Tex Var Manual

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TexVar – Manual

TexVar – LaTeX math calculations

Version: 1.5.22

Sebastian Pech

November 27, 2018

Contents

1 Description 2

2 Installation 2

2.1 Prerequisites ...................................... 2

2.2 Installation ....................................... 2

2.2.1 Conguration for Gnuplot . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Getting Started - Hello World 2

4 General Information on tVar Environment and Macro 3

5 TexVar - Commands 4

5.1 CreatingVariables ................................... 4

5.1.1 Creating Variables in Equations . . . . . . . . . . . . . . . . . . . . . . . . 5

5.1.2 Auto-Formatting of variable names . . . . . . . . . . . . . . . . . . . . . . 5

5.2 CreatingFunctions................................... 6

5.3 Indexing Matrices and Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5.4 Output ......................................... 8

5.4.1 print()...................................... 8

5.4.2 outRES() .................................... 9

5.4.3 Other Output Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.4.4 L

EXOutput.................................. 10

5.4.5 Precise Manipulation of Output . . . . . . . . . . . . . . . . . . . . . . . . 10

5.4.6 NumberFormat ................................ 11

5.4.7 Grouping Math Environments . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.5 GlobalParameters ................................... 13

5.5.1 Details on automatic removal of trailing zeros . . . . . . . . . . . . . . . . 14

5.6 PlottingwithGnuplot ................................. 15

5.6.1 Conguration.................................. 15

5.6.2 CreatingaPlot................................. 16

5.7 MathematicalCommands ............................... 18

5.7.1 General ..................................... 18

5.7.2 MatricesandVectors.............................. 18

5.8 TheLinkFunction ................................... 18

6 Examples 20

6.1 U-Value ......................................... 20

6.2 RotatingaVector.................................... 21

2 3 Getting Started - Hello World

6.3 Vector Calculations - Custom Function . . . . . . . . . . . . . . . . . . . . . . . . 22

1 Description

TexVar (short tVar) is a basic L

EX math calculations tool written in Lua. For integration into

X it has to be used together with LuaLaTeX. Compared to software like Mathcad TexVar is

a lot more exible. You can ll custom designed tables with results, do calculations within text

documents and print beautiful LaTeX equations. The current version also supports 2D-plotting

with gnuplot.

2 Installation

2.1 Prerequisites

The following software is needed in order to use TexVar:

• Lua 5.1 or higher

• LuaLaTeX (MikTex or Texlive)

• GnuPlot 5.0 (only needed for plotting)

By default the command \si{} is used for displaying units, so the siunitx package is mandatory.

If you want to dene your own command you can change the value of tVar.unitCommand = "\\si".

2.2 Installation

Download TexVar from https://gitlab.com/spech/TexVar and copy the folder tVar and the

le texvar.sty (subfolder package) to a location that is visible to L

EX. (e.g. the folder your

*.tex le is in or a global L

EX-folder 1)

2.2.1 Conguration for Gnuplot

In order to use Gnuplot with TexVar you have to allow LuaLaTeX to call external commands

during runtime. This works through the command-line switch --shell-escape. Your complete

call for LuaLaTeX could look like this: lualatex -synctex=1 -interaction=nonstopmode

--shell-escape %.tex.

3 Getting Started - Hello World

To ensure your installation is working test the following code. When using an luacode based

environment like tVar it’s important that the commands \begin{tVar} \end{tVar} are not

indented.

1\documentclass{article}

3\usepackage{texvar}

4\ usepackage[ fleqn ]{ amsmath }

1You can nd information on global L

X-folders athttps://www.math.hmc.edu/computing/support/tex/

installing/

4 General Information on tVar Environment and Macro 3

6\begin{document }

7\begin{tVar}

8#Hello World! I'm using TexVar

9tVar.getVersion()

10 \end{tVar}

11 \end{document}

Output

Hello World! I’m using TexVar Version: 1.5.22

4 General Information on tVar Environment and Macro

To execute TexVar commands from L

EX, the TexVar package oers two options:

•\begin{tVar} \end{tVar}, for commands blocks

•\tv{}, for inline calls

Both forward the commands to the TexVar interpreter.

