Writing Word documents for multiple formats
Emma Cliffe
May 2012
This work was
carried out as part of a HESTEM Mathematics Curriculum Innovation project. We
have explored methods to produce flexible and accessible learning resources for
mathematics with a focus on producing a guide for staff in HEI to enable them
as individuals to create flexible resources efficiently and robustly.
A significant
barrier for disabled students who enroll on HE programmes of study involving
any mathematical or statistical content is the suitability of the resource
format for their particular situation. To date, there is no single facility to
produce such resources in a flexible format which can be modified according to
individual requirements. We hope to provide staff with the requisite knowledge
to access and make use of a small selection of currently available software to
produce a variety of accessible formats automatically from a single master
document. This will enable departments to:
- design inclusive curriculum delivery;
- anticipate potential barriers and
resolve these in a proactive manner;
- communicate realistic expectations to
prospective entrants and support staff;
- avoid the use of inflexible learning
resources which cannot be tailored to particular needs and
- avoid making costly reactive
adjustments for individual students which often result in additional
versions of documents which cannot be reused and which are not updated.
Contents
Introduction. 1
Document
structure. 3
Global
settings. 3
The
transformations. 3
Writing
a structured document 4
Structure,
navigation, text 4
Labels
and references. 5
Standard structures. 5
Quotations. 5
Lists. 5
Frames and rules. 6
Tables. 6
Maths
symbols. 6
Standard. 6
Greek. 7
Letter-like
symbols. 7
Operators. 7
Arrows. 7
Negated
relations. 8
Scripts. 8
Frakturs. 8
Double
struck. 8
Geometry. 8
Maths
structures. 9
Displayed
math. 9
Word
structures. 10
Graphics. 11
Bibliography. 12
A fontsize of
12pt on A4 paper should be specified. This is the smallest size considered to
be appropriate for a clear print format by the RNIB (1). Using a clear print
format will ensure your base document format can be immediately accessed by
more people. The RNIB also recommends that the text layout be simple and clear
hence text should be presented in one column only.
Other RNIB
guidelines include:
- The font you choose should be clear,
avoiding anything stylized.
- All body text should be left aligned.
- Use bold sparingly, only highlight a
few words rather than a paragraph.
- Don’t use blocks of capitalised
letters, and try not to use any italics or underlining.
- All text should be the same
orientation on the page.
The
transformations will not be covered in this document. Please see accompanying
documents.
It is more
important to remember that what you are writing will be transformed. Many authors
will write a Word document expecting the reader to view it in the same font,
fontsize and using the same software as they are. It is important to remember
that the act of transforming the document can destroy or alter much of the
formatting and layout (consider a version delivered only in speech, or a format
in a 20pt font size for instance).
Ideally, of
course, you should proofread all output formats in use
—
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjxmWaIq
ubqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr
Ffpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0F
irpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaa
GcbaqefeKCPfgBaGqbaKqzagaeaaaaaaaaa8qacaWFuacaaa@3DBE@
and
if the format supports speech then you should in addition proofread the speech
output. However, practically speaking it is admitted that this is likely to be
very time-consuming. Student feedback acknowledges this but recommends that at
least a subset of the documents you produce are proofread in all formats.
Authors are likely to find this a useful exercise as it can assist in the
transition of mindset from using Word as a “what you see is what you get” or
WYSIWYG word processor to using it primarily to encode content and describe
structure.
Content must be
structured to ensure that transformations which produce html, xhtml or LaTeX documents
produce structured output that is useful for a screenreader / text-to-speech
user and which aids navigation e.g. in large print versions. Another
consideration is that very long structureless webpages are quite unnatural.
In structured Word,
even in short documents, as much as the document as possible (all except
paragraphed text interspersing the other elements) should be laid out using
Word tools. For instance, a new page must be introduced using the Page Break
button, not by adding multiple newlines. Another example is that by numbering each
paragraph you can visually mimic a numbered list but structurally it is not
equivalent. In longer documents Styles should always be used rather than
visually breaking creating section titles using bold text and font size changes
(visually mimicking the sections). This will permit a table of contents to be
automatically generated and allow the outline view and navigation pane to
function. In transformed formats it will permit the document to be sectioned,
to be broken down into shorter pieces and navigated directly. For extensive
guidance on produced structured Word documents please see the JISC TechDis
guidelines on Authoring Accessible Documents (2).
In the following
sections the structuring commands, symbols and graphics manipulation available
in the transformations, the requirements of using these and our advice on them
is given.
You may align
text left, center text or align text right however, this information will all
be lost to a screenreader user:
Centered text
Align text left
Align text right
You may style
short pieces of text using font size and text style commands however, this
information will be lost to a screenreader user. Text should not be made
smaller in order to fit it on a page width or height
—
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjxmWaIq
ubqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr
Ffpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0F
irpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaa
GcbaqefeKCPfgBaGqbaKqzagaeaaaaaaaaa8qacaWFuacaaa@3DBE@
this is a WYSIWYG approach, rather than encoding of content, and will
not be retained in transformations. It should be remembered that styled text
may impede a partially sighted reader or a reader with a specific reading
disability. In general a style should as Emphasis or Strong should be used for emphasis rather than
selecting italic or bold text as this allows the user to modify the appearance
of emphasized text and to understand the intend. The following text sizes will
transform to different size text in each of the transformations.
Size 8. Size 12. Size 14. Size 16. Size 18. Size 20. Size 24.
Standard text. Bold
text. Italics text. Underlined
text.
When referring to another part of the document internal
hyperlinks should be used to enable
the reader to navigate and locate the information as required. For mathematical
symbols, see the section Maths symbols. These are inserted by selecting the text, right
clicking and selecting Hyperlink. Select Place in this Document and then select
the required section heading. This is only possible in structured documents
which have headings.
For quotes the
quote or intense quote styles should be used to ensure that these are styled
appropriately in transformed formats. However, the emphasis, colour or space is
lost to the screenreader user and so double quotes must also be used.
“Microsoft Word 2010 makes it easy to
use styles without having to know much about them.”
Basic use of references
and an automatically generated bibliography is possible. The quotation above is
from “Style
basics in Word” one of the articles at the site “Word 2010 Help and How-to” (3). Footnotes cannot be used as they cause
display problems in XHTML with IE9.
You should use
the default Bullets and Numbering, no others list
variants were tested in transform. All list points should be punctuated e.g.
with a full stop, comma, colon or semi-colon at the end of each line to ensure
appropriate pauses for the screenreader or text-to-speech user.
· A bullet list,
· using default bullets.
o
With
a level 2 sub-point.
§ With a level 3 sub-point.
· With a level 4 sub-point.
§ Punctuation is important for screenreaders
and text to speech.
1.
A
numbered list,
2.
using
default numbering.
a.
With
a level 2 sub-point.
i. With a level 3 sub-point.
1.
With
a level 4 sub-point.
ii. Punctuation is important for screenreaders
and text to speech.
Frames of any kind cannot be used by several transformations. To break up
text or to highlight an equation etc. it is appropriate to use a rule before
and after instead. However, this is not
retained in the transformation to LaTeX.
Rules are
produced by typing --- and then return on an empty line.
Tables should be
created using Insert Table. When in the table click on the Design tab and
select whether there is a first row or column. Notice how the equations are
encoded using the equation editor. All mathematics must be encoded either using
this or MathType to ensure it is transformed correctly.
All tables and
images must have captions or the incorrect caption will be used in the
transformation to LaTeX. To insert a caption hover on the top left corner until
a cross appears, right click and select Insert Caption.
