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STADYN Wave Equation Program 1: HTML Formatted Output

This is the first installment of a new series on the development of the STADYN wave equation program for analyzing impact driven foundation piles. This program was the subject of this study and what you’ll see on this site is the sequel to that study.

The first in the series, however, isn’t really about technical aspects of the program and application, but something more mundane: formatting the output in a way that one can easily read the output. Although STADYN is written in FOTRAN 77 (with extensions) the techniques shown here are useful elsewhere and in other languages. In fact, techniques similar to these were used in the development of this routine, which is in PHP.

Engineers have done tabular output in regimented text format for many years. While it gets the job done, it’s not very pretty or easy to read, and requires some very regimented formatting to keep the columns straight. The simplest way to illustrate this is to use a worked example. Although ultimately the idea is to apply this to STADYN, the program used is a revision of the BENT1 program which is available on this site and goes back to the 1970’s.

BENT1 is a program designed to analyze pile groups for axial and lateral response to loading, and is in fact the ancestor of programs such as the COM624 series (it’s the first of those,) LPILE and APILE. It starts off with output that looks like this:

EX 1  COPANO BAY CAUSEWAY, ARKANSAS COUNTY TEXAS, US HIGHWAY 35    


          LIST OF INPUT DATA ---


          PV              PH             TM           TOL    KNPL KOSC
     0.8440E+06     0.3640E+05     0.1682E+08     0.1000E-02  4    0


        CONTROL DATA FOR PILES AT EACH LOCATION 

     PILE NO    DISTA        DISTB      BATTER         POTT       KS   KA
         1    -0.1260E+03  0.0000E+00 -0.2440E+00  0.1000E+01    1   1
         2    -0.9000E+02  0.0000E+00  0.0000E+00  0.2000E+01    1   1
         3     0.9000E+02  0.0000E+00  0.0000E+00  0.2000E+01    1   1
         4     0.1260E+03  0.0000E+00  0.2440E+00  0.1000E+01    1   1



  PILE NO.  NN         HH            DPS      NDEI   CONNECTION FDBET
     1     31    0.36000E+02    0.12000E+03    1      FIX    0.0000E+00
     2     31    0.36000E+02    0.12000E+03    1      FIX    0.0000E+00
     3     31    0.36000E+02    0.12000E+03    1      FIX    0.0000E+00
     4     31    0.36000E+02    0.12000E+03    1      FIX    0.0000E+00

Note the text is all caps (typical for the era) and formatted in a fixed-pitch format. The programmer had to exercise some care to get the columns and headers lined up properly, which in FORTRAN 77 could be a job.

HTML documents—which are still, in their various forms, what you see most often when you browse the web—are basically ASCII text documents with formatting markup. This is also true of XML documents as well. Just about any language can readily generate ASCII files, and FORTRAN 77 is no exception. One of the biggest changes in the Internet, however, is that, in the early days, HTML documents were generated by hand (including the markup) and were uploaded to a server as static web pages. Today virtually all pages are generated « dynamically » to varying degrees. (The major downside to dynamic generation is that many security flaws in web pages come from holes in the code, but that’s another post.) In a sense we’re going to make FORTRAN 77 become a dynamic page generator.

Getting back to the output above, the first line was generated by the following code:

 1111 FORMAT(20A4)
  100 READ(3,111,END=800) ANUM
      CALL UPPER(ANUM,72)
  111 FORMAT(72A1)
      READ(3,1111)IBUF
      CALL UPPER(IBUF,80)
...
  132 WRITE(4,111)(ANUM(IK),IK=KII,72)

Here the title is read one character at a time into a character array, converted to upper case using the « UPPER » routine, and then output to the file using the same format statement it was read with.