1\begin{tVar}

2a:=10

3b:=3

4c:=a+b

5\end{tVar}

6The result is: \tv{c:outRES ()}

Output

a= 10

b= 3

c=a+b= 10 + 3 = 13

The result is: c= 13

Generally, there are two key commands the TexVar interpreter searches for 2:

1. #, for text output

2. :=, for calculations and assignments

Every other command is directly forwarded to the Lua interpreter. This means you can write

any Lua code you want inside the tVar environment.

1\begin{tVar}

2function mypow(a,b)

3return a^b

2Details on these key commands are discussed in Section 5

4 5 TexVar - Commands

4end

5for i=0,2 do

6tex.print("Step " .. mypow(2,i) .. "\\\\")

7end

8\end{tVar}

Output

Step 1

Step 2

Step 4

5 TexVar - Commands

5.1 Creating Variables

TexVar knows three types of variables:

tVar is the basic type for scalar values.

tMat is used for matrices.

tVec is used for vectors.

The following code generates a variable of each type. Every assignment is made with :=.

1\begin{tVar}

2a:=13

3e:={1,2,4}

4A:={{1,0},{2,4},{3,9.1}}

5\end{tVar}

Output

a= 13

~e =











A=





1 0

2 4

3 9.1







5 TexVar - Commands 5

5.1.1 Creating Variables in Equations

New variables can also be created inside equations. The notation for vectors and matrices is

explained in Section 5.1. Lua knows - by default - how to do calculations with numbers, so

any equation which does not contain tVar objects, can only be printed as it’s result. Any

mathematical operation with a tVar object and a decimal number results in a tVar value.

1\begin{tVar}

2# Variable a is created from the equation ...

3a:=13*2^2

4# To preserver the equation some of the ...

5a:= tVar :New (13) *2^2

6# At first Lua calculates $2^2=4$ ...

7# To print the whole ...

8a :=13* tVar :New(2) ^2

9# Matrices and Vectors

10 c:={{1,2 ,3} ,{4 ,2,6} ,{1,3,2}}*{1 ,2 ,3}* a

11 \end{tVar}

Output

Variable a is created from the equation 13 ·22. Since all numbers are

just decimal values, Lua calculates the result and creates the tVar object

afterwards.

a= 52

To preserver the equation some of the numbers have to be initialized as

tVar objects. In this case it’s the number 13.

a= 13 ·4 = 52

At rst Lua calculates 22= 4 and then multiplies the tVar object 13 with

4which results in a tVar object containing the equation. To print the

whole equation, one number from the rst calculation has to be trans-

formed into a tVar object.

a= 13 ·22= 52

Matrices and Vectors

~c =





123

426

132







·











·a=





123

426

132







·











·52 = 





728

1352

676







5.1.2 Auto-Formatting of variable names

The L

EX-representation of a variable is automatically generated from the variable name. The

rst occurrence of an underline starts the subscript the rst occurrence of a double underline

starts the superscript. Every other underline becomes a comma.

6 5 TexVar - Commands

1\begin{tVar}

2a_1_3 :=13

3a__10_2 :=3

4b_1_x__y_2:=12

5\end{tVar}

Output

a1,3= 13

a10

2= 3

by,2

1,x = 12

5.2 Creating Functions

Functions can easily be dened with the following syntax. The auto-formatting of function

names and attribute names works according to Section 5.1.2.

1\begin{tVar}

2f(x,y):=x^2+y^2+4

3a:=f(2,3)+11

4\end{tVar}

Output

f(x, y) = x2+y2+ 4

a=f(2,3) + 11 = 22+ 32+ 4 + 11 = 28

5.3 Indexing Matrices and Vectors

The syntax for indexing a matrix is similar to the Matlab syntax. To access a matrix you have to

use square brackets and a string as key. The key has to be formatted according to the following

examples.