Table 1:
This is a test table
First
|
Second
|
Third
|
This is the first line
|
|
|
This is the second line
|
1×2
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiabgEna0kaaikdaaaa@3999@
|
|
This is the third line
|
1×2×3
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiabgEna0kaaikdacqGHxdaTcaaIZaaaaa@3C6D@
|
6
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGOnaaaa@36CB@
|
This is the fourth line
|
1×2×3×4
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiabgEna0kaaikdacqGHxdaTcaaIZaGaey41aqRaaGinaaaa
@3F42@
|
24
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGOmaiaaisdaaaa@3785@
|
This is the fifth line
|
1×2×3×4×5
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiabgEna0kaaikdacqGHxdaTcaaIZaGaey41aqRaaGinaiab
gEna0kaaiwdaaaa@4218@
|
120
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiaaikdacaaIWaaaaa@383C@
|
This is the sixth line
|
1×2×3×4×5×6
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiabgEna0kaaikdacqGHxdaTcaaIZaGaey41aqRaaGinaiab
gEna0kaaiwdacqGHxdaTcaaI2aaaaa@44EF@
|
720
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaG4naiaaikdacaaIWaaaaa@3842@
|
This is the seventh line
|
1×2×3×4×5×6×7
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiabgEna0kaaikdacqGHxdaTcaaIZaGaey41aqRaaGinaiab
gEna0kaaiwdacqGHxdaTcaaI2aGaey41aqRaaG4naaaa@47C7@
|
5040
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGynaiaaicdacaaI0aGaaGimaaaa@38FC@
|
This is the eighth line
|
1×2×3×4×5×6×7×8
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGymaiabgEna0kaaikdacqGHxdaTcaaIZaGaey41aqRaaGinaiab
gEna0kaaiwdacqGHxdaTcaaI2aGaey41aqRaaG4naiabgEna0kaaiI
daaaa@4AA0@
|
40320
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaaGinaiaaicdacaaIZaGaaGOmaiaaicdaaaa@39B6@
|
|
The
|
End
|
Maths symbols
All mathematics
must be encoded either using the equation editor or MathType to ensure they are
transformed correctly. This test document was encoded using the standard
equation editor as MathType is considered to be a transform. Not all symbols
available in the Word equation editor can be transformed. Those that can are
listed below.
a,b,c,d,e,f,g,h,i,j,k,l,m,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaamyyaiaacYcacaWGIbGaaiilaiaadogacaGGSaGaamizaiaacYca
caWGLbGaaiilaiaadAgacaGGSaGaam4zaiaacYcacaWGObGaaiilai
aadMgacaGGSaGaamOAaiaacYcacaWGRbGaaiilaiaadYgacaGGSaGa
amyBaiaacYcaaaa@4AF7@
n,o,p,q,r,s,t,u,v,w,x,y,z
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaamOBaiaacYcacaWGVbGaaiilaiaadchacaGGSaGaamyCaiaacYca
caWGYbGaaiilaiaadohacaGGSaGaamiDaiaacYcacaWG1bGaaiilai
aadAhacaGGSaGaam4DaiaacYcacaWG4bGaaiilaiaadMhacaGGSaGa
amOEaaaa@4AF0@
A,B,C,D,E,F,G,H,I,J,K,L,M,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaamyqaiaacYcacaWGcbGaaiilaiaadoeacaGGSaGaamiraiaacYca
caWGfbGaaiilaiaadAeacaGGSaGaam4raiaacYcacaWGibGaaiilai
aadMeacaGGSaGaamOsaiaacYcacaWGlbGaaiilaiaadYeacaGGSaGa
amytaiaacYcaaaa@4957@
N,O,P,Q,R,S,T,U,V,W,X,Y,Z
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaamOtaiaacYcacaWGpbGaaiilaiaadcfacaGGSaGaamyuaiaacYca
caWGsbGaaiilaiaadofacaGGSaGaamivaiaacYcacaWGvbGaaiilai
aadAfacaGGSaGaam4vaiaacYcacaWGybGaaiilaiaadMfacaGGSaGa
amOwaaaa@4950@
α,β,γ,δ,ε,ϵ,ζ,η,θ,ϑ,ι,κ,λ,μ,ν,ξ,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeqySdeMaaiilaiabek7aIjaacYcacqaHZoWzcaGGSaGaeqiTdqMa
aiilaiabew7aLjaacYcatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0H
gip5wzaGqbciab=v=aYlaacYcacqaH2oGEcaGGSaGaeq4TdGMaaiil
aiabeI7aXjaacYcacqaHrpGscaGGSaGaeqyUdKMaaiilaiabeQ7aRj
aacYcacqaH7oaBcaGGSaGaeqiVd0Maaiilaiabe27aUjaacYcacqaH
+oaEcaGGSaaaaa@6646@
ο,π,ϖ,ρ,ϱ,σ,ς,τ,υ,φ,ϕ,χ,ψ,ω
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaeq4Vd8Maaiilaiabec8aWjaacYcacqaHwpGDcaGGSaGaeqyWdiNa
aiilamrr1ngBPrwtHrhAXaqeguuDJXwAKbstHrhAG8KBLbacfiGae8
x8deVaaiilaiabeo8aZjaacYcacqaHcpGvcaGGSaGaeqiXdqNaaiil
aiabew8a1jaacYcacqaHgpGAcaGGSaGaeqy1dyMaaiilaiabeE8aJj
aacYcacqaHipqEcaGGSaGaeqyYdChaaa@61CD@
The upper case Greek letters inserted as
standard are upright; they will not transform well and should be changed to
italic.
Α,Β,Γ,Δ,Ε,Ζ,Η,Θ,Ι,Κ,Λ,Μ,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeuyKdeKaaiilaiabfk5acjaacYcacqqHtoWrcaGGSaGaeuiLdqKa
aiilaiabfw5afjaacYcacqqHwoGwcaGGSaGaeu4LdGKaaiilaiabfI
5arjaacYcacqqHzoqscaGGSaGaeuOMdSKaaiilaiabfU5amjaacYca
cqqHCoqtcaGGSaaaaa@4F74@
Ν,Ξ,Ο,Π,Ρ,Σ,Τ,Υ,Φ,Χ,Ψ,Ω