Turning to how to do this in HTML—and the HTML you’re going to see here is very old and basic—we start by generating the header for the page with this code:


 write(4,*)'<head><title>BENT2 Run for Case ',casenm,
&'</title></head><body>
<div align="center">' 

Just about all HTML pages have a header, and here we use the case name variable to « personalise » the title, which appears at the top of the page. Note also that, when we transition to the body portion of the page, we use a div tag to center all of the content. That’s a matter of personal preference. It’s also possible to put CSS in the head as well, which opens up possibilities to liven up the page. Whether you do that depends upon how deep into HTML you want to get. With twenty years of experience doing this, I could have done more, but what you’ll see will be an improvement.

From here we change the last line of the original code shown above to generate the title as follows:

 90 WRITE (4,*) '
<h2>',(anum(ik),ik=kii,72),'</h2>
'

The header tags (Level 2, I think Level 1 generally makes it too large) are placed at the start and end of line and the title is in the middle. We could have gotten rid of the all-caps business, but for starters we did not.

Now to the tabular data. The title and table immediately below the original code was generated using this:

     WRITE(4, 150)
 150 FORMAT ( // , 5X, ' LIST OF INPUT DATA ---'
    & /// 4X, ' PV PH '
    & , ' TM TOL KNPL KOSC')
     WRITE(4, 160) PV, PH, TM, TOL, KNPL, KOSC
 160 FORMAT (4E15.4, I3, I5)

This is a simple one-row table with a header above it. Doing this in HTML using HTML tables (which, I know, are hopelessly obsolete but in this case handy) results in the following:

 WRITE (4,110)
110 FORMAT ('
<table border="2" cellspacing="2" cellpadding="3">',
&'<caption>List of Input Data</caption>',
&'
<tr>
<td>Vertical Load on Foundation, kips</td>
',
&'
<td align="center">Horizontal Load on Foundation, kips</td>
',
&'
<td align="center">Moment on Foundation, in-kips',
&'</td>
<td align="center">Iteration Tolerance, in.',
&'</td>
<td align="center">Number of Pile Locations',
&'</td>
<td align="center">Solution Oscillation Control</td>
</tr>
')
WRITE (4,120) 0.001*pv,0.001*ph,0.001*tm,tol,knpl,kosc
120 FORMAT ('
<tr>
<td>',4(g15.4,'</td>
<td align="center">'),
&i3,'</td>
<td align="center">',i5,
&'</td>
</tr>
</table>
')

The last table shown earlier is only slightly harder to write. The original code (which includes the read statement) is as follows:

      WRITE(4, 170)
  170 FORMAT ( // , 5X, '   CONTROL DATA FOR PILES'
     &     , ' AT EACH LOCATION ' // 4X, ' PILE NO   '
     &     , ' DISTA        DISTB      BATTER         '
     &     , 'POTT       KS   KA')
      DO 200 K = 1, KNPL
      READ(3,*) LINNO, DISTA(K), DISTB(K), THETA(K),
     &      POTT(K), KS(K), KA(K)
      WRITE(4, 190)   K, DISTA(K), DISTB(K),
     &      THETA(K), POTT(K), KS(K), KA(K)
  180 FORMAT (4E10.4, 2I5)
  190 FORMAT (5X, I5, 1E15.4, 3E12.4, I5, I4)
  200 CONTINUE

The new table generation code looks like this:

 130 format ('
<table border="2" cellspacing="2" cellpadding="3">',
&'<caption>Control Data for Piles at Each Location</caption>',
&'
<tr>
<td>Pile Number',
&'</td>
<td align="center">Horizontal Coordinate of Pile Top, in.',
&'</td>
<td align="center">Vertical Coordinate of Pile Top, in.',
&'</td>
<td align="center">Batter, Degrees',
&'</td>
<td align="center">Number of Piles at Location',
&'</td>
<td align="center">p-y Curve Identifier',
&'</td>
<td align="center">t-z Curve Idenfifier',
&'</td>
<td align="center">Number of Pile Increments',
&'</td>
<td align="center">Increment Length, in.',
&'</td>
<td align="center">',
&'Distance from Pile Head to Soil Surface, in.',
&'</td>
<td align="center">Number of Flexural Stiffness Values',
&'</td>
<td align="center">Head Connection of Pile',
&'</td>
<td align="center">Rotational Restraint Value',
&'</td>
</tr>
')
DO 150 k=1,knpl
READ (3,*) linno,dista(k),distb(k),theta(k),
&pott(k),ks(k),ka(k)
150 CONTINUE
DO 180 i=1,knpl
READ (3,40) ibuf
CALL upper (ibuf, 80)
ieod=0
istrt=1
CALL iget (linno)
CALL iget (nn(i))
CALL fget (hh(i))
CALL fget (dps(i))
CALL iget (ndei(i))
CALL strget (tc(i), 3)
CALL fget (fdbet(i))
CALL fget (e(i))
WRITE (4,170) i,dista(i),distb(i),57.295779513*theta(i),
&pott(i),ks(i),ka(i),
&nn(i),hh(i),dps(i),ndei(i),tc(i),fdbet(i)
170 FORMAT ('
<tr>
<td>',i5,
&1('</td>
<td align="center">',g15.4),
&3('</td>
<td align="center">',g12.4),
&2('</td>
<td align="center">',i5),
&1('</td>
<td align="center">',i7),
&2('</td>
<td align="center">',g15.5),
&1('</td>
<td align="center">',i5),
&1('</td>
<td align="center">',a3),
&1('</td>
<td align="center">',g14.4),
&'</td>
</tr>
')
ndst=ndei(i)
DO 180 j=1,ndst
READ (3,*) linno,rri(i,j),xx1(i,j),xx2(i,j)
180 CONTINUE
write(4,*)'</table>
'

The biggest difference is the need to write multiple table rows. On the other hand, we were able to combine two tables into one, which makes for easier reading.

Note: WordPress (which powers this site) may power a quarter of the web, but it’s a very “vertical” format and doesn’t always “do horizontal” very well.  With non-mobile devices, the wider tables will bleed off to the right, but you can see them.  With mobile devices, it just cuts them off because these don’t have a left-right scroll.  Also, it doesn’t always reproduce FORTRAN 77 code very gracefully, we apologize for the inconvenience.

The final result of all of this coding looks like this:

EX 1 COPANO BAY CAUSEWAY, ARKANSAS COUNTY TEXAS, US HIGHWAY 35

List of Input Data

Vertical Load on Foundation, kips

Horizontal Load on Foundation, kips

Moment on Foundation, in-kips

Iteration Tolerance, in.

Number of Pile Locations

Solution Oscillation Control

844.0

36.40

0.1682E+05

0.1000E-02

4

0

Control Data for Piles at Each Location

Pile Number

Horizontal Coordinate of Pile Top, in.

Vertical Coordinate of Pile Top, in.

Batter, Degrees

Number of Piles at Location

p-y Curve Identifier

t-z Curve Idenfifier

Number of Pile Increments

Increment Length, in.

Distance from Pile Head to Soil Surface, in.

Number of Flexural Stiffness Values

Head Connection of Pile

Rotational Restraint Value

1

-126.0

0.0000

-13.98

1.000

1

1

31

36.000

120.00

1

FIX

0.0000

2

-90.00

0.0000

0.0000

2.000

1

1

31

36.000

120.00

1

FIX

0.0000

3

90.00

0.0000

0.0000

2.000

1

1

31

36.000

120.00

1

FIX

0.0000

4

126.0

0.0000

13.98

1.000

1

1

31

36.000

120.00

1

FIX

0.0000

So how does this look when implemented in STADYN? We’ll start with the case which compares STADYN’s output with Finno (1989,) and the output (after complete conversion to HTML) looks like this:

Output for STADYN Wave Equation Program

Case finno2, 7: 5:41:78 9 May 2017

Hammer Properties
Ram Mass, kg 0.295E+04
Hammer Equivalent Stroke, mm 914.
Hammer Efficiency, Percent 67.0
Ram Velocity at Impact, m/sec 3.46
Ram O.D., mm 286.
Ram I.D., mm 0.000
Cross-Sectional Area of Ram, mm**2 0.642E+05
Ram Length, mm 0.583E+04
Cap Properties
Mass of Cap, kg 465.
Cap O.D., mm 483.
Cap I.D., mm 0.000
Cap Body Thickness, mm 323.
Cushion Thickness, mm 127.
Cushion Material Micarta & Aluminium
Cushion Area Same as Ram
Pile Properties
Pile Length, m 15.5
Pile Length Immersed in Soil, m 15.2
Head Cross-Sectional Area, mm**2 0.134E+05
Head Impedance, kN-sec/m 541.
omega2 (c/L), 1/sec 330.
2L/c,msec 6.07
Number of Complete Cycles for Pile Stress Wave, L/c 8
Ratio of Actual to Ideal Interface Stiffness 4.00
Minimum Distance from Pile for Model Side, m 15.0
Width of Soil Box (x), m 15.2
Depth of Soil Box (y), m 30.5
Material Properties for Hammer and Pile Materials
Material Type Material Code Modulus of Elasticity, MP Poissons Ratio Density, kg/m^3 Cohesion, MPa Yield Strength MPa Phi Degrees Psi Degrees Acoustic speed, m/sec
Steel 1 0.207E+06 0.300 0.788E+04 0.131E+04 0.262E+04 0.000 0.000 0.512E+04
Concrete 2 0.275E+05 0.300 0.241E+04 50.0 100. 0.000 0.000 0.338E+04
Wood 3 0.965E+04 0.300 800. 75.0 150. 0.000 0.000 0.347E+04
Aluminium 4 0.690E+05 0.300 0.271E+04 0.100E+04 0.200E+04 0.000 0.000 0.504E+04
Micarta & Aluminium 5 0.241E+04 0.300 0.183E+04 100. 200. 0.000 0.000 0.115E+04
Data for Region 1 (Pile )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 219.1, y = -304.8), mm 10 3(x= 228.6, y= -304.8), mm
100 Corner Locations Nodes and Connectivity 100
1(x = 219.1, y = 0.0), mm 2 4(x = 228.6, y = 0.0), mm
Data for Region 2 (Pile )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 16
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 219.1, y = 0.0), mm 1 3(x= 228.6, y= 0.0), mm
100 Corner Locations Nodes and Connectivity 5
1(x = 219.1, y = 15211.4), mm 3 4(x = 228.6, y = 15211.4), mm
Data for Region 3 (Pile )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 219.1, y = 15211.4), mm 2 3(x= 228.6, y= 15211.4), mm
100 Corner Locations Nodes and Connectivity 6
1(x = 0.0, y = 15220.9), mm 4 4(x = 228.6, y = 15220.9), mm
Data for Region 4 (Pile )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 0.0, y = 15220.9), mm 3 3(x= 228.6, y= 15220.9), mm
100 Corner Locations Nodes and Connectivity 7
1(x = 0.0, y = 15240.0), mm 8 4(x = 228.6, y = 15240.0), mm
Data for Region 5 (Soil )
Number of Nodes in a Regional Row 21
Number of Full Element Columns 20
Geometric Squeeze in x-direction 3
Number of Nodes in a Regional Column 16
Number of Full Element Rows 3
Geometric Squeeze in y-direction 1
2(x = 228.6, y = 0.0), mm 100 3(x= 15240.0, y= 0.0), mm
2 Corner Locations Nodes and Connectivity 101
1(x = 228.6, y = 15211.4), mm 6 4(x = 15240.0, y = 15211.4), mm
Data for Region 6 (Soil )
Number of Nodes in a Regional Row 21
Number of Full Element Columns 20
Geometric Squeeze in x-direction 3
Number of Nodes in a Regional Column 2
Number of Full Element Rows 3
Geometric Squeeze in y-direction 1
2(x = 228.6, y = 15211.4), mm 5 3(x= 15240.0, y= 15211.4), mm
3 Corner Locations Nodes and Connectivity 101
