I have been teaching psychologists to work with MAC for several years and noticed how differently there is an acquaintance, understanding and mastering of this amazing tool. Someone is trying to direct the whole process into a logical channel, someone only into an intuitive one, someone immediately during training begins consultations with metaphorical maps, and someone cannot start even after a year. Everyone has their own pace, their own motivation, their own tasks. But when working with MAC there is one very important thing - questions. You must master the art of asking questions. Without this, a full consultation with the use of MAC cannot be expected. And it’s just working with questions, which is the most difficult for some novice psychologists.
But now there is a way out. Our colleague Yekaterina Radchenko has created special question matrices, which, in my opinion, will be very useful, especially for those who are just learning to work with metaphorical cards. Thanks to this, you can perfectly work out a variety of problems: partnerships, and your career, and self-awareness, and low self-esteem, etc.

I am pleased to share a fragment of the consultation and the Sphere of Life technique with the permission of the client.

I considered something like a wheel of life balance, covering all areas of the client's life. Used the deck of Subpersonality and HE.
Instruction.
1. From the Subpersonalities to the closed one, get the cards and spread them out to all the questions of the finished matrix.
2. Open up, discuss.

3. Then take out a pair of cards (picture-word) from HE into a closed one and place them near the sphere where the client is not satisfied and wants to change it.

4. Open, discuss, summarize.
I will not give all the comments of the client, try, looking at the photo, to assume for yourself that he could answer. But, as an example, I'll tell you about those where changes are needed.
So:
“In finance, I’m like a first grader. I am constantly studying, but this is not mine, for sure.
How can I improve my financial condition? Well, I thought about it. I need to find a decent, mature man. I will give him my youth, attractiveness, respect - and he will give me financial support. For me this is honest and understandable.
My career really looks like it does on the map. I am afraid to go out into the world and assert myself. I sit behind a chair like a little girl. And how can I deal with this fear? Develop a habit, like on this card, to loudly declare yourself, your desires and capabilities! Intuitively I felt that it should be so!
My leisure time also leaves much to be desired ((.
I am constantly amusing everyone, like a jester. Judging by the following cards: as long as I communicate with others like a caring mother, thinking about their well-being, interests, forgetting about my desires, so I will remain a cleaver.
Well, my living conditions. I am like a child in a tank who does not know how to properly control it. They really don't suit me. Too much has to be watched, monitored, and so on. How can this be changed? You know, it seems to me that we need to get rid of the unnecessary. Eliminate everything that I don't need, that gets in the way and takes my time and energy ... "

I repeat: such ready-made matrices can serve as a good help in consulting both for specialists and for their clients.
Let me remind you that we have started another enrollment in the IAC Training School. Details on the link: http://ohcards.ru/news/651/

Tags: Viktoria GOLOBORODOVA, training to work with IAC, training in metaphorical cards, school of training IAC, distance learning in metaphorical associative cards

Events occur in the life of each of us, the memory of which lives on for a long time. One of such events for me is participation in the conference “Metaphorical cards in the work of a psychologist”, which took place in October last year in Moscow.

Two days of wonderful, rich, professional interaction with colleagues, exchange of experience and knowledge, acquaintance with new products, two days of interesting meetings and just human communication ... Such events charge you with energy so much that then you feel inspired for a long time.

The most valuable resource of the conference is, of course, people. Organizers, masters, participants - so different, but infinitely interesting in this diversity. One of these "jewels" in my "box of memories" is Oksana Stepanova. An amazing person ... You know, sometimes it seems to me that fairy tale therapists, over time, themselves become a little magicians.)))

I carefully keep the author's set of cards "Magic helpers from good fairy tales" received from Oksana as a gift, and from time to time I receive important tips from them.
Our acquaintance with Oksana continued after we went home - Oksana went to Krasnodar, and I returned to my native Minsk.

And, although now we can only communicate using Internet technologies, our communication is still filled with warmth and mutual respect for each other's professional success. I am very pleased to see how much energy and love Oksana invests in her developments, what interesting author products she creates, and how much important work is going on in the Idyllia center.

And I, for my part, really appreciate Oksana's opinion about my professional findings and new ideas. Oksana enjoys using one of my author's developments - matrices for working with metaphorical maps “MAK Fields”, and I am pleased that my product is in such good hands and benefits people.

And to you, friends, I am proud to recommend my author's products - sets of matrices for working with metaphorical maps "MAK fields" and "MAK glades". This is a good help for those specialists who work with MAC, and experience shows that the use of matrices in the work of a psychologist is very effective, since it allows you to solve several problems at once.