1\begin{tVar}

2A:={{1 ,2,6} ,{2,4 ,6},{7 ,6,9}}

3# Index one element with syntax [row , column ]

4A["1,2"]:outRES ()

5# Index a range

6A["1:2 ,1:end"]:outRES()

7# The range 1: end is equal to :

8A["1:2,:"]: outRES()

5 TexVar - Commands 7

9# You can also set matrices this way

10 A[" 1:2 ,: "]:={{1 ,2 ,3} ,{4 ,5 ,6}}

11 A["1:2,:"]: outRES()

12 # Adress vector

13 c:=A[":,2"]

14 d:=A["2,:"]

15 # The above also applies to vectors

16 {plain

17 v_1:={1,4,3}

18 #,~

19 v_1["2"]: outRES ()

20 #,~

21 v_1["1" ]:=9

22 v_1:outRES ()

23 }

24 \end{tVar}

Output

A=





126

246

769







Index one element with syntax [row,column]

A[1,2] = 2

Index a range

A[1:2,1:end] = 126

246!

The range 1:end is equal to :

A[1:2,:] = 126

246!

You can also set matrices this way

A[1:2,:] = 123

456!

Adress vector

~c =









=











8 5 TexVar - Commands

d=456=456

The above also applies to vectors

~v1=









, ~v1[1] = 9, ~v1=











The command {plain } groups equations to one math environment. For details see Section

5.4.7

5.4 Output

5.4.1 print()

The [tVar]:print() command creates the output according to the global parameter tVar.OUTPUT_MODE

. The following options are supported:

Output

a= 10

b= 2

c=a+b= 10 + 2 = 12

tVar.OUTPUT_MODE = "RES_EQ_N"

c=a+b= 10 + 2 = 12

tVar.OUTPUT_MODE = "RES_EQ"

c=a+b= 12

tVar.OUTPUT_MODE = "RES"

c= 12

If you do your calculations inside \begin{tVar} and \end{tVar} the [tVar]:print() command

is automatically added to your calculations. This means c:=(a+b) creates an output using the

[tVar]:print() command. To suppress the automatic output just add a ”;” at the end of the

line.

1\begin{tVar}

2# With output:

3a:=10

4b:=3

5c:=a+b

6# Without output (Lines 7 and 8 produce no output ):

5 TexVar - Commands 9

7a:=10;

8b:=3;

9c:=a+b

10 \end{tVar}

Output

With output:

a= 10

b= 3

c=a+b= 10 + 3 = 13

Without output (Lines 7 and 8 produce no output):

c=a+b= 10 + 3 = 13

5.4.2 outRES()

The [tVar]:outRES() command is equal to the combination of [tVar]:print() with tVar.OUTPUT

\_MODE = "RES". If you do your calculations inside \begin{tVar} and \end{tVar} the [tVar

]:outRES() command is automatically added to any assignment of a new variable. That means

a:=10 creates and output using the [tVar]:outRES() command.

In some cases you might want to print an equation without assigning it to a variable. This

can be achieved by directly calling the function tVar.outRES([tVar]) (now with a dot) and

passing your equation as argument to the function.

1\begin{tVar}

2a:=2

3b:=13

4tVar.outRES (( a+b) /2+b)

5\end{tVar}

Output

a= 2

b= 13

a+b

2+b= 20.5

This method also works for the output commands listed in Section 5.4.3.

5.4.3 Other Output Commands

For every output mode mentioned in Section 5.4.1 there is an equal output function.