1(x = 228.6, y = 15220.9), mm 7 4(x = 15240.0, y = 15220.9), mm
Data for Region 7 (Soil )
Number of Nodes in a Regional Row 21
Number of Full Element Columns 20
Geometric Squeeze in x-direction 3
Number of Nodes in a Regional Column 2
Number of Full Element Rows 3
Geometric Squeeze in y-direction 1
2(x = 228.6, y = 15220.9), mm 6 3(x= 15240.0, y= 15220.9), mm
4 Corner Locations Nodes and Connectivity 101
1(x = 228.6, y = 15240.0), mm 9 4(x = 15240.0, y = 15240.0), mm
Data for Region 8 (Soil )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 21
Number of Full Element Rows 1
Geometric Squeeze in y-direction 3
2(x = 0.0, y = 15240.0), mm 4 3(x= 228.6, y= 15240.0), mm
100 Corner Locations Nodes and Connectivity 9
1(x = 0.0, y = 30480.0), mm 101 4(x = 228.6, y = 30480.0), mm
Data for Region 9 (Soil )
Number of Nodes in a Regional Row 21
Number of Full Element Columns 20
Geometric Squeeze in x-direction 3
Number of Nodes in a Regional Column 21
Number of Full Element Rows 3
Geometric Squeeze in y-direction 3
2(x = 228.6, y = 15240.0), mm 7 3(x= 15240.0, y= 15240.0), mm
8 Corner Locations Nodes and Connectivity 101
1(x = 228.6, y = 30480.0), mm 101 4(x = 15240.0, y = 30480.0), mm
Data for Region 10 (Hammer )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 219.1, y = -304.8), mm 11 3(x= 228.6, y= -304.8), mm
100 Corner Locations Nodes and Connectivity 100
1(x = 219.1, y = -304.8), mm 1 4(x = 228.6, y = -304.8), mm
Data for Region 11 (Hammer )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 14.3, y = -627.3), mm 14 3(x= 142.9, y= -627.3), mm
13 Corner Locations Nodes and Connectivity 12
1(x = 219.1, y = -304.8), mm 10 4(x = 228.6, y = -304.8), mm
Data for Region 12 (Hammer )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 142.9, y = -627.3), mm 100 3(x= 241.3, y= -627.3), mm
11 Corner Locations Nodes and Connectivity 100
1(x = 228.6, y = -304.8), mm 100 4(x = 241.3, y = -304.8), mm
Data for Region 13 (Hammer )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 0.0, y = -627.3), mm 100 3(x= 14.3, y= -627.3), mm
100 Corner Locations Nodes and Connectivity 11
1(x = 0.0, y = -304.8), mm 100 4(x = 219.1, y = -304.8), mm
Data for Region 14 (Hammer )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 2
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Micarta & Aluminium
2(x = 0.0, y = -627.3), mm 15 3(x= 142.9, y= -627.3), mm
100 Corner Locations Nodes and Connectivity 100
1(x = 14.3, y = -627.3), mm 11 4(x = 142.9, y = -627.3), mm
Data for Region 15 (Hammer )
Number of Nodes in a Regional Row 2
Number of Full Element Columns 1
Geometric Squeeze in x-direction 1
Number of Nodes in a Regional Column 7
Number of Full Element Rows 1
Geometric Squeeze in y-direction 1
Region Material Steel
2(x = 0.0, y = -6458.1), mm 100 3(x= 142.9, y= -6458.1), mm
100 Corner Locations Nodes and Connectivity 100
1(x = 0.0, y = -627.3), mm 14 4(x = 142.9, y = -627.3), mm
General Properties of Run
Total Number of Nodes 860
Maximum Number of Nodes Allowed 10000
Percent of Available Nodes Used 8.60
Number of Elements Used 789
Maximum Number of Elements Allowed 7500
Percent of Available Elements Used 10.5
Total Number of Degrees of Freedom 1660