I can point out the main advantages of the products: convenient, visual diagrams, a wide coverage of the subject of client requests, a gentle “introduction” of the client into working with a metaphor, and a decrease in the client's level of resistance. I am proud that these products are not only well thought out and structured, but also executed at a high technical level, so working with them is both convenient and pleasant. I hope that they will be interesting and useful for you friends!

For more detailed product descriptions, please follow the links below.
If you have any additional questions, please contact me by writing to the email address This email address is being protected from spambots. You need JavaScript enabled to view it. and I will definitely provide you with all the information you need.

And in the near future I will share with you some "highlights" that I use when working with "MAK fields" and "MAK glades".

… I believe there will be new meetings. We will again find ourselves in one place at the same time, and recall last year's conference, master classes, and the Golden Metaphor awards that Oksana and I received at the closing of the event (thanks to colleagues for recognizing our products!), Share our accumulated news and new plans.
After all, life does not stand still, and a pleasant "aftertaste" after such meetings remains ...
Ekaterina Radchenko, psychologist, MAK-practitioner, author of PUZZLE-maxi, MAK fields, MAK glades, author and host of intensive training programs.

Another notation for an inline formula provided by LA TE X is to write \ begin (math) at the beginning of the formula and \ end (math) at the end (in other words, an inline formula can be formatted as an environment named math).

The off formula LA TE X allows you to surround on both sides not only with pairs of dollar signs, as provided by the standard, but with \ [(at the beginning) and \] (at the end). Alternatively, you can style the turned off formula as an environment named displaymath. Both standard and LA TE X designations for formulas can be used in the same file.

These alternative designations are completely equivalent to the standard TE X's (with dollar signs), with one important exception: if off formulas are denoted by LA TE X's and not TE X's, then you can make the off formulas not centered , and pressed to the left (see p. 159).

3. A set of matrices

First, we will explain how to type matrices with the amsmath package connected (which is better and more convenient in all respects), and at the end of this section we will tell, for the sake of completeness, about those matrix set tools that are available in the "pure" LA TE X ( without connecting additional style packs).

So, let's assume the amsmath package is included. Then, for a set of matrices enclosed in parentheses, it is worth using the pmatrix environment. This is how it works:

Matrix rows are separated using the \\ command (you do not need to end the last row with the \\ command), and elements within the same row that belong to different columns are separated from each other using the & symbol. The text corresponding to one line of the matrix on printing does not have to fit into one line of the TE X's file; in one line of a TE X file, you can put text corresponding to several lines of the matrix on printing. In short, the TE X principle of "end of line is equal to a space" also operates in the matrix environment.

Rectangular tables of formulas are not only enclosed in parentheses; accordingly, the bmatrix, vmatrix and Vmatrix environments are defined, which differ from pmatrix only in that instead of parentheses, the table is enclosed, respectively, in square brackets, vertical bars | | and doubled vertical bars k k. There is also a matrix environment, which produces only a rectangular table for printing, without any brackets. By combining the matrix environment with a couple of constraints, you can get a more exotic-looking matrix with parentheses.

If you want matrices with more than ten columns, you need to change the maximum number of columns by writing something like the following in the preamble:

(after that, the maximum number of columns in the matrix will be equal to twenty; in TE X'nic language this action is called "assigning a new value to the MaxMatrixCols counter"; see chapter VII). You can also give this command not in the preamble, but at the beginning of the off formula, which includes your matrix; then the permission to increase the number of columns will be valid only for matrices included in this excluded formula.

Here's how to type Pascal's triangle using the matrix environment:

The original text for it looks like this:

\ setcounter (MaxMatrixCols) (20)

&&& 1 && 2 && 1\\ && 1 && 3 && 3 && 1\\

& 1 && 4 && 6 && 4 && 1 \\ 1 && 5 && 10 && 10 && 5 && 1 \ end (matrix)

(note by the way that in this example empty table elements at the end of the line are omitted, so the number of & characters in different rows of the table

Other). If we hadn't incremented MaxMatrixCols, the last line would have raised an error message.

To get a horizontal row of points in the matrix, extending over several columns, use the command \ hdotsfor; its required argument is the number of dotted columns. In the example below, pay attention to the placement of & in lines containing \ hdotsfor:

You can also adjust the density of dots obtained using the \ hdotsfor command: in an optional argument (it is placed before the required one), you can specify a decimal fraction - "dilution factor". If you say \ hdotsfor (5) instead of \ hdotsfor (5), then the dots will go one and a half times less often.