10 5 TexVar - Commands

RES_EQ_N [tVar]:outRES_EQ_N(numbering,environment)

RES_EQ [tVar]:outRES_EQ(numbering,environment)

RES [tVar]:outRES(numbering,environment)

The attributes numbering and environment are boolean values and dene if the output is created

with numeration and a math environment. Both parameters are optional and can also be dened

via the global parameters tVar.EQUATION_NUMBERING and tVar.MATH_ENVIRONMENT3

Additionally there are the functions [tVar]:out() for printing the result without the variable

name and [tVar]:outN() for printing the variable name the equation with numbers and the

result.

5.4.4 L

EX Output

Inside \begin{tVar} and \end{tVar} the symbol # can be used to print a text in L

Inside such a text you can use %%[tVar]%% to print a variables name and $$[tVar]$$ to print

a variables value.

X commands used within # have to be escaped. For example \textbf{} has to be written

as \\textbf{}.

1\begin{tVar}

2#\\ subsection *{ First Subsection }

3a_1_2 :=22.4 :setUnit("m")

4# Linebreaks are a bit confusing \\\\

5# The variable %%a_1_2 %% has the value $$a_1_2$$

6\end{tVar}

Output

First Subsection

a1,2= 22.4m

Linebreaks are a bit confusing

The variable a1,2has the value 22.4m

5.4.5 Precise Manipulation of Output

The following functions manipulate equations directly and can be used for detailed formatting.

1\begin{tVar}

2a:=10: setUnit("m")

3b:=3: setUnit("m")

4c:=((((a+b):bracR()^2):bracB() *5): bracC() *22): setUnit("m^2")

5#In case you do a really long calculation you can insert a

linebreak \\\\

3In case tVar.MATH_ENVIRONMENT is set to ”” no math environment is used.

5 TexVar - Commands 11

6c:=((a+a+a+a+a+a+a+a+b+b):CRLF("+")+b+b+b:CRLF_EQ("+")+b+b+b+

a+a+a+a):CRLFb("=")

7tVar.DEBUG_MODE = "off"

8\end{tVar}

Output

a= 10 m

b= 3 m

c=nh(a+b)2i·5o·22 = nh(10 + 3)2i·5o·22 = 18590 m2

In case you do a really long calculation you can insert a linebreak

c=a+a+a+a+a+a+a+a+b+b+b+b+b+

+b+b+b+a+a+a+a=

= 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 3 + 3+

+3+3+3+3+3+3+10+10+10+10=144

5.4.6 Number Format

The number format can be controlled globally and locally. The function [tVar]:setFormat([

string]) denes the local number format of a tVar object. In case no local format was dened,

tVar falls back to the global format set with tVar.NUMBERFORMAT = [string].

Common values are:

Output

Variable a is set to 192.6345

Integer %d

a= 192

Exponential %.2E

a= 1.93 ·102

Float %.3f

a= 192.635

There is one case where TexVar automatically changes the number format: When the output

precision return 0but the calculation precision is unequal to 0the number format is changed to

%.3E.

12 5 TexVar - Commands

[tVar]:bracR() Surrounds the [tVar] object with round brackets.

[tVar]:bracB() … boxed brackets.

[tVar]:bracC() … curly brackets.

[tVar]:bracR_EQ() Surrounds the equation part of the [tVar] object

with round brackets.

[tVar]:bracB_EQ() … boxed brackets.

[tVar]:bracC_EQ() … curly brackets.

[tVar]:bracR_N() Surrounds the numerical part of the [tVar] ob-

ject with round brackets.

[tVar]:bracB_N() … boxed brackets.

[tVar]:bracC_N() … curly brackets.

[tVar]:CRLF ([string]) Inserts a line break in N after the [tVar] ob-

ject and adds the string before and after the line

break.

[tVar]:CRLFb([string]) Inserts a line break in N before the [tVar] ob-

ject and adds the string before and after the line

break.

[tVar]:CRLF_EQ ([string]) Inserts a line break in EQ after the [tVar] ob-

ject and adds the string before and after the line

break.