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeuyNd4Kaaiilaiabf65ayjaacYcacqqHFoWtcaGGSaGaeuiOdaLa
aiilaiabfg6asjaacYcacqqHJoWucaGGSaGaeuiPdqLaaiilaiabfw
6avjaacYcacqqHMoGrcaGGSaGaeu4PdmKaaiilaiabfI6azjaacYca
cqqHPoWvaaa@4FB4@
∀,∁,ℂ,∂,ð,Ϝ,Ⅎ,ℋ,ℌ,h,ℏ,ı,ℑ,j,ϰ,ℒ,ℓ,ℕ,℘,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyiaIiIaaiilamrr1ngBPrwtHrhAXaqeguuDJXwAKbstHrhAG8KB
LbacfaGae8xaIaVaaiilamrr1ngBPrwtHrhAYaqehuuDJXwAKbstHr
hAGq1DVbacgaGae4NaHmKaaiilaiabgkGi2kaacYcacaGGWdGaaiil
aGqbciab9X9a0laacYcacqWFYes9caGGSaGae83cHGKaaiilamrr1n
gBPrMrYf2A0vNCaebcfv3ySLgzGyKCHTgD1jhaiCaacqaFmecscaGG
SaGaamiAaiaacYcacqWIpecAcaGGSaGaamymbiaacYcacqaFressca
GGSaGaamOAaiaacYcacqqFWpq+caGGSaGae8NeHWKaaiilaiablori
SjaacYcacqGFveItcaGGSaGaeqigHmSaaiilaaaa@7948@
ℚ,ℛ,ℜ,ℝ,ℤ,℧,ℬ,ℰ,∃,∄,ℱ,ℳ,ℵ,ℶ,ℷ,ℸ
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAYaqeguuDJXwAKbstHrhAGq1DVbacfaaeaaaaaaaaa8qacqWFAesu
caGGSaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiyaacq
GFBeIucaGGSaWefv3ySLgzgjxyRrxDYbqeiuuDJXwAKbIrYf2A0vNC
aGWbaiab9XrisjaacYcacqWFDeIucaGGSaGae8hjHOLaaiilaiablE
sikjaacYcacqGFSeIqcaGGSaGae4hmHuKaaiilaiabgoGiKiaacYca
cqGFeiY8caGGSaGae4xmHyKaaiilaiab+ntinjaacYcacqaH1ecWca
GGSaGae4NnHSVaaiilaiab+Dti8laacYcacqGF4es=aaa@72E8@
±,÷,×,∓,∝,a/b,*,∘,⋅,
∩
,
∪
,⊎,⊓,⊔,∧,∨
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyySaeRaaiilaiabgEpa4kaacYcacqGHxdaTcaGGSaGaeS4eI0Ma
aiilaiabg2Hi1kaacYcacaWGHbGaai4laiaadkgacaGGSaGaaiOkai
aacYcacqWIyiYBcaGGSaGaeyyXICTaaiila8aadaqfGaqabSqabeaa
caaMb8oaneaapeGaeyykICmaaOGaaiila8aadaqfGaqabSqabeaaca
aMb8oaneaapeGaeyOkIGmaaOGaaiilamrr1ngBPrwtHrhAYaqeguuD
JXwAKbstHrhAGq1DVbacfaGae8NJIiUaaiilaiab=nPiZlaacYcacq
WFukI8caGGSaGaey4jIKTaaiilaiabgIIiAdaa@6AC2@
=,≠,<,>,≤,≥,≮,≰,≯,≱,≡,∼,≃,≈,≅,≇,∝,≪,≫,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaeyypa0JaaiilaiabgcMi5kaacYcacqGH8aapcaGGSaGaeyOpa4Ja
aiilaiabgsMiJkaacYcacqGHLjYScaGGSaWefv3ySLgznfgDOjdary
qr1ngBPrginfgDObcv39gaiuaacqWFUjIJcaGGSaGae8hCIiPaaiil
aiab=9MipkaacYcacqWFXjYKcaGGSaGaeyyyIORaaiilaiabgYJi+j
aacYcacqWIdjYocaGGSaGaeyisISRaaiilaiabgwKiajaacYcatuuD
JXwAK1uy0HwmaeXbfv3ySLgzG0uy0Hgip5wzaGGbaiab+DKiUkaacY
cacqGHDisTcaGGSaGaeSOAI0JaaiilaiablUMi=iaacYcaaaa@7252@
∈,∋,∉,⊂,⊃,⊆,⊇,≺,≻,≼,≽,⊏,⊐,⊑,⊒,∥,⊥,⊢,⊣,≍
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyicI4Saaiilamrr1ngBPrwtHrhAYaqeguuDJXwAKbstHrhAGq1D
VbacfaGae83cIuUaaiilaiabgMGiplaacYcacqGHckcZcaGGSaGaey
4GIKSaaiilaiabgAOinlaacYcacqGHhkIYcaGGSaGaeSOEIaNaaiil
aiablUNiMjaacYcacqWF8jcScaGGSaGae8xFIeRaaiilaiab=9OiWl
aacYcacqWFqks8caGGSaGae8xKIqVaaiilaiab=jPi1laacYcacqWI
LicucaGGSaGaeyyPI4Laaiilamrr1ngBPrwtHrhAXaqehuuDJXwAKb
stHrhAG8KBLbacgaGae4NOIaPaaiilaiab+nQiukaacYcacqGFnjsQ
aaa@7A8C@
∑
∫
∬
∮
∏
∐
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaavacabeWcbe
qaaiaaygW7a0qaaabaaaaaaaaapeGaeyyeIuoaaOWdamaavacabeWc
beqaaiaaygW7a0qaa8qacqGHRiI8aaGcpaWaaubiaeqaleqabaGaaG
zaVdqdbaWexLMBbXgBd9gzLbvyNv2CaeHbcfgDH52zaGqba8qacaWF
SicaaOWdamaavacabeWcbeqaaiaaygW7a0qaa8qacaWFUicaaOWdam
aavacabeWcbeqaaiaaygW7a0qaa8qacqGHpis1aaGcpaWaaubiaeqa
leqabaGaaGzaVdqdbaWdbiablcHidbaaaaa@51F5@
∑
x,
∫
x,
∬
x,
∮
x,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaavacabeWcbe
qaaiaaygW7a0qaaabaaaaaaaaapeGaeyyeIuoaaOGaamiEaiaacYca
paWaaubiaeqaleqabaGaaGzaVdqdbaWdbiabgUIiYdaakiaadIhaca
GGSaGaaiiOa8aadaqfGaqabSqabeaacaaMb8oaneaatCvAUfeBSn0B
KvguHDwzZbqegiuy0fMBNbacfaWdbiaa=XIiaaGccaWG4bGaaiila8
aadaqfGaqabSqabeaacaaMb8oaneaapeGaa8NlIaaakiaadIhacaGG
Saaaaa@532D@
∏
x,
∐
x,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaavacabeWcbe
qaaiaaygW7a0qaaabaaaaaaaaapeGaey4dIunaaOGaamiEaiaacYca
paWaaubiaeqaleqabaGaaGzaVdqdbaWdbiablcHidbaakiaadIhaca
GGSaaaaa@3FF0@
∔,∖,⋒,⋓,⊟,⊠,⊡,⊞,⋇,⋉,⋊,⋋,⋌,⋏,⋎,⊺,⊕,⊖,⊗,
a
b
,⊙,⊛,⊚,†,‡,⋆,⋄,≀,△,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFuiI6
caGGSaGae8NfIiOaaiilamrr1ngBPrwtHrhAYaqehuuDJXwAKbstHr
hAGq1DVbacgaGae4N0ImTaaiilaiab+nTislaacYcacqWFFkYjcaGG
SaGae8hOIKIaaiilaiab=fQiQiaacYcacqWFEkckcaGGSaGae83XIy
Uaaiilaiab=LSiIlaacYcacqWFklY4caGGSaGae83YIaUaaiilaiab
=XSiHlaacYcacqGFplIYcaGGSaGae4NZISSaaiilaiab=PRi6laacY
cacqGHvksXcaGGSaGae8NLIeIaaiilaiabgEPielaacYcadaWcaaWd
aeaapeGaamyyaaWdaeaapeGaamOyaaaacaGGSaGaeSyMIuMaaiilai
ab=TPiJiaacYcacqWFAkIicaGGSaGaaiiiGiaacYcacaGGHaIaaiil
aiab=zSiLlaacYcacqGHelc4caGGSaGae8hqIOQaaiilaiabloBjwj
aacYcaaaa@9259@
