]> Writing Word documents for multiple formats