[tVar]:CRLFb_EQ([string]) Inserts a line break in EQ before the [tVar] ob-

ject and adds the string before and after the line

break.

[tVar]:clean() Removes the calculation history from an object.

[tVar]:setUnit([string]) Sets the unit for a tVar object.

[tVar]:setFormat([string]) Sets the numberformat for a tVar Object. For

details see Section 5.4.6

Output

Variable a is set to 0.00001. Default number format is %.3f. Calculation

precision is 10

a= 1 ·10−5

b= 123432

c=a·b= 1 ·10−5

·123432 = 1.234

5 TexVar - Commands 13

5.4.7 Grouping Math Environments

By default TexVar creates a new mathematical environment for every output (except plain text-

output with #). To group equations into one environment, you can enclose them with curly

brackets. The group operator automatically adds an alignment symbol at the beginning of the

line and a line-break at the end. If you want to suppress this behavior you can open the group

with the command {plain.

1\begin{tVar}

3a:=1

4b:=10

5c:=3

7d:=(a+b):bracR ()/c

8#It's also possible to create environments without line -

breaks and alignment:

9{plain

10 f:=3

11 #,~

12 g:=f+d

13 }

14 \end{tVar}

Output

a= 1

b= 10

c= 3

d=(a+b)

c=(1 + 10)

3= 3.667

It’s also possible to create environments without line-breaks and align-

ment:

f= 3, g =f+d= 3 + 3.667 = 6.667

5.5 Global Parameters

Global parameters can be set during runtime and aect all commands.

14 5 TexVar - Commands

Tab. 1: Global parameters with default values and description

tVar.NUMBERFORMAT = "%.3f" Denes the number format for printing.

tVar.MATH_ENVIRONMENT = "align" Denes the environment used around equations.

tVar.OUTPUT_MODE = "RES_EQ_N" Denes the outputmode (Section 5.4.1).

tVar.EQUATION_NUMBERING = true Disables and enables numeration of equations.

tVar.DECIMAL_SEPARATOR = "." Denes the decimal separator.

tVar.MATRIX_COMMAND = "mathbf" Denes the style for matrices.

tVar.MATRIX_EQUATION_AS_MATRIX = false Enables and disables output of a matrix as vari-

able name or matrix with variable names

tVar.UNIT_COMMAND = "\\si"" Sets the macro for displaying units.

tVar.VECTOR_COMMAND = "vec" Denes the style for vectors.

tVar.CALC_PRECISION = 10 Denes the how many decimal places are used

for comparison.

tVar.OUTPUT_DISABLED = false Disables the complete output.

tVar.REMOVE_ZEROS = true Removes trailing zeros from a decimal number.

tVar.REMOVE_DECIMAL_SEPARATOR = true In case tVar.REMOVE_DECIMAL_SEPARATOR is

true remove the decimal separator if all trail-

ing zeros have been removed. Else show num-

ber with one decimal zero. (Only works if

tVar.REMOVE_DECIMAL_SEPARATOR = true)

tVar.DEBUG_MODE = "off" In case debugMode is set to ”on” the equations

are printed as L

Xcode.

tVar.DEBUG_LOG_COMMANDS_TO_FILE = false Enables logging of interpreted commands. Cre-

ates a le tVarLog.log

tVar.OUTPUT_COLORED = false Prints all variables with value=nil red.

5.5.1 Details on automatic removal of trailing zeros

The following example shows the dierence between the global parameters tVar.REMOVE_DECIMAL_SEPARATOR

and tVar.REMOVE_ZEROS. If tVar.REMOVE_ZEROS is disabled the number format from tVar.NUMBERFORMAT

get’s applied.