∴,∵,⋘,⋙,≦,≧,≲,≳,⋖,⋗,≶,⋚,≷,⋛,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyinIWLaaiilaiablwJirjaacYcatuuDJXwAK1uy0HMmaeHbfv3y
SLgzG0uy0HgiuD3BaGqbaiab=HTimkaacYcacqWFzlsJcaGGSaGae8
NzIyOaaiilaiab=DMihkaacYcacqWFYjcIcaGGSaGae83CIKOaaiil
aiab=zTiakaacYcacqWFxlsGcaGGSaGae8NDImQaaiilaiab=PTiLk
aacYcacqWF3jcPcaGGSaGae832IyQaaiilaaaa@6215@
≑,≒,≓,∽,≊,≼,≽,⋞,⋟,≾,≿,⋜,⋝
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFrjcP
caGGSaGae8NuIuQaaiilaiab=nLiJkaacYcatCvAUfeBSn0BKvguHD
wzZbqehiuy0fMBNbacgaGaa4xpIiaacYcacqWFkjcRcaGGSaWefv3y
SLgznfgDOjdarGqr1ngBPrginfgDObcv39gaiCaacqqF8jcScaGGSa
Gae0xFIeRaaiilaiab95TiYkaacYcacqqFFlYScaGGSaGae0NFIyRa
aiilaiab99Ni3kaacYcacqqFClIGcaGGSaGae0x3Imiaaa@70D3@
⊆,⊇,⊲,⊳,⊴,⊵,⊨,⋐,⋑,⊏,⊐,⊩,⊪,≖,≗,≜,≏,≎,∝,⋔,≐
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyOHI0SaaiilaiabgEOiklaacYcacqWIYkcpcaGGSaGaeS4SI4Ja
aiilamrr1ngBPrwtHrhAYaqeguuDJXwAKbstHrhAGq1DVbacfaGae8
hTIGIaaiilaiab=vRiNiaacYcatuuDJXwAK1uy0HwmaeXbfv3ySLgz
G0uy0Hgip5wzaGGbaiab+HQirkaacYcacqWFqlc0caGGSaGae8x0Ie
Taaiilaiab=9OiWlaacYcacqWFqks8caGGSaGae4xQIiPaaiilaiab
+PQitkaacYcacqGFwjIOcaGGSaGae43vIeQaaiilaiablYLiajaacY
cacqGFpjIPcaGGSaGae4NtICQaaiilaiabg2Hi1kaacYcacqWFulY4
caGGSaGaeSiuIieaaa@7CAA@
←,→,↑,↓,↔,↕,⇐,⇒,⇑,⇓,⇔,⇕,↗,↖,↘,↙,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyiKHWQaaiilaiabgkziUkaacYcacqGHrgsRcaGGSaGaey4KH8Qa
aiilaiabgsziRkaacYcacqWIvgIycaGGSaGaeyi0HWTaaiilaiabgk
DiElaacYcacqGHrhs3caGGSaGaey40H8TaaiilaiabgsDiBlaacYca
cqWIvhYycaGGSaGaeS4LHOLaaiilaiablAziEjaacYcacqWIygsxca
GGSaGaeSyMHSLaaiilaaaa@609C@
↚,↛,↮,⇍,⇏,⇎,↦,↼,↽,⇀,⇁,↿,↾,⇃,⇂,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFAgcV
caGGSaGae83MH0Raaiilaiab=5AialaacYcacqWFnhIVcaGGSaGae8
3ZH8Raaiilaiab=5CiblaacYcacqWIMgsycaGGSaGae8hVHqRaaiil
aiabl2BihkaacYcacqWIahIHcaGGSaGae8xWHCRaaiilaiab=9Bi6k
aacYcacqWF+gcUcaGGSaGae83WHSRaaiilaiab=jCi5kaacYcaaaa@68E8@
⇋,⇌,⇇,⇉,⇈,⇊,⇆,⇄,↫,↬,↢,↣,↰,↱,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFlhYX
caGGSaGaeSiZHmOaaiilaiab=DCiclaacYcacqWFjhYWcaGGSaGae8
hYHqSaaiilaiab=PCiflaacYcacqWFghIXcaGGSaGaeSiXHaOaaiil
aiab=TAinlaacYcacqWFSgcZcaGGSaGae8NOHeRaaiilaiab=nAiWk
aacYcacqWFWgYYcaGGSaGae8xSHOSaaiilaaaa@66CE@
⇚,⇛,↞,↠,↶,↷,↺,↻,⊸,↭,⇝
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFAhsY
caGGSaGae832HGSaaiilaiab=5ziZkaacYcacqWFGgIScaGGSaGae8
NTHeTaaiilaiab=DBiqlaacYcacqWF6gY0caGGSaGae83UHiTaaiil
aiab=HRiOkaacYcacqWFTgYZcaGGSaGae8x3H4maaa@5E30@
≠,≮,≯,≰,≱,≁,≇,≨,≩,⊀,⊁,⋠,⋡,∉,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyiyIKRaaiilamrr1ngBPrwtHrhAYaqeguuDJXwAKbstHrhAGq1D
VbacfaGae8NBI4Oaaiilaiab=9MipkaacYcacqWFWjIKcaGGSaGae8
xCImPaaiilamrr1ngBPrwtHrhAXaqehuuDJXwAKbstHrhAG8KBLbac
gaGae4xqI0Qaaiilaiab+DKiUkaacYcacqWFOjcMcaGGSaGae8xAIK
Paaiilaiab=bOi6kaacYcacqWFbkYUcaGGSaGae8h4I4Raaiilaiab
=fUi=kaacYcacqGHjiYZcaGGSaaaaa@6B92@
⊄,⊈,⊉,⊊,⊋,⋦,⋧,⋨,⋩,⋪,⋫,⋬,⋭,∤,∦,⊬,⊭,⊮,⊯,∄
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaeyiHISSaaiilamrr1ngBPrwtHrhAYaqeguuDJXwAKbstHrhAGq1D
VbacfaGae8NqQJTaaiilaiab=nK6zlaacYcacqWFkkI1caGGSaGae8
3IICTaaiilaiab=zUiEkaacYcacqWFNlYNcaGGSaGae8h6IySaaiil
aiab=LUihlaacYcacqWFQlIkcaGGSaGae836IKIaaiilaiab=XUiSi
aacYcacqWFTlYkcaGGSaWefv3ySLgznfgDOfdarCqr1ngBPrginfgD
ObYtUvgaiyaacqGFKicJcaGGSaGae4NjI0Oaaiilaiab+XQiwkaacY
cacqGFTkYLcaGGSaGae4NRIGPaaiilaiab+9QizkaacYcacqGFeiY8
aaa@7D5B@
Not all letters in the script alphabet will be spoken as
script-letter by MathPlayer.
A,ℬ,C,D,ℰ,ℱ,G,ℋ,ℐ,K,ℒ,ℳ,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFaeFq
caGGSaGae8hlHiKaaiilaiab=jq8djaacYcacqWFdeprcaGGSaGae8
hmHuKaaiilaiab=ftigjaacYcacqWFge=rcaGGSaGae83cHGKaaiil
aiab=brijjaacYcacqWFke=scaGGSaGae8NeHWKaaiilaiab=ntinj
aacYcaaaa@5800@
N,O,Q,ℛ,S,T,U,V,W,X,Y,Z
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFneVt
caGGSaGae8NdX=Kaaiilaiab=br8rjaacYcacqWFBeIucaGGSaGae8
NeXpLaaiilaiab=nr8ujaacYcacqWFueFvcaGGSaGae8xfXBLaaiil
aiab=zr8xjaacYcacqWFxepwcaGGSaGae8hgXNLaaiilaiab=Lr8Ab
aa@5CC3@
For unknown reasons our MathType cannot
transform script P correctly to MathML so you will see a transformation error
at this point
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAXaqeguuDJXwAKbstHrhAG8KBLbacfaaeaaaaaaaaa8qacqWFpepu
aaa@416A@
***TRANSLATION
ERROR*** in all formats created from the MathType format. Presumably this will
be corrected in the near future since the rest of the alphabet transforms.
Not all letters in the Fraktur alphabet will be spoken as
fraktur-letter by MathPlayer.