Along with horizontal rows of dots, vertical and diagonal ellipses have to be used in matrices. To set them, use the \ vdots and \ ddots commands:

a 11a 12

a 21a 22

. . .. . .

a n1a n2

The \ vdots and \ ddots commands can be used not only in matrices, but also anywhere in mathematical formulas.

Along with the matrices used in excluded formulas, sometimes you have to put a small matrix in the inline formula. Naturally, both the size of the characters and the spacing between them in such a matrix should be more modest. The smallmatrix environment is intended for such purposes (it also becomes available when the amsmath package is connected). Here's an example of using it:

\ end (smallmatrix) \ bigr) $

As you may have noticed, you have to put parentheses around such a small matrix yourself. The smallmatrix environment does not have any options with ready-made parentheses.

Now, as we promised, we will let you know what opportunities for a set of matrices remain, if you do not connect additional packages. In this case, use the LA TE X array environment. Here's how to get the p. Example with these tools. 72:

Compared to what pmatrix gives, the differences are as follows:

1) The parentheses around a matrix typed with the array environment should always be set by yourself.

2) The \ begin (array), which opens the environment, must be followed (in curly braces, since it is the array environment argument) the so-called matrix preamble, which describes how many and what columns should be in the matrix. In our case, the preamble is three letters ccc. This means that there are 3 columns in the matrix (one letter per column), and that the contents of each of these columns must be centered on the column (c for "centered"). (In addition to c, the preamble may contain the letter l, which means that the corresponding column will be aligned to the left (left), or r, which means that the column will be aligned to the right (right).)

V the rest of the syntax is the same as for the pmatrix environment and its analogues. \ Ldots, \ vdots and \ ddots commands can still be used, but \ hdotsfor is not. There is also no analogue of MaxMatrixCols for the array environment (since the preamble already determines the exact number of columns). Environment

smallmatrix in "pure" LA TE X'e (without connecting additional packages) is also not provided.

4. One above the other

This section will focus on those cases where you need to place one character on top of another in a formula. In sect. 1.2 we have already discussed a particular case of this problem: setting "limits" at the sign of a sum, an integral, or something else like that. We will now consider the general case.

4.1. The simplest cases

To begin with, consider the following possibilities of positioning one part of the formula above the other:

1) The top of the formula is slightly above the line, the bottom is slightly below (as in the fraction generated by the \ frac command, but possibly without the fractional slash).

2) The bottom of the formula is flush with the rest of the text, the top is above it.

3) A horizontal curly brace is drawn above or below the formula fragment, and another formula fragment is located above or below this bracket.

Let us examine these options sequentially.

Let's start with one addition to the \ frac command for fractions described in the first chapter. If the fraction specified using the \ frac command occurs in an inline formula, then its numerator and denominator are printed in rather small print, which is not always acceptable. To avoid this, you can use the \ dfrac command by connecting the amsmath package: then the font will be larger. If the fraction in the inline formula is included in the exponent or index, then it sometimes makes sense to set it using the \ tfrac command (again, so that the font is not too small; this command is also available when amsmath is included). Here are some examples:

Now about how to arrange the parts of the formula "the same as in a fraction", but without the fractional line. There are two (unfortunately, mutually exclusive) ways to do this: with and without the amsmath package.

If you have the amsmath package connected, you can achieve the desired effect using constraints and the smallmatrix environment:

Of course, if you have a lot of such formulas in your text, using such long designations is unthinkable: you need to develop an abbreviation based on the smallmatrix (read in Chapter VII how to define "macros with parameters").

For the most common case of "binomial coefficients", when the delimiters are regular parentheses, the amsmath package provides a special \ binom command that works similarly to \ frac:

The \ binom command also has analogs \ dbinom and \ tbinom related to

To it is the same as \ dfrac and \ tfrac refer to \ frac.

V the amsmath package also provides a "generalized fraction" construct to create commands like \ frac and \ binom. By definition, a generalized fraction is a fragment of a formula structured like this: the left delimiter, then the fraction (the thickness of the fractional bar can be arbitrary, including zero), then the right delimiter. Recall that delimiters are brackets and similar symbols that can automatically resize (p. 67); in the generalized fraction, there may be no limiters (so that an ordinary fraction is really a special case of a generalized one). The \ genfrac command with six arguments is provided for generalized fractions. To understand how it works, let's look at an example:

The first and second arguments to \ genfrac are the left and right delimiters, respectively; the third argument is the thickness of the decimal line (if the thickness is zero, then the decimal line is not printed); the fourth argument contains instructions about the font size for the numerator and denominator: if you leave it blank, writing just () instead of (0), then TE X will choose the size on its own; digit 0 means that the size of the characters will be the same as when using the \ dfrac command (in Section 5.2 you will learn that in TE X's technical terminology this is called displaystyle), digit 1 is the size as when using the \ tfrac command (it the same textstyle), numbers 2 and 3 set even smaller sizes; finally, the fifth and sixth arguments are actually the numerator and denominator.

