust compilers installed, this may be as simple as running:

$cargo install tectonic However, Tectonic requires various C/C++ support libraries that may not be available on your system by default. There are also various build options that you can turn on and off if you have more specialized needs. For all the details, consult the How To Build Tectonic guide. # How To: Build Tectonic This document lays out the options available for building the Tectonic Rust crate and/or executable from source code. Because Tectonic relies on a large number of system libraries and tightly-integrated C/C++ code, it can be more challenging to compile than most Rust code. For this reason, if you just want to run Tectonic, we recommend that you start by installing a pre-built version if possible. Using a pre-compiled binary will save you time and, possibly, headaches. ## Basic Prerequisites To build Tectonic you will need Rust, C, and C++ compilers installed. It is beyond the scope of this document to give instructions on this topic, besides pointing you to the Rust installation page. You do not necessarily need to download a copy of the Tectonic source code, if the cargo install command will meet your needs. ## Third-Party Dependencies Tectonic relies on a number of well-established third-party libraries that deal with fonts, Unicode, text shaping, and so on. Specifically: • fontconfig for discovering system fonts (except on macOS) • freetype2 for parsing font files • graphite2 for shaping certain unusual scripts • Harfbuzz for text shaping • ICU4C for Unicode data and algorithms • libpng for parsing PNG images • OpenSSL for HTTPS if you’re not on a Mac or Windows machine (or whichever SSL library is required for your system by the rust-native-tls crate) • zlib for compression algorithms To build Tectonic, your first task is to decide where you want these library dependencies to come from. • Tectonic can provide some dependencies internally (“vendor” them). This is the default for Harfbuzz. You can use Cargo features, described below, to control when this happens. For some third-party libraries needed by Tectonic, vendoring is not possible. • You can install the dependencies externally, with a system such as your OS’s package manager, and tell the Tectonic build system how to access them. Read how to install Tectonic’s dependencies externally for quick recipes as to how to do that. • As an intermediate approach, you can use cargo-vcpkg to compile the dependencies for Tectonic’s use with vcpkg. Read this page to learn how to do that. You’ll have to set up one of two ways for the Tectonic build system to gather the appropriate information about how to compile against the external dependencies: • pkg-config, the default system, is the appropriate choice in most cases. Generally all you need to do is make sure that the pkg-config program is installed using the same framework as you used to install the library dependencies. You can force the Tectonic build system to use pkg-config for dependency discovery by setting the environment variable TECTONIC_DEP_BACKEND to the value pkg-config. • vcpkg is the choice to use if you installed your dependencies this way, either using cargo-vcpkg or separately. Activate this mode by setting the environment variable TECTONIC_DEP_BACKEND to the value vcpkg. If using pkg-config, setting the environment variable TECTONIC_PKGCONFIG_FORCE_SEMI_STATIC will cause the build system to attempt to link with external libraries statically rather than dynamically. System libraries, such as libc and libm on Unix systems, will still be linked dynamically. This mode is planned to be superseded by better support for “vendoring” dependent libraries. ## Choose Cargo Features The Cargo build framework offers the concept of features to control build options. Tectonic offers the following features: • external-harfbuzz. By default, the Tectonic crates will build and link to a “vendored” (static, internal) version of the Harfbuzz text shaping library. If you would like to link to an externally-supplied version instead, enable this feature. • geturl-curl. Uses the curl crate to get URLs. In order for this to take effect, you must use --no-default-features because geturl-reqwest is a default feature and it takes precedence. • geturl-reqwest (enabled by default). Uses the reqwest crate to get URLs. This is a good portable default. • native-tls-vendored. If using reqwest, activate the vendored option in the native-tls crate, causing OpenSSL to be vendored. This can be useful when cross-compiling or building static binaries, but is discouraged because that means that the resulting binaries won't benefit from security fixes to system TLS libraries. Some lesser-used features are: • serialization (enabled by default). Disabling this feature turns off all Tectonic features that require the serde crate. This option is provided because Tectonic’s use of serde requires procedural macro support, which is not available by default on static-only compilation environments. However, it is likely that serialization support will become mandatory in the future, and one can still produce static tectonic executables using a cross-compilation approach. Therefore we do not recommend that you rely on this feature. • profile. Compile Tectonic code in such a way as to make it profile-able. In particular, this forces the C/C++ compiler to include frame pointer information unless it is known that such information is not needed for profiling on the target platform. To avoid activating a feature that is enabled by default, you must pass the --no-default-features flag to the cargo command that you run. Features are enabled with a flag such as --features "serialization profile". ## Compile the Code To build the latest released version of Tectonic without needing to download its source code, first ensure that your build environment variables are set up properly and determine what feature flags you need. Then run: cargo install tectonic inserting any feature flags after the install. To install the latest version from Git, do the same but use: cargo install --git https://github.com/tectonic-typesetting/tectonic.git Many other variations are possible. See the cargo install documentation for more. If you have downloaded its source code (perhaps because you wish to make your own improvements), make sure that you’re inside the Tectonic source tree and run: cargo build once again adding any feature flags and ensuring that any necessary build environment variables are set up properly. Read The Cargo Book for vastly more information about where you can go from there. # How To: Build Tectonic: Install System Dependencies Here are quick commands to for install Tectonic’s dependencies using various package managers: If none of these fit your needs, you’ll need to figure out the right packages for your particular setup. Tectonic require the following libraries: ## Debian and Ubuntu Linux Install Tectonic’s dependencies with: sudo apt-get install \ libfontconfig1-dev libgraphite2-dev libharfbuzz-dev libicu-dev libssl-dev zlib1g-dev ## RHEL, CentOS, and Fedora Linux Install Tectonic’s dependencies with: sudo dnf install \ gcc-c++ fontconfig-devel graphite2-devel harfbuzz-devel libicu-devel openssl-devel zlib-devel ## Homebrew on macOS If you use Homebrew, be aware that you can install Tectonic with it directly! brew install tectonic If you want to compile Tectonic yourself, the following command will install the dependencies: brew install --only-dependencies tectonic You will also need to make sure that your environment has pkg-config set up to find the Homebrew libraries correctly. ## Conda If you use Conda, be aware that you can install Tectonic with it directly, using the conda-forge channel! conda install -c conda-forge tectonic But if you want to compile Tectonic yourself, the following command will install the dependencies: conda install fontconfig freetype graphite2 harfbuzz icu libpng openssl zlib You will also need to make sure that your environment has pkg-config set up to find the Conda libraries correctly. ## vcpkg If you wish to use vcpkg to provide Tectonic’s build dependencies, we recommend that you use the cargo-vcpkg tool. But for the record, to install Tectonic’s dependencies through vcpkg directly, you should probably run: vcpkg install fontconfig freetype "harfbuzz[icu,graphite2]" # How To: Build Tectonic: Install Dependencies With cargo-vcpkg A convenient, fairly cross-platform way to install Tectonic’s dependencies is using the cargo-vcpkg tool. It will take care of setting up vcpkg, providing the needed dependencies, and informing Tectonic’s build system about how to find them. It will, however, generally require that the dependencies be compiled from scratch. First, install cargo-vcpkg if needed: cargo install cargo-vcpkg Then, in the Tectonic source tree, run the command to obtain all of the needed dependencies: cargo vcpkg build Then set the VCPKG_ROOT environment variable to tell the build system where the dependencies may be found. In a bash shell, a good command is: export VCPKG_ROOT="${CARGO_TARGET_DIR:-$(pwd)/target}/vcpkg" If you’re building on Windows, you’ll likely want to make sure that your RUSTFLAGS variable includes a +crt-static target feature to get the vcpkg build scripts to use the x64-windows-static vcpkg triplet, which is the default one used by our cargo-vcpkg setup, as opposed to x64-windows-static-md, which is activated otherwise. And if you’ve done the full vcpkg install, you might as well build with an external Harfbuzz. Therefore a full Windows build invocation — launched from bash — might look like this: cargo vcpkg build export VCPKG_ROOT="${CARGO_TARGET_DIR:-\$(pwd)/target}/vcpkg"
export RUSTFLAGS='-Ctarget-feature=+crt-static'  # Windows only
export TECTONIC_DEP_BACKEND=vcpkg
cargo build --features external-harfbuzz