A,B,ℭ,D,E,F,G,ℌ,ℑ,J,K,L,M,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrMrYf
2A0vNCaeHbfv3ySLgzGyKCHTgD1jhaiuaaqaaaaaaaaaWdbiab=ba8
bjaacYcacqWFbaVqcaGGSaGae8xlHmKaaiilaiab=na8ejaacYcacq
WFeaFrcaGGSaGae8xbWBKaaiilaiab=za8hjaacYcacqWFmecscaGG
SaGae8xeHKKaaiilaiab=La8kjaacYcacqWFka=scaGGSaGae83cWZ
Kaaiilaiab=Xa8njaacYcaaaa@5E62@
N,O,P,Q,ℜ,S,T,U,V,W,X,Y,ℨ
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrMrYf
2A0vNCaeHbfv3ySLgzGyKCHTgD1jhaiuaaqaaaaaaaaaWdbiab=1a8
ojaacYcacqWFoa=tcaGGSaGae83dWdLaaiilaiab=bb8rjaacYcacq
WFCeIucaGGSaGae8NeWpLaaiilaiab=nb8ujaacYcacqWFuaFvcaGG
SaGae8xfWBLaaiilaiab=zb8xjaacYcacqWFxapwcaGGSaGae8hgWN
Laaiilaiab=HsiAbaa@5FB4@
a,b,c,d,e,f,g,h,i,j,k,l,m,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrMrYf
2A0vNCaeHbfv3ySLgzGyKCHTgD1jhaiuaaqaaaaaaaaaWdbiab=Pb8
HjaacYcacqWFBaVycaGGSaGae8hhWpMaaiilaiab=1b8KjaacYcacq
WFEaFzcaGGSaGae83hWBMaaiilaiab=bc8NjaacYcacqWFHapAcaGG
SaGae8NiWNMaaiilaiab=nc8QjaacYcacqWFKa=AcaGGSaGae8xjWZ
Maaiilaiab=zc8TjaacYcaaaa@6388@
n,o,p,q,r,s,t,u,v,w,x,y,z
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrMrYf
2A0vNCaeHbfv3ySLgzGyKCHTgD1jhaiuaaqaaaaaaaaaWdbiab=Dc8
UjaacYcacqWFOa=BcaGGSaGae8xkWdNaaiilaiab=Pc8XjaacYcacq
WFRaVCcaGGSaGae8hlWpNaaiilaiab=1c80jaacYcacqWFUaFDcaGG
SaGae83lWBNaaiilaiab=bd83jaacYcacqWFXapEcaGGSaGae8NmWN
Naaiilaiab=nd86baa@642A@
Not all letters in the double struck alphabet will be spoken
as double struck-letter by MathPlayer.
A,B,ℂ,D,E,F,G,ℍ,I,J,K,L,M,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAYaqeguuDJXwAKbstHrhAGq1DVbacfaaeaaaaaaaaa8qacqWFacFq
caGGSaGae8xGWlKaaiilaiab=jqidjaacYcacqWFdcprcaGGSaGae8
hHWxKaaiilaiab=vi8gjaacYcacqWFgc=rcaGGSaGae8xdHGKaaiil
aiab=Hi8jjaacYcacqWFjcVscaGGSaGae8NIWVKaaiilaiab=Ti8mj
aacYcacqWFmcFtcaGGSaaaaa@6360@
ℕ,O,ℙ,ℚ,ℝ,S,T,U,V,W,X,Y,ℤ
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr
hAYaqeguuDJXwAKbstHrhAGq1DVbacfaaeaaaaaaaaa8qacqWFveIt
caGGSaGae8NJW=Kaaiilaiab=LriqjaacYcacqWFAesucaGGSaGae8
xhHiLaaiilaiab=jj8tjaacYcacqWFtcpvcaGGSaGae8hLWxLaaiil
aiab=vj8wjaacYcacqWFwc=vcaGGSaGae83LWJLaaiilaiab=Hj8zj
aacYcacqWFKeIwaaa@6042@
∟,∠,∡,∢,⊥,∤,∥,∦,∶,∴,∵
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamXvP5wqSX2qVr
wzqf2zLnharyGqHrxyUDgaiuGaqaaaaaaaaaWdbiaa=9HicaGGSaGa
eyiiIaTaaiilaiablgIisjaacYcacqWIIiYucaGGSaGaeyyPI4Laai
ilamrr1ngBPrwtHrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae4hj
IWOaaiilaiablwIiqjaacYcacqGFMisJcaGGSaacfaGaa0NnIiaacY
cacqGH0icxcaGGSaGaeSynIefaaa@5C40@
Notice how the
equations are encoded using the equation editor. All mathematics must be
encoded either using this or MathType to ensure it is transformed correctly. This test document was encoded using the
standard equation editor as MathType is considered to be a transform. Not all
structures available in the Word equation editor can be transformed. Those that
can are listed below.
Equations can be
placed inline in the text
A
i,j,k
2
n
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaamyqa8aadaqhaaWcbaWdbiaadMgacaGGSaGaamOAaiaacYcacaWG
Rbaapaqaa8qacaaIYaWdamaaCaaameqabaWdbiaad6gaaaaaaaaa@3D65@
like
so or displayed.
∑
i=1
13
x
i
2
=
x
1
2
+
x
2
2
+
x
3
2
+
x
4
2
+
x
5
2
+
x
6
2
+
x
7
2
+
x
8
2
+
x
9
2
+
x
10
2
+
x
11
2
+
x
12
2
+
x
13
2
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaybCaeqal8aabaWdbiaadMgacqGH9aqpcaaIXaaapaqaa8qacaaI
XaGaaG4maaqdpaqaa8qacqGHris5aaGccaWG4bWdamaaDaaaleaape
GaamyAaaWdaeaapeGaaGOmaaaakiabg2da9iaadIhapaWaa0baaSqa
a8qacaaIXaaapaqaa8qacaaIYaaaaOGaey4kaSIaamiEa8aadaqhaa
WcbaWdbiaaikdaa8aabaWdbiaaikdaaaGccqGHRaWkcaWG4bWdamaa
DaaaleaapeGaaG4maaWdaeaapeGaaGOmaaaakiaacckacqGHRaWkca
GGGcGaamiEa8aadaqhaaWcbaWdbiaaisdaa8aabaWdbiaaikdaaaGc
caGGGcGaey4kaSIaaiiOaiaadIhapaWaa0baaSqaa8qacaaI1aaapa
qaa8qacaaIYaaaaOGaaiiOaiabgUcaRiaacckacaWG4bWdamaaDaaa
leaapeGaaGOnaaWdaeaapeGaaGOmaaaakiaacckacqGHRaWkcaGGGc
GaamiEa8aadaqhaaWcbaWdbiaaiEdaa8aabaWdbiaaikdaaaGccaGG
GcGaey4kaSIaaiiOaiaadIhapaWaa0baaSqaa8qacaaI4aaapaqaa8
qacaaIYaaaaOGaaiiOaiabgUcaRiaacckacaWG4bWdamaaDaaaleaa
peGaaGyoaaWdaeaapeGaaGOmaaaakiaacckacqGHRaWkcaGGGcGaam
iEa8aadaqhaaWcbaWdbiaaigdacaaIWaaapaqaa8qacaaIYaaaaOGa
ey4kaSIaamiEa8aadaqhaaWcbaWdbiaaigdacaaIXaaapaqaa8qaca
aIYaaaaOGaey4kaSIaamiEa8aadaqhaaWcbaWdbiaaigdacaaIYaaa
paqaa8qacaaIYaaaaOGaey4kaSIaamiEa8aadaqhaaWcbaWdbiaaig
dacaaIZaaapaqaa8qacaaIYaaaaaaa@8472@
x
1
2
=
x
2
2
=
x
3
2
=
x
3
2
=
x
4
2
=
x
5
2
=
x
6
2
=
x
7
2
=
x
8
2
=
x
9
2
=
x
10
2
=
x
11
2
=
x
12
2
=
x
13
2
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaamiEa8aadaqhaaWcbaWdbiaaigdaa8aabaWdbiaaikdaaaGccqGH
9aqpcaWG4bWdamaaDaaaleaapeGaaGOmaaWdaeaapeGaaGOmaaaaki
abg2da9iaadIhapaWaa0baaSqaa8qacaaIZaaapaqaa8qacaaIYaaa