Total Degrees of Freedom Available 20000
Percent of Available Used 8.30
Number of Stiffness Matrix Entries 88208
Total Stiffness Matrix Entries Available 2000000
Percent of Available Entries Used 4.41
Node at Pile Head 3
Node at Pile Middle 19
Node at Pile Toe 37
Element at Pile Toe 18
Node at Ram Point 847
Element at Soil Corner 759
Level of Water Table from Soil Surface, m 5.18
Estimated Time Steps Used in Dynamic vtk output 143
Parameters for Explicit Dynamic Analysis:
Number of Time Steps 38239
Time Step, msec 0.635E-03
Element for Minimum Time Step 779
Newmark Constants:
Beta 0.000
Gamma 0.500
c1 0.202E-12
c2 0.317E-06
c3 0.317E-06
c4 0.000
c5 0.635E-06
Results of Dynamic Run
Actual Time Steps for vtk Run 143
Pile Set, mm 16.9
Blowcount, blows/300 mm 17.7
Layer Data For Static Load Test
Layer Bottom y-coordinate, m xi eta E, kPa Poissons Ratio Unit Mass, kg/m**3 c, kPa Yield Strength, kPa Friction Angle, Deg. Dilitancy Angle, Deg. Acoustic Speed, m/sec Gs Total Stress, kPa u, kPa Effective Stress kPa xi Optimisation Index eta Optimisation Index
1 5.18 -1.00 -0.560 0.188E+05 0.250 0.161E+04 0.000 0.000 30.5 0.000 108. 2.65 81.8 0.000 81.8 1 2
2 7.32 -1.00 -0.560 0.188E+05 0.250 0.200E+04 0.000 0.000 30.5 0.000 108. 2.65 124. 20.9 103. 1 2
3 15.2 0.000 -0.600 0.180E+05 0.350 0.193E+04 28.0 56.0 15.1 0.000 111. 2.71 273. 98.6 175. 3 4
4 30.5 0.000 -0.600 0.180E+05 0.350 0.193E+04 28.0 56.0 15.1 0.000 111. 2.71 561. 248. 313. 5 6
Davisson and Randolph-Wroth Coefficients
Davisson Inverse Slope, N/m 0.179E+09
Davisson Offset, mm 7.81
Randolph & Wroth Inverse Slope, N/m 0.197E+09
Static Load Data
Meyerhof Maximum Pile Capacity, kN 0.153E+05
Number of Static Load Steps 1000
Load Increment per Step, kN 15.3
Maximum Number of Newton Steps 25000
Davisson Load, kN 976.
Brinch-Hansen 80% Load, kN 0.104E+04
Brinch-Hansen 90% Load, kN 996.
Maximum Curvature Load, kN 0.101E+04
Slope-Tangent Load, kN 946.

At the end, the page needs to be closed with a statement like this:

 write(4,*)'</div>
</body></html>'

 

In addition to the changes to the output, extensive changes were made to the input. The original code was a research type of code and the input was strictly from a file. Moving forward, the program was made more interactive to allow the program itself to generate the text file necessary for the input. Because of compiler limitations, for STADYN the dialogue is of a text type. It’s also possible to use dialog boxes and entry, depending upon the compiler and language you’re coding in. Many of the program’s options were « hard coded » into the program, as some preferences are fixed. Newer ones will be introduced, and discussed in later instalments.

Although all of what’s discussed here is fairly primitive, the result is considerably easier to read and understand. It can also be copied into either word processing or spreadsheet software with little difficulty.

As noted earlier, later instalments of this series will get into more technical aspects of the program, but improving the output will make these discussions easier for this or any program.

References

All references for this series are in the original study, unless otherwise noted.

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