1\begin{tVar}

2#Default settings

4a:=2.0

5b:=3.3

6c:= tVar.sqrt(a^2+b ^2)

8#Disable \\verb|tVar.REMOVE_DECIMAL_SEPARATOR|

9tVar.REMOVE_DECIMAL_SEPARATOR = false

10 {

11 a:=2.0

12 b:=3.3

5 TexVar - Commands 15

13 c:= tVar.sqrt(a^2+b ^2)

14 }

15 #Disable \\verb|tVar.REMOVE_ZEROS|

16 tVar.REMOVE_ZEROS = false

17 {

18 a:=2.0

19 b:=3.3

20 c:= tVar.sqrt(a^2+b ^2)

21 }

22 \end{tVar}

Output

Default settings

a= 2

b= 3.3

c=pa2+b2=p22+ 3.32= 3.859

Disable tVar.REMOVE_DECIMAL_SEPARATOR

a= 2.0

b= 3.3

c=pa2.0+b2.0=p2.02.0+ 3.32.0= 3.859

Disable tVar.REMOVE_ZEROS

a= 2.000

b= 3.300

c=pa2.000 +b2.000 =p2.0002.000 + 3.3002.000 = 3.859

5.6 Plotting with Gnuplot

Plotting in TexVar is support via Gnuplot. The code describing the gure is generated in TexVar

and is sent to Gnuplot which creates the graphics.

5.6.1 Conguration

For enabling plotting the path to the Gnuplot executable has to be set via a global parameter.

By default its set to tVar.GNUPLOT_LIBRARY ="gnuplot". In case you work on a windows

system and want to specify the absolute path to your Gnuplot install the command has to be

tVar.GNUPLOT_LIBRARY =[==["WINDOWSPATH"]==].

The Gnuplot terminal is by default tVar.GNUPLOT_TERMINAL = "postscript eps enhanced

color font 'Helvetica,12'" and the le extension is tVar.GNUPLOT_FILE_NAME_EXTENSION

= "eps".

16 5 TexVar - Commands

5.6.2 Creating a Plot

Every parameter set through [tPlot].* is directly translated to a gnuplot command. Actually

tPlot is only aware of the following commands

tPlot:New(present[tPlot]) Creates a new plot. Present is an optional pa-

rameter. If a value gets passed the conguration

of the plot is used as template for the new plot.

[tPlot].steps = 0.1 Resolution for functions

[tPlot].conf.size = "14cm,8

cm"

Size of the plot

[tPlot].xrange = "[0,10]" Range of the x axis and min and max value for

function creation.

[tPlot]:add(f or

{{1,2},{3,2}},"f(x)", "

with line lt 1 lc 2")

Adds a functions or points to the plot.

[tPlot]:plot() Generates the plot and returns the include-

graphics command.

1\begin{tVar}

2f(x):=1/ x

4plot1=tPlot :New ()

5plot1.xlabel = "{/ Symbol e}_c"

6plot1.ylabel = "{/ Symbol s}_c"

7plot1.steps = 0.001

9plot1.xtics = "0.1"

10 plot1.xrange = "[0:1] "

11 plot1.yrange = "[0:16] "

12 plot1.conf.size = "6cm ,6cm"

13 plot1:add(f,"f(x)", "with line lt 1 lc 2")

14 plot1 :add({{0.2 ,6} ,{0 .5 ,12}} , "pt", "with points lc 1")

15 #\\ begin{ center }

16 plot1:plot ()

17 #\\end{center}

18 \end{tVar}

Output

f(x) = 1

5 TexVar - Commands 17

0 0.2 0.4 0.6 0.8 1

σc

εc

f(x)

Currently TexVar only supports 2D plots and functions with one attribute. If you want to

print a function with more than one attribute you can create a helper function.

1\begin{tVar}

2-- use plot1 as template

3plot2=tPlot :New(plot1)

5f(x,z):=(1/x)^z

6-- helper functions with fixed z values

7f_h_1(x):=f(x,2);

8f_h_2(x):=f(x,1);

10 plot2:add(f_h_1 ,"z=2","with line lt 1 lc 2")

11 plot2:add(f_h_2 ,"z=1","with line lt 1 lc 3")

13 #\\ begin{ center }

14 plot2:plot ()

15 #\\end{center}

16 \end{tVar}

Output

f(x, z) = 1

0 0.2 0.4 0.6 0.8 1

σc

εc

z=2

z=1

18 5 TexVar - Commands

5.7 Mathematical Commands

The following subsections are just a listing of currently implemented mathematical functions.