aOGaeyypa0JaamiEa8aadaqhaaWcbaWdbiaaiodaa8aabaWdbiaaik
daaaGccqGH9aqpcaWG4bWdamaaDaaaleaapeGaaGinaaWdaeaapeGa
aGOmaaaakiabg2da9iaadIhapaWaa0baaSqaa8qacaaI1aaapaqaa8
qacaaIYaaaaOGaeyypa0JaamiEa8aadaqhaaWcbaWdbiaaiAdaa8aa
baWdbiaaikdaaaGccqGH9aqpcaWG4bWdamaaDaaaleaapeGaaG4naa
WdaeaapeGaaGOmaaaakiabg2da9iaadIhapaWaa0baaSqaa8qacaaI
4aaapaqaa8qacaaIYaaaaOGaeyypa0JaamiEa8aadaqhaaWcbaWdbi
aaiMdaa8aabaWdbiaaikdaaaGccqGH9aqpcaWG4bWdamaaDaaaleaa
peGaaGymaiaaicdaa8aabaWdbiaaikdaaaGccqGH9aqpcaWG4bWdam
aaDaaaleaapeGaaGymaiaaigdaa8aabaWdbiaaikdaaaGccqGH9aqp
caWG4bWdamaaDaaaleaapeGaaGymaiaaikdaa8aabaWdbiaaikdaaa
GccqGH9aqpcaWG4bWdamaaDaaaleaapeGaaGymaiaaiodaa8aabaWd
biaaikdaaaaaaa@6F21@
∏
i=1
13
x
i
2
=
x
1
2
x
2
2
x
3
2
x
4
2
x
5
2
x
6
2
x
7
2
x
8
2
x
9
2
x
10
2
x
11
2
x
12
2
x
13
2
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaybCaeqal8aabaWdbiaadMgacqGH9aqpcaaIXaaapaqaa8qacaaI
XaGaaG4maaqdpaqaa8qacqGHpis1aaGccaWG4bWdamaaDaaaleaape
GaamyAaaWdaeaapeGaaGOmaaaakiabg2da9iaadIhapaWaa0baaSqa
a8qacaaIXaaapaqaa8qacaaIYaaaaOGaamiEa8aadaqhaaWcbaWdbi
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paWaa0baaSqaa8qacaaIXaGaaGimaaWdaeaapeGaaGOmaaaakiaadI
hapaWaa0baaSqaa8qacaaIXaGaaGymaaWdaeaapeGaaGOmaaaakiaa
dIhapaWaa0baaSqaa8qacaaIXaGaaGOmaaWdaeaapeGaaGOmaaaaki
aadIhapaWaa0baaSqaa8qacaaIXaGaaG4maaWdaeaapeGaaGOmaaaa
aaa@69D0@
∏
i=1
13
x
i
2
=
x
1
2
⋅
x
2
2
⋅
x
3
2
⋅
x
4
2
⋅
x
5
2
⋅
x
6
2
⋅
x
7
2
⋅
x
8
2
⋅
x
9
2
⋅
x
10
2
⋅
x
11
2
⋅
x
12
2
⋅
x
13
2
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaybCaeqal8aabaWdbiaadMgacqGH9aqpcaaIXaaapaqaa8qacaaI
XaGaaG4maaqdpaqaa8qacqGHpis1aaGccaWG4bWdamaaDaaaleaape
GaamyAaaWdaeaapeGaaGOmaaaakiabg2da9iaadIhapaWaa0baaSqa
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Waa0baaSqaa8qacaaI0aaapaqaa8qacaaIYaaaaOGaeyyXICTaamiE
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xlaadIhapaWaa0baaSqaa8qacaaI3aaapaqaa8qacaaIYaaaaOGaey
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cqGHflY1caWG4bWdamaaDaaaleaapeGaaGyoaaWdaeaapeGaaGOmaa
aakiabgwSixlaadIhapaWaa0baaSqaa8qacaaIXaGaaGimaaWdaeaa
peGaaGOmaaaakiabgwSixlaadIhapaWaa0baaSqaa8qacaaIXaGaaG
ymaaWdaeaapeGaaGOmaaaakiabgwSixlaadIhapaWaa0baaSqaa8qa
caaIXaGaaGOmaaWdaeaapeGaaGOmaaaakiabgwSixlaadIhapaWaa0
baaSqaa8qacaaIXaGaaG4maaWdaeaapeGaaGOmaaaaaaa@8548@
∑
i=1
13
x
i
2
=
x
1
2
+
x
2
2
+
x
3
2
+
x
4
2
+
x
5
2
+
x
6
2
+
x
7
2
+
x
8
2
+
x
9
2
+
x
10
2
+
x
11
2
+
x
12
2
+
x
13
2
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaOaaa8aabaWdbmaawahabeWcpaqaa8qacaWGPbGaeyypa0JaaGym
aaWdaeaapeGaaGymaiaaiodaa0WdaeaapeGaeyyeIuoaaOGaamiEa8
aadaqhaaWcbaWdbiaadMgaa8aabaWdbiaaikdaaaaabeaakiabg2da
9maakaaapaqaa8qacaWG4bWdamaaDaaaleaapeGaaGymaaWdaeaape
GaaGOmaaaakiabgUcaRiaadIhapaWaa0baaSqaa8qacaaIYaaapaqa
a8qacaaIYaaaaOGaey4kaSIaamiEa8aadaqhaaWcbaWdbiaaiodaa8
aabaWdbiaaikdaaaGccqGHRaWkcaWG4bWdamaaDaaaleaapeGaaGin
aaWdaeaapeGaaGOmaaaakiabgUcaRiaadIhapaWaa0baaSqaa8qaca
aI1aaapaqaa8qacaaIYaaaaOGaey4kaSIaamiEa8aadaqhaaWcbaWd
biaaiAdaa8aabaWdbiaaikdaaaGccqGHRaWkcaWG4bWdamaaDaaale
aapeGaaG4naaWdaeaapeGaaGOmaaaakiabgUcaRiaadIhapaWaa0ba
aSqaa8qacaaI4aaapaqaa8qacaaIYaaaaOGaey4kaSIaamiEa8aada
qhaaWcbaWdbiaaiMdaa8aabaWdbiaaikdaaaGccqGHRaWkcaWG4bWd
amaaDaaaleaapeGaaGymaiaaicdaa8aabaWdbiaaikdaaaGccqGHRa
WkcaWG4bWdamaaDaaaleaapeGaaGymaiaaigdaa8aabaWdbiaaikda
aaGccqGHRaWkcaWG4bWdamaaDaaaleaapeGaaGymaiaaikdaa8aaba
WdbiaaikdaaaGccqGHRaWkcaWG4bWdamaaDaaaleaapeGaaGymaiaa
iodaa8aabaWdbiaaikdaaaaabeaaaaa@74D8@
You can align equations by creating them
as separate displayed items, selecting them, right clicking and clicking on
Align at =.
a=b+c
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaamyyaiabg2da9iaadkgacqGHRaWkcaWGJbaaaa@3AA8@
=d
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaeyypa0Jaamizaaaa@37FA@
However, the layout will not be
maintained in other formats
–
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjxmWaIq
ubqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr
Ffpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0F
irpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaa
GcbaqefeKCPfgBaGqbaKqzagaeaaaaaaaaa8qacaWFtacaaa@3DBD@
the line breaks will be lost
–
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjxmWaIq
ubqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr
Ffpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0F
irpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaa
GcbaqefeKCPfgBaGqbaKqzagaeaaaaaaaaa8qacaWFtacaaa@3DBD@
and is likely to cause significant layout
problems on translation to LaTeX. Keep equations separate. Don’t align, keep
each equation line separate, and don’t select centred as a group.