If you leave the third argument empty by simply writing () instead of the curly braces that indicate the thickness, the default decimal bar weight will be selected (it is equal to 0.4 points). If you leave the first and second arguments empty, then there are no delimiters (if, however, a left delimiter is specified, then a right delimiter must be specified). For example, \ dfrac (x) (y) is the same as

\ genfrac () () () (0) (x) (y)

In particular, our example with the Christoffel symbol can be written as

$ \ genfrac (\ () (\)) (0pt) () (ij) (k) $

Of course, the \ genfrac command is not great on its own, but as a raw material for defining macros tailored to your specific needs.

Now let's talk about what to do if you don't include the amsmath package.

In this case, it is convenient to use the TE X command \ atop:

In this case, we also used the \ left and \ right commands to place curly braces of the required size.

For binomial coefficients there is a TE X command \ choose:

(n \ choose k) = \ frac (n{k!(n-k)!}!}

Notice the curly braces around the n \ choose k expression: the \ choose command places the part of the formula from the opening curly brace to \ choose at the top, and the part of the formula from \ choose to the closing curly brace below. If these curly braces were not there,

the whole fraction n would go down too! together with an equal sign.

The \ atop command determines what goes up and what goes down, following the same rules as \ choose. In the example above with \ atop, we have dispensed with curly braces, since in the mathematical formula their function is also performed by the \ left and \ right commands.

When the amsmath package is included, the \ atop and \ choose commands cannot be used.

An interesting case of using fractions is the so-called "continued fractions":

The result doesn't look the best. In sect. 5 explains why everything turned out so badly and how to fix it "manually", but in practice it is best to include the amsmath package and do this:

If you want any of the numerators in the continued fraction to be not centered, but off to the left or right, instead of \ cfrac, say \ cfrac [l] or \ cfrac [r], respectively.

Another case when you need to print two formulas of the same size, one below the other, occurs when the expression for the summation indices takes several lines. In this case, by connecting the amsmath package, use the \ substack command:

The only argument to the \ substack command contains formulas that must be under the sum sign (or product, or any other "operation with limits"); the lines are separated by \\ (as in environments intended for a set of matrices).

Consider a case where the bottom of a formula should remain at the row level. To achieve this effect, the LA TE X command \ stackrel is used. This command has two arguments: the first is what will be above the line, the second is what will remain on the line:

If the text to be written above the arrow is long, the \ stackrel trick will give unsatisfactory results. In this case, by connecting the amsmath package, use the \ xleftarrow and \ xrightarrow commands, which are specially designed for labeling above and below the arrows. In the mandatory argument of these commands, the caption is placed above the arrow, in the optional argument - under the arrow (the optional argument, if any, is placed before the required one). If the label is long, the arrow size is automatically increased:

Finally, to draw a horizontal curly brace under the expression (and perhaps a caption under that brace as well), use the \ underbrace command. The argument of this command is the fragment of the formula under which you need to draw a parenthesis; the caption under the parenthesis, if required, is formatted as a subscript. For example, such a formula

1 + 3 + 5 + 7 +. ... ... + (2n - 1) = n2

| (z) n terms

turns out as follows:

\ underbrace (1 + 3 + 5 + 7 +

\ ldots + (2n-1)) _ (\ mbox ($ n $ terms)) = n ^ 2

If you have amsmath package enabled, it is wise to use the \ text command instead of \ mbox.

The horizontal curly brace above the formula fragment is generated by the \ overbrace command, the caption above it is formatted as a superscript. One formula can contain horizontal curly braces both above and below the formula fragment:

In our example, the bottom horizontal bracket was positioned entirely inside the top horizontal bracket. You can also make the upper and lower horizontal brackets not contain each other, but overlap, but this requires additional tricks (p. 93).

4.2. Multi-line shutdown formulas

The TE X program never makes automatic hyphenation in off-form formulas, so if your formula does not fit into a line, you need to break it into separate lines yourself. The first thing that comes to mind for beginners is to design each of these lines as a separate off-formula using $$ ... $$ and write these off formulas in a row. In this case, the vertical distance between the two lines turns out to be too large, so that by eye they do not

are perceived as part of the same formula. In this section, we describe how to intelligently organize such a partition.