5.7.1 General

These functions can be used with every tVar object.

• tVar.sqrt([tVar],[tVar] nth-root)

• tVar.PI

• tVar.abs([tVar])

• tVar.acos([tVar])

• tVar.acosd([tVar])

• tVar.cos([tVar])

• tVar.cosd([tVar])

• tVar.cosh([tVar])

• tVar.asin([tVar])

• tVar.asind([tVar])

• tVar.sin([tVar])

• tVar.sind([tVar])

• tVar.sinh([tVar])

• tVar.atan([tVar])

• tVar.atand([tVar])

• tVar.tan([tVar])

• tVar.tand([tVar])

• tVar.tanh([tVar])

• tVar.ceil([tVar])

• tVar.oor([tVar])

• tVar.exp([tVar])

• tVar.ln([tVar])

• tVar.log10([tVar])

• tVar.atan2(X[tVar],Y[tVar])

• tVar.fact([tVar])

5.7.2 Matrices and Vectors

These functions can only be used with tMat or tVec objects.

• [tMat]:T()

• [tMat]:Det()

• [tMat]:Inv()

• tVec.crossP([tVec],[tVec])

5.8 The Link Function

If you want to use your own functions within TexVar, you can use the Link function to link

them to tVar functions. This only applies to functions that don’t use TexVar objects for calcu-

lation. If you want to write a TexVar function see Section 5.2. The following code shows the

implementation of the factorial function with the link function.

1\begin{tVar}

2function mycalcFactorial(n)

5 TexVar - Commands 19

3-- no tVar objects here just numbers

4if n <=1 then return 1end

5return n*mycalcFactorial(n-1)

6end

8-- link it

9myfact = tVar.link ( mycalcFactorial ,"","!",nil,nil,nil,true)

11 a:=10

12 b:=myfact(a)

13 \end{tVar}

Output

a= 10

b=a! = 10! = 3628800

The link function has the following attributes:

•function: The function that should be transformed to a TexVar function.

•texBefore: Text which is added before the return value.

•texAfter: Text which is added after the return value.

•returntype (optional): Denes the type of the return objecte, possible values are tVar,

tMat, tVec

•inputUnit (optional): Required unit for input attributes.

•outputUnit (optional): Unit of returned function.

•pipeUnit (optional): If true, the input and output unit is derived from the rst passed

argument.

All Lua math functions are implemented this way.

For example the Lua function math.atan2:

1--- calculates inverse tangens with with appr. quadrant

2--

3-- @param opposite (tVar ,number ) values

4-- @param adjacent (tVar ,number ) values

5-- @return ( tVar)

6tVar.link(math.atan2 ,"\\ text { atan2 }\\ left(" ,"\\ right )",nil,

tVar.units("m"),tVar.units ("rad"),false)

20 6 Examples

Output

a= 3 m

b= 4 m

c=atan2 (a;b) = atan2 (3; 4) = 0.644

6 Examples

6.1 U-Value

This is a very simple example using only the basic functionality of TexVar.

1Calculating the U-Value for an element with two layers. \\

2\begin{tVar}

3#\\ noindent Resistance of surface

4{plain

5R_se := 0.3: setUnit("m^2.K/W")

6#,~

7R_si := 0.13:setUnit("m^2.K/W")

9#Parameters for elements

10 {

11 d_1 := 0.20:setUnit("m")

12 \\ lambda_1 := 0 .035:setUnit ("W/( m.K )")

13 d_2 := 0.10:setUnit("m")

14 \\ lambda_2 := 0.5: setUnit("W/( m.K) ")

15 }

16 #Calculate thermal resistance

17 R := (R_se + d_1/ lambda_1 + d_2/ lambda_2 + R_si ): setUnit("m^2

.K/W")

18 #Calculate U-Value

19 U:=(1/R): setUnit("W/(m^2 .K)")

20 \end{tVar}

Output

Calculating the U-Value for an element with two layers.