∑
i=1
13
2
i
=
2
1
+
2
2
+
2
3
+
2
4
+
2
5
+
2
6
+
2
7
+
2
8
+
2
9
+
2
10
+
2
11
+
2
12
+
2
13
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaybCaeqal8aabaWdbiaadMgacqGH9aqpcaaIXaaapaqaa8qacaaI
XaGaaG4maaqdpaqaa8qacqGHris5aaGccaaIYaWdamaaCaaaleqaba
WdbiaadMgaaaGccqGH9aqpcaaIYaWdamaaCaaaleqabaWdbiaaigda
aaGccqGHRaWkcaaIYaWdamaaCaaaleqabaWdbiaaikdaaaGccqGHRa
WkcaaIYaWdamaaCaaaleqabaWdbiaaiodaaaGccqGHRaWkcaaIYaWd
amaaCaaaleqabaWdbiaaisdaaaGccqGHRaWkcaaIYaWdamaaCaaale
qabaWdbiaaiwdaaaGccqGHRaWkcaaIYaWdamaaCaaaleqabaWdbiaa
iAdaaaGccqGHRaWkcaaIYaWdamaaCaaaleqabaWdbiaaiEdaaaGccq
GHRaWkcaaIYaWdamaaCaaaleqabaWdbiaaiIdaaaGccqGHRaWkcaaI
YaWdamaaCaaaleqabaWdbiaaiMdaaaGccqGHRaWkcaaIYaWdamaaCa
aaleqabaWdbiaaigdacaaIWaaaaOGaey4kaSIaaGOma8aadaahaaWc
beqaa8qacaaIXaGaaGymaaaakiabgUcaRiaaikdapaWaaWbaaSqabe
aapeGaaGymaiaaikdaaaGccqGHRaWkcaaIYaWdamaaCaaaleqabaWd
biaaigdacaaIZaaaaaaa@64F2@
=2+4+8+16+32+64+128+256+1024+2048+4096+8192
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaeyypa0JaaGOmaiabgUcaRiaaisdacqGHRaWkcaaI4aGaey4kaSIa
aGymaiaaiAdacqGHRaWkcaaIZaGaaGOmaiabgUcaRiaaiAdacaaI0a
Gaey4kaSIaaGymaiaaikdacaaI4aGaey4kaSIaaGOmaiaaiwdacaaI
2aGaey4kaSIaaGymaiaaicdacaaIYaGaaGinaiabgUcaRiaaikdaca
aIWaGaaGinaiaaiIdacqGHRaWkcaaI0aGaaGimaiaaiMdacaaI2aGa
ey4kaSIaaGioaiaaigdacaaI5aGaaGOmaaaa@57C5@
=16382 and in equation tools is a button for placing normal text
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaeyypa0JaaGymaiaaiAdacaaIZaGaaGioaiaaikdacaGGGcGaaeyy
aiaab6gacaqGKbGaaeiOaiaabMgacaqGUbGaaeiOaiaabwgacaqGXb
GaaeyDaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaaeiOaiaabsha
caqGVbGaae4BaiaabYgacaqGZbGaaeiOaiaabMgacaqGZbGaaeiOai
aabggacaqGGcGaaeOyaiaabwhacaqG0bGaaeiDaiaab+gacaqGUbGa
aeiOaiaabAgacaqGVbGaaeOCaiaabckacaqGWbGaaeiBaiaabggaca
qGJbGaaeyAaiaab6gacaqGNbGaaeiOaiaab6gacaqGVbGaaeOCaiaa
b2gacaqGHbGaaeiBaiaabckacaqG0bGaaeyzaiaabIhacaqG0baaaa@7343@
a
b
,a/b,
a
b
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaSaaa8aabaWdbiaadggaa8aabaWdbiaadkgaaaGaaiilaiaadgga
caGGVaGaamOyaiaacYcadaWcaaWdaeaapeGaamyyaaWdaeaapeGaam
Oyaaaaaaa@3E21@
x
2
,
x
2
,
x
1
2
,
x
1
2
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
GaamiEa8aadaahaaWcbeqaa8qacaaIYaaaaOGaaiilaiaadIhapaWa
aSbaaSqaa8qacaaIYaaapaqabaGcpeGaaiilaiaadIhapaWaa0baaS
qaa8qacaaIXaaapaqaa8qacaaIYaaaaOGaaiila8aadaqhbaWcbaWd
biaaigdaa8aabaWdbiaaikdaaaGccaWG4baaaa@422A@
a,
a
b
,
a
2
,
a
3
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaOaaa8aabaWdbiaadggacaGGSaaaleqaaOWaaOqaa8aabaWdbiaa
dggaaSWdaeaapeGaamOyaaaakiaacYcadaGcbaWdaeaapeGaamyyaa
Wcpaqaa8qacaaIYaaaaOGaaiilamaakeaapaqaa8qacaWGHbaal8aa
baWdbiaaiodaaaaaaa@3F76@
∫
x,
∫
a
b
x,
∫
a
b
x,
∬
x,
∬
a
b
x,
∬
a
b
x,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaavacabeWcbe
qaaiaaygW7a0qaaabaaaaaaaaapeGaey4kIipaaOGaamiEaiaacYca
daGfWbqabSWdaeaapeGaamyyaaWdaeaapeGaamOyaaqdpaqaa8qacq
GHRiI8aaGccaWG4bGaaiilamaawahabeWcpaqaa8qacaWGHbaapaqa
a8qacaWGIbaan8aabaWdbiabgUIiYdaakiaadIhacaGGSaWdamaava
cabeWcbeqaaiaaygW7a0qaamXvP5wqSX2qVrwzqf2zLnharyGqHrxy
UDgaiuaapeGaa8hlIaaakiaadIhacaGGSaWaaybCaeqal8aabaWdbi
aadggaa8aabaWdbiaadkgaa0WdaeaapeGaa8hlIaaakiaadIhacaGG
SaWaaybCaeqal8aabaWdbiaadggaa8aabaWdbiaadkgaa0Wdaeaape
Gaa8hlIaaakiaadIhacaGGSaaaaa@5F78@
∮
x,
∮
a
b
x,
∮
a
b
x,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaavacabeWcbe
qaaiaaygW7a0qaamXvP5wqSX2qVrwzqf2zLnharyGqHrxyUDgaiuaa
qaaaaaaaaaWdbiaa=5IiaaGccaWG4bGaaiilamaawahabeWcpaqaa8
qacaWGHbaapaqaa8qacaWGIbaan8aabaWdbiaa=5IiaaGccaWG4bGa
aiilamaawahabeWcpaqaa8qacaWGHbaapaqaa8qacaWGIbaan8aaba
Wdbiaa=5IiaaGccaWG4bGaaiilaaaa@4D59@
∑
x,
∑
a
b
x,
∑
a
b
x,
∑
a
x,
∑
a
x
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaavacabeWcbe
qaaiaaygW7a0qaaabaaaaaaaaapeGaeyyeIuoaaOGaamiEaiaacYca
daGfWbqabSWdaeaapeGaamyyaaWdaeaapeGaamOyaaqdpaqaa8qacq
GHris5aaGccaWG4bGaaiilamaawahabeWcpaqaa8qacaWGHbaapaqa
a8qacaWGIbaan8aabaWdbiabggHiLdaakiaadIhacaGGSaWaaybuae
qal8aabaWdbiaadggaaeqan8aabaWdbiabggHiLdaakiaadIhacaGG
SaWaaybuaeqal8aabaWdbiaadggaaeqan8aabaWdbiabggHiLdaaki
aadIhaaaa@50F8@
∏
x,
∏
a
b
x,
∏
a
b
x,
∏
a
x,
∏
a
x,
∐
x,
∐
a
b
x,
∐
a
b
x,
∐
a
x,
∐
a
x
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaavacabeWcbe
qaaiaaygW7a0qaaabaaaaaaaaapeGaey4dIunaaOGaamiEaiaacYca
daGfWbqabSWdaeaapeGaamyyaaWdaeaapeGaamOyaaqdpaqaa8qacq
GHpis1aaGccaWG4bGaaiilamaawahabeWcpaqaa8qacaWGHbaapaqa
a8qacaWGIbaan8aabaWdbiabg+GivdaakiaadIhacaGGSaWaaybuae
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aapeGaeSieImeaaOGaamiEaaaa@6944@
(
x
),[ x ],{ x },| x |, [ x [ ,] x ],] x [,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
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a8aabaWdbiaadIhaaiaaw2facaGLBbaacaGGSaaaaa@51C4@
( x, [ x ,{ x ,|x,…,x|,x },x ], x )
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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caGGSaWaaeGaa8aabaWdbiaadIhaaiaawMcaaaaa@4EE1@
{
a
b
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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Waaiqaa8aabaqbaeqabiqaaaqaa8qacaWGHbaapaqaa8qacaWGIbaa
aaGaay5Eaaaaaa@393D@
{
a
b
c
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Waaiqaa8aabaqbaeqabmqaaaqaa8qacaWGHbaapaqaa8qacaWGIbaa