As in the case with matrices, the most convenient (and recommended by us) tools are opened by connecting the amsmath package; we will begin with their description, and at the end we will describe the modest means of a set of multi-line formulas, available without connecting additional packages.

So, suppose you include amsmath. Then the simplest way to set multi-line exclusion formulas is the multline environment:

The first of the lines is printed off to the left, the last - off to the right, the rest of the lines are centered. Like the equation environment, the multline environment must not be enclosed in $$ characters. As you may have noticed, the formula, formatted as a multline environment, is automatically numbered. To avoid this numbering, you need to use the "variant with an asterisk" - the multline * environment.

In fact, the first and last lines are not printed close to the margins, but indented equal to \ multlinegap. The value of this parameter can be changed in the usual way by writing something like

\ multlinegap = .5in

To make some of the middle lines not centered, but off to the left, you need to use the \ shoveleft command, writing, say,

\ shoveleft (+ 46 + 47 + 48 + \ ldots) \\

instead of + 46 + 47 + 48 + \ ldots \\. To justify right, use the \ shoveright command in the same way.

When several excluded formulas go in a row, you don't need to design each of them using $$ or the equation environment, but use the gather environment:

When using gather, formulas must also not be enclosed in $$. Each of the formulas collected in gather is automatically numbered. In order to be able to refer to a formula numbered in this way (otherwise why number it?), You need to mark it by placing the \\ command \ label before the \\ command (see examples of labels and links in section 2.1; details in section IV.9 below) ...

If you do not need to number any of them, you should put the \\ command \ notag immediately before it. If you do not want to number any of the formulas, you can use the “asterisk variant” - the gather * environment.

When breaking an off-line formula into parts, it is often desirable to arrange the lines one below the other so that they are aligned in a certain way. To achieve this effect, it is convenient to use the split environment:

\ begin (equation)

1999 = 1000 + 900 +

(5) 1999&=1000+900+{}\\

Formula breaks are still specified with \\, and the & sign appears in front of the alignment characters. For technical reasons, a formula split into lines using split cannot be specified using the $$ characters (which is why we used the equation environment in the example). On the other hand, because of equation, our formula got a number. If you do not need numbering, you can either write \ notag before \ end (equation), or use the equation * environment, which does not number formulas.

Split formulas can also be used inside a gather or align environment (the latter will be discussed below), with or without asterisks.

It is often necessary to print one or more aligned formula columns. The align environment is intended for these purposes:

equality. In our example, the second & character in the row separates the first column of formulas from the second, the third & is the alignment in the second column, the fourth &, if it were, would separate the second column from the third, and so on. Still not needed $$ signs, each line of equations is automatically numbered, which can be suppressed by writing \ notag before \\, and there is still a variant with an asterisk align * that does not number formulas.

With the correct use of the align environment, an odd number of & characters should be in the line. Namely, if we have n columns with equations, then there are n - 1 signs &, separating the columns from each other, plus n more signs - one for each column, and in total (n - 1) + n = 2n - 1.

A useful use of align occurs when successive off-form formulas contain textual comments. It is desirable that these comments be aligned. Here's how you can achieve this with align:

Notice the two ampersands separating the comment from the formulas (see the small print above). It is also worth noting that, as with the multline and gather environments, formulas specified with align cannot be formatted with dollar signs.

It is not always convenient to include comments to calculations directly in formulas. Sometimes you want some of the comments to go on a separate line. The \ intertext command allows you to do this without breaking the alignment:

Along with the align environment, which immediately gives the whole off formula, there is the aligned environment, which can be used as a part of a larger formula. Here's how you can define a system of equations using this environment:

To create a curly brace covering the entire system, we used the \ left and \ right commands, and the \ right command contains an "empty delimiter" - a period (see Section 2.5).

Finally, another type of multi-line turn-off formulas occurs when the expression on the right side of an equality must look different in different cases. For this case, the amsmath package provides the cases environment. Let's demonstrate its work immediately with an example:

| x | = \ begin (cases) x, & \ text (if $ x> 0 $;) \\ 0, & \ text (if $ x = 0 $;) \\ -x, & \ text (if $ x<0$.} \end{cases}

Now that you have familiarized yourself with the capabilities of a set of multi-line formulas using the amsmath package, we will also tell you about what you can do in this direction without connecting additional style packs.