Note that if you are going to run additional commands such as cargo test, you’re going to need to ensure that the same environment variables and feature flags are used consistently.


text:
# Transforming an NFA into an NFA of similar size but without $\epsilon$-transitions

I'm learning for the exam and have problems with this task:

Describe an algorithm that transforms a given NFA $A = (Q, \Sigma, \delta, q_0, F)$ (which may have $\epsilon$-transitions) into an equivalent NFA without $\epsilon$-transitions with the same condition number. And then determine the maturity of the algorithm. The algorithm should have a running time $O(|Q| · |\delta|)$ where $$|\delta| := \sum_{\substack{q\in Q\\ a\in\Sigma\cup\{\epsilon\}}} |\delta(q,a)|$$

• What does “condition number” mean? What does “maturity of the algorithm” mean? These are bad translations, and I don't know what the right concept is. May 21 '12 at 23:36
• What have you tried? What techniques have did you learn in your lessons, that may be applicable here? Where are you stuck? May 21 '12 at 23:37
• condition->state; maturity->complexity (: looks like google-translate. May 22 '12 at 2:54
• Exercise 5.1, due May 24th.
– Raphael
May 30 '12 at 8:05

The obvious answer is: the powerset construction gets rid of $\varepsilon$-transitions, so you can use it. It blows up the automaton exponentially in the worst case, though, so it is not directly applicable. However, you can use the part that deals with $\varepsilon$-transitions and keep nondeterminism.

That is, if a state $q$ has an $\varepsilon$-transition to $q'$, add all outgoing transitions of $q'$ to $q$ and remove the $\varepsilon$-transition. You have to iterate this process for every state because there may be chains of $\varepsilon$-transitions. In the worst case, you reach all transitions (for every state), causing the required runtime bound (to be sharp).

Note that formally, this does not change the number of states. It might lead to isolated states, though, that can safely be dropped.

• and why this algorithm has this runtime O(|Q|⋅|δ|) ?
– user1619
May 23 '12 at 20:38
• @sad: The argument is given in the spoiler area. What part do you not understand? Obviously, it is only a rough outline. Detailed analysis remains for you to do.
– Raphael
May 23 '12 at 20:58
• has the algorithm the runtime of O(|Q|⋅|δ|) because he visits all states and transitions or just in worst case ?
– user1619
May 23 '12 at 21:24
• @mikley: In the worst case, it visits all transistions for every state, so the actual runtime is at most that large (up to constant factors). This is very basic; please stop abusing answer for commenting. If this is a problem for you, please consider asking a new question.
– Raphael
May 23 '12 at 21:52