paqaa8qacaWGJbaaaaGaay5Eaaaaaa@3A46@
a
b
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaauaabeqaceaaae
aaqaaaaaaaaaWdbiaadggaa8aabaWdbiaadkgaaaaaaa@3804@
(
a
b
)
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaeWaa8aabaqbaeqabiqaaaqaa8qacaWGHbaapaqaa8qacaWGIbaa
aaGaayjkaiaawMcaaaaa@39AC@
sinx,cosx,tanx,cscx,secx,cotx
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaci4CaiaacMgacaGGUbGaamiEaiaacYcaciGGJbGaai4Baiaacoha
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aacohacaGGJbGaamiEaiaacYcaciGGZbGaaiyzaiaacogacaWG4bGa
aiilaiGacogacaGGVbGaaiiDaiaadIhaaaa@5049@
sin
−1
x,
cos
−1
x,
tan
−1
x,
csc
−1
x,
sec
−1
x,
cot
−1
x
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaci4CaiaacMgacaGGUbWdamaaCaaaleqabaWdbiabgkHiTiaaigda
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caWG4bGaaiilaiGacohacaGGLbGaai4ya8aadaahaaWcbeqaa8qacq
GHsislcaaIXaaaaOGaamiEaiaacYcaciGGJbGaai4BaiaacshapaWa
aWbaaSqabeaapeGaeyOeI0IaaGymaaaakiaadIhaaaa@5C3D@
sinhx,coshx,tanhx,cschx,sechx,cothx,
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaci4CaiaacMgacaGGUbGaaiiAaiaadIhacaGGSaGaci4yaiaac+ga
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aadIhacaGGSaGaae4yaiaabohacaqGJbGaaeiAaiaadIhacaGGSaGa
ae4CaiaabwgacaqGJbGaaeiAaiaadIhacaGGSaGaci4yaiaac+gaca
GG0bGaaiiAaiaadIhacaGGSaaaaa@5675@
sinh
−1
x,
cosh
−1
x,
tanh
−1
x,
csch
−1
x,
sech
−1
x,
coth
−1
x
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
Gaci4CaiaacMgacaGGUbGaaiiAa8aadaahaaWcbeqaa8qacqGHsisl
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4bGaaiilaiGacogacaGGVbGaaiiDaiaacIgapaWaaWbaaSqabeaape
GaeyOeI0IaaGymaaaakiaadIhaaaa@61B9@
log
a
b,logb,
lim
a
b,
min
a
b,
max
a
b,lnb
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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GaciiBaiaac+gacaGGNbWdamaaBaaaleaapeGaamyyaaWdaeqaaOWd
biaadkgacaGGSaGaciiBaiaac+gacaGGNbGaamOyaiaacYcapaWaaC
beaeaapeGaciiBaiaacMgacaGGTbaal8aabaWdbiaadggaa8aabeaa
k8qacaWGIbGaaiila8aadaWfqaqaa8qaciGGTbGaaiyAaiaac6gaaS
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biGac2gacaGGHbGaaiiEaaWcpaqaa8qacaWGHbaapaqabaGcpeGaam
OyaiaacYcaciGGSbGaaiOBaiaadkgaaaa@54CB@
∶=,==,+=,−=,≜,
←
x
,
→
x
,
←
x
,
→
x
,
⇐
x
,
⇒
x
,
⇐
x
,
⇒
x
,
↔
x
,
↔
x
,
⇔
x
,
⇔
x
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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daWfqaqaa8qacqGHugYQaSWdaeaapeGaamiEaaWdaeqaaOWdbiaacY
capaWaaCbiaeaapeGaeyiLHSkal8aabeqaa8qacaWG4baaaOGaaiil
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aacYcapaWaaCbiaeaapeGaeyi1HSnal8aabeqaa8qacaWG4baaaaaa
@7EF6@
1
0
0
1
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaauaabeqaciaaae
aaqaaaaaaaaaWdbiaaigdaa8aabaWdbiaaicdaa8aabaWdbiaaicda
a8aabaWdbiaaigdaaaaaaa@3962@
1
0
0
0
1
0
0
0
1
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaauaabeqadmaaae
aaqaaaaaaaaaWdbiaaigdaa8aabaWdbiaaicdaa8aabaWdbiaaicda
a8aabaWdbiaaicdaa8aabaWdbiaaigdaa8aabaWdbiaaicdaa8aaba
Wdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaaigdaaaaaaa@3DA7@
(
1
⋯
0
⋮
⋱
⋮
0
⋯
1
)
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaeWaa8aabaqbaeqabmWaaaqaa8qacaaIXaaapaqaa8qacqWIVlct
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qaa8qacqWIUlsta8aabaWdbiaaicdaa8aabaWdbiabl+UimbWdaeaa
peGaaGymaaaaaiaawIcacaGLPaaaaaa@4557@
[
1
⋯
0
⋮
⋱
⋮
0
⋯
1
]
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr
0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaamWaa8aabaqbaeqabmWaaaqaa8qacaaIXaaapaqaa8qacqWIVlct
a8aabaWdbiaaicdaa8aabaWdbiabl6UinbWdaeaapeGaeSy8I8eapa
qaa8qacqWIUlsta8aabaWdbiaaicdaa8aabaWdbiabl+UimbWdaeaa
peGaaGymaaaaaiaawUfacaGLDbaaaaa@45C0@
(
1
0
0
1
),[
1
0
0
1
],|
1
0
0
1
|
MathType@MTEF@5@5@+=
feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
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0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape
WaaeWaa8aabaqbaeqabiGaaaqaa8qacaaIXaaapaqaa8qacaaIWaaa
paqaa8qacaaIWaaapaqaa8qacaaIXaaaaaGaayjkaiaawMcaaiaacY
cadaWadaWdaeaafaqabeGacaaabaWdbiaaigdaa8aabaWdbiaaicda
a8aabaWdbiaaicdaa8aabaWdbiaaigdaaaaacaGLBbGaayzxaaGaai
ilamaaemaapaqaauaabeqaciaaaeaapeGaaGymaaWdaeaapeGaaGim
aaWdaeaapeGaaGimaaWdaeaapeGaaGymaaaaaiaawEa7caGLiWoaaa
a@486A@
Inserted graphics should always be given an ‘alt tag’ which
describes the content. A screenreader will convey this information to the user.
To add an alt tag first insert the picture then right click and select Format
Picture.
Select
Alt Text and then enter the alternative text for the image into the description
box. Captions are important for other readers and to assist with navigation if
an image must be referred to. These can also be added by right clicking on the
image
Only
PNG images are correctly transformed to all formats.
Figure 1: Inserted
PNG
1. RNIB. Clear Print. [Online] 2011.
http://www.rnib.org.uk/professionals/accessibleinformation/
text/pages/clear_print.aspx.
2. JISC TechDis.
Authoring Accessible Documents. [Online] http://www.jisctechdis.ac.uk/AccessibilityEssentials/2007/AE2/modules/authoring%20accessible%20docs/index.html.
3. Microsoft.
Word 2010 Help and How-to. [Online] 2012.
http://office.microsoft.com/en-us/word-help/CL010256357.aspx?CTT=97.