Systems of equations can be typed using the array environment like this:

x ^ 2 + y ^ 2 & = & 7 \\ x + y & = & 3. \\

We have assigned one column to the left side of each equation, the equal sign, and the right side. In doing so, we asked that the left-hand sides of the equations be right-aligned (hence the r in the preamble), the right-hand sides

are left justified (l in the preamble) and the equal sign is centered in its column (hence the second letter in the preamble is c).

You may notice that the spaces (padding) before and after the equal sign are larger than allowed by typographic rules (and that is obtained when using the aligned environment from the amsmath package). Unfortunately, this is difficult to combat; it's easier to get a kit that includes the amsmath package.

If it is necessary that individual equations in the system be numbered, you can use the eqnarray environment. It works in the same way as the array environment with the rcl preamble in the above example, but it automatically prints a number for each equation (similar to the way it automatically prints a number for a turned off formula created using the equation environment - see Section 2.1). If you label an equation with the \ label command, then you can refer to it later using the \ ref or \ pageref command. Example:

Note that the eqnarray environment does not create a curly brace that encloses the system of equations. In this example, the ~ character between "s."

and \ pageref is supplied to make the word "c." and the page number did not fall on different lines (see p. 103); for similar purposes we have used this symbol

and the second time.

When using the eqnarray environment, you do not need to write $$ characters (just as you do not need to write them when using the equation environment).

If you do not want to number all the equations, you need to mark the equations that you will not number with the \ nonumber command (immediately before \\):

Z ∞ e − x 2 dx = √ π

−∞ √

\ begin (eqnarray) \ int _ (- \ infty) ^ \ infty e ^ (- x ^ 2) dx & = & \ sqrt (\ pi) \ nonumber \\

(10) \ sqrt (576) & = & 24 \ end (eqnarray)

Finally, if you do not want to number the equations at all, you can use the "variant with an asterisk" - the eqnarray * environment.

The array environment can be used not only in off, but also in inline formulas, although the result usually looks ugly. The eqnarray and eqnarray * environments only create excluded formulas.

You can also use the eqnarray or eqnarray * environment to split the off-formula into several aligned parts:

Notice that we preceded the first + in the second line of the formula with a pair of opening and closing curly braces; this is done so that the + sign does not come too close to the first character of the second line on print, which, in combination with the increased space around the equal sign, would be too much (you can experiment on your own). The nature of the described effect is explained below in Sec. 5; it is partially taken into account in the package amsmath (unfortunately, different versions of this package may give different results).

4.3. A set of commutative diagrams

To type commutative diagrams in LA TE X, you need to connect the amscd style package. Let it be done. Then the commutative diagram takes the form of a CD environment. To a reader familiar with AM S-TE X, the rest can be explained in one phrase: between \ begin (CD) and \ end (CD), you must put exactly the same text as in AM S-TE X they write in a similar case between \ CD and \ endCD (see). For everyone else, it is more convenient to explain the rules for the collection of commutative diagrams by an example. Consider the following diagram:

With the amscd package connected, it is typed as follows:

0 @ >>> E ’@> f >> E @> g >> E’ ’@ >>> 0 \\

@. @VVpV @VVqV @VVrV @. \\

0 @ >>> F ’@> f >> F @> g >> F’ ’@ >>> 0 \ end (CD)

The first line in this entry corresponds to the top line of the chart. The left-to-right arrow is @ >>> (and the right-to-left arrow is @<<<); если над стрелкой надо поставить какую-то надпись (например, просто букву), то нужно ее разместить между первым и вторым знаками неравенства; чтобы надпись

turned out under the arrow, you need to place it between the second and third inequality signs.

The second line defines vertical arrows. The @VVV construct specifies an arrow pointing down; if an inscription is needed to the right of the arrow, then it must be placed between the second and third letters V (for the inscription to be to the left of the arrow, it must, of course, be between the first and second letters V). A vertical arrow pointing up is specified by @AAA (the letter A is the closest approach to an upward pointing arrow); to the right and left of it, you can also make an inscription (in the same way).

The @ construction. sets an "empty" arrow (in our case, between two zeros); it is necessary so that LA TE X does not lose track of figuring out which columns to put vertical arrows in.

Let's describe the work of the CD environment more accurately. Each commutative diagram is considered by the CD environment as a table consisting of alternating "horizontal" and "vertical" lines. Each "horizontal" line consists of formulas interspersed with horizontal arrows. All horizontal lines must have the same number of formulas. If some of the places intended for formulas should remain empty, then you should leave a space in this place or, if you prefer, write (). There should be an arrow between each pair of formulas. If any of these arrows are not needed, place @ in their place. ("Empty" arrow).