Resistance of surface

Rse = 0.3m2K/W, Rsi = 0.13 m2K/W

6 Examples 21

Parameters for elements

d1= 0.2m

λ1= 0.035 W/(m K)

d2= 0.1m

λ2= 0.5W/(m K)

Calculate thermal resistance

R=Rse +d1

λ1

+d2

λ2

+Rsi = 0.3 + 0.2

0.035 +0.1

0.5+ 0.13 = 6.344 m2K/W

Calculate U-Value

U=1

R=1

6.344 = 0.158 W/(m2K)

6.2 Rotating a Vector

This example shows the usage of the parameter tMat.eqTexAsMatrix as mentioned in Section

5.5.

1\begin{tVar}

2tMat.MATRIX_EQUATION_AS_MATRIX = true

4#Rotation angle in degree

5\\ theta :=45: setUnit ("°")

7#Rotation matrix in R2

9A := {{ tVar.cos ( theta ),- tVar.sin ( theta )},{ tVar.sin ( theta ),

tVar.cos( theta )}}: outRES_EQ ()

10 e_x :={1 ,0}

11 }

14 tMat.MATRIX_EQUATION_AS_MATRIX = false

15 e:=(A*e_x)

16 \end{tVar}

Output

Rotation angle in degree

θ= 45 °

22 6 Examples

Rotation matrix in R2

A= cos (θ) (−sin (θ))

sin (θ)cos (θ)!= 0.525 (−0.851)

0.851 0.525 !

~ex= 1

~e =A·~ex= 0.525 (−0.851)

0.851 0.525 !· 1

0!= 0.525

0.851!

6.3 Vector Calculations - Custom Function

This example shows how to create a custom TexVar function for calculating the angle between

two vectors. The function has an extra parameter for disabling printing.

1\begin{tVar}

3tVar.OUTPUT_MODE = " RES_EQ"

4function angleBetweenVectors(a,b, disablePrinting)

5if disablePrinting then

6tVar.OUTPUT_DISABLED = true

7end

9#Calculate the length of the vectors

11 len_a := tVar.sqrt (a*a)

12 len_b := tVar.sqrt (b*b)

14 #Normalize the vectors

16 a_n :=(a/len_a)

17 b_n :=(b/len_b)

19 \\ alpha := tVar.acosd (a_n* b_n ):setUnit ("°")

21 if disablePrinting then

22 tVar.OUTPUT_DISABLED = false

23 end

25 return alpha

26 end

28 #With output

29 {

30 v_1 :={1 ,0 .4 ,0 .5 }

31 v_2 :={0.3 ,1,0}

32 }

6 Examples 23

34 \\ alpha_1 := angleBetweenVectors (v_1 , v_2)

36 #Without output

37 {

38 v_3:={4,0.2,5}

39 v_4 :={9.3 ,8,1}

40 }

41 \\ alpha_2 := angleBetweenVectors (v_3 ,v_4 ,true)

42 \end{tVar}

Output

With output

~v1=





0.4

0.5







~v2=





0.3







Calculate the length of the vectors

lena=p~v1·~v1= 1.187

lenb=p~v2·~v2= 1.044

Normalize the vectors

~an=~v1

lena

=





0.842

0.337

0.421







bn=~v2

lenb

=





0.287

0.958







α=acos ~an·~

bn= 0.971 °

α1=α= 0.971 °

24 6 Examples

Without output

~v3=





0.2







~v4=





9.3







α2=α= 0.982 °

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