Each "vertical" line consists of vertical arrows. There should be as many of them as there are formulas in any of the horizontal lines. If some of the vertical arrows are not needed, place @ in their place. (empty arrow).

If the inscription with the arrow pointing down (and, therefore, by the construction @VVV) itself contains the letter V, then you need to enclose it (the inscription) in curly brackets - otherwise TE X will not be able to understand which of the letters V belongs to the inscription, and which one - to the arrow designation. Similar measures must be taken if the inscription with the arrow pointing up contains the letter A (and also, of course, if the inscription with the horizontal arrow contains the> or<, хотя ввиду математического смысла таких надписей последнее менее вероятно).

Along with arrows, in commutative diagrams there are horizontal and vertical "stretched equal signs":

As you can see from this example, such signs are specified by the constructions @ = (horizontal) and @ | (vertical). Notice also how we protected the V character in the caption to the left vertical arrow with curly braces.

\ Pretend. ... ... \ haswidth of the AM STE X system (see the book) is not supported in LA TE X.

Mathematicians know that not only horizontal and vertical arrows can be found in commutative diagrams: there are also oblique, curved, and dashed arrows. ... ... The capabilities of the amscd package for printing such arrows are not enough; if you need such more complex diagrams, you should use the XY -pic style package (see Appendix E).

In the "clean" (without connecting style packs) LA TE X, a set of diagrams is not provided. As a last resort, if there is neither amscd nor XY -pic, you can do this:

\ begin (array) (ccccccccc) 0 & \ longrightarrow & E '& \ stackrel (f) (\ longrightarrow) & E & \ stackrel (g) (\ longrightarrow) & E' '& \ longrightarrow & 0 \\ && \ downarrow \ lefteqn (p) && \ downarrow

\ lefteqn (q) && \ downarrow \ lefteqn (r) \\ 0 & \ longrightarrow & F '& \ stackrel (f) (\ longrightarrow) & F & \ stackrel (g) (\ longrightarrow) & F' '& \ longrightarrow & 0

As a result, you will get almost the same diagram as in our first example (however, letters with vertical arrows will be larger than letters with horizontal ones, since the \ stackrel command decreases letters). The only thing that needs clarification here is the \ lefteqn commands. They are needed so that the vertical arrows with the labels are correctly centered. If you omit these \ lefteqn's (and write p instead of \ lefteqn (p), etc.), then the vertical arrows with the captions will appear not in the center, but shifted to the left.

• “I liked the game very much! The cards are large and dense, I think they will serve us for a long time. We play with the whole family: at first it was difficult, but then you swing and the speed game begins. My husband and I, as adults, did not have any advantages, it seemed that my daughter finds the right combinations even faster. We also have a neuropsychological game "Try Again", we decided to combine them, because The puzzle cards, which are designed to make the game more difficult, are very similar to the Try Repeat cards. Now we play like this: in advance we choose simple cards from "Try it again" with poses that can be really repeated. Then we shuffle and open one card from the deck of "puzzles", remember it, and then put it face down. Whoever finds the right combination must repeat the pose from the closed card and shout "To the dacha". If the pose is correct, then you can pick up a combination and open a new card from the deck of "puzzles", if not correct, then the participant can try again after one of the opponents tries to pick up the combination. "

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“The book (1st part) really liked my children. We listened with pleasure, asked a lot of questions. There are exercises after each chapter that get more difficult from chapter to chapter. Therefore, it is better to read the book not before bedtime, but to stock up on time for an interesting dialogue with children. The exercises are designed in such a way that they provide a field for creativity for parents and children, depending on the specific situation. My children especially liked to paint their portraits, to populate houses of kindness, generosity, etc. After the section on perception, we cheered up and began to come up with our own exercises for the 5 senses. The children also liked to play out a fairy tale with the participation of 4 types of temperament. Perhaps the most favorite game for knowing yourself and your character. We improved it a little, added several qualities that were not suggested by the author. For example, honesty, cunning, self-esteem. Each of us filled out 4 sheets - 1 about ourselves and 3 other family members. While filling out, talking, specifying, explaining, clarifying, portraying and even laughing. My children love such tasks where you can learn more about yourself, show another his portrait and see yourself through the eyes of another. They remember such moments and from time to time ask them to repeat them. By the way, when you decide to do such a thing with your children, do not forget to write the name and date on each sheet. Everything is changing. Save these pieces of paper. After a while, you can return to them, do it again and see what will change and what will remain the same. I am very glad that the author decided to make a continuation of the 1st part of Psychology for kids. Children are looking forward to the new adventures of Yulia and her dad. There are few children's literature on the market aimed at knowing oneself, one's inner world. There are even fewer quality publications. The tale of Igor Vachkov's most soulful science is based on the best achievements of psychological science in recent years, written in simple language and in fact invites children and adults on an exciting journey. A journey that works for the development of a child and an adult. I am pleased to recommend for active reading to parents, teachers and everyone who is interested in the development of the child's personality. "

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“I looked through the topics of the authors' Ph.D. theses, they are very far from the practice of preschool education. The impression is that the whole work is based on inferences, and not on the results of scientific research. All information has long been known to scientists dealing with this problem. Authors-philologists do not know at all the psychological and pedagogical research in this area, and there are quite a lot of them. The content of the work resembles the FQP of a bachelor's or master's degree in Pedagogical Education, philological education is manifested in places. That's all. Thanks to the authors for the abstract work. "

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“A wonderful program for the development of the emotional intelligence of children. I am an educational psychologist, I have worked in kindergartens for 14 years. She worked with children according to various good programs. For the last 2 years I have been studying with senior and preparatory groups under the "Life Skills" program. It differs from other programs in that the theoretical basis is very well written, all practical tasks are tied to theory, and a lot of explanations are given to what, why and how to do it. There are both simple and very difficult tasks. It seems that children cannot cope with them. But no, they do it. And the kids really like it. "

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“Excellent metaphorical cards! The structure is unusual: the deck consists of 31 sets of photographs (each set contains 3 cards). You can work both with sets (instructions will come to the rescue), and with individual cards (according to the standard principle). There are a lot of possibilities for using the deck! The quality of the cards themselves is also very good. Thanks to the publisher for continuing to look for something new in the world of metaphorical cards! ”

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“The kits are so-so. The old model, in some places with the drawings of the Calednarian 2007, and the poster with emotions is generally useful and there are valuable quotes. For example, the bill of rights of the individual. But it's easier to find them on the Internet yourself, to order a print in a printing house than to pay extra for delivery. "

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“I am a child psychologist, I have worked in a kindergarten for 12 years. During this time, I led group classes in various programs, including this one. I think this is a GREAT program. And children are interested in it, and it is interesting for a psychologist to work and see what happens, how children change. I highly recommend it, despite the fact that there are many other good programs now. The only thing in the subgroup must be 6-7 people maximum for everything to work. "

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“I express my gratitude to the author for the depth of consideration of the issue. After reading the book, superstitions about what is given to some children and not to others disappear. An understanding of the literacy formation process is emerging. In fact, the book gives: 1. Understanding how literacy is formed in different children. 2. A simple step-by-step literacy learning tool. Regards, Mikhail."

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“A book for thinking educators and responsible parents. Helps to better understand the origins of problems. Written in good language, the author presents specific material in an accessible and engaging manner. I teach a foreign language, but even for me the book turned out to be useful in terms of methodology and psychological aspects. "

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“Hello! I want to say thank you for the program“ Year to School: from A to Z ”. I work as a teacher-psychologist and for the last academic year led a group on psychological preparation of children for school. This year I have a similar task, but unfortunately in online stores, including yours, there are no workbooks for this program. Do you plan to publish this product in the near future? "

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“The second deck - and even more delight :) I was expecting a release for almost a year, after the purchase of the“ about you ”deck. And not in vain !!! This is another masterpiece by Irina Logacheva and the team of psychologists. Of my 25 decks, these two are the most :) Very interesting images, plots ... and the artist's work is simply magnificent. Yesterday I tried it in work - sheer pleasure, and the same positive customer reviews about the deck. Beauty and professionalism! "

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“I recently bought a kit for working with preschoolers. The emphasis in this game is on the development of fine motor skills and the cognitive sphere of the child. The manual is very detailed, with illustrations. This game can be easily played by parents with children at home. I would especially like to praise the map: it depicts a lot of characters, and therefore it will definitely not be left without the attention of children. "

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“Thank you for these cards. This kit is one of the most used in my work with clients in many areas from initial counseling to remedial developmental activities. Moreover, it is interesting and effective to use these cards in prevention. ”

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“Gorgeous book. Many thanks to Inna Sergeevna for the work with which she illuminated the difficult life of children in the orphanage. The book changed my view not only of disadvantaged children, but also helped me find an approach to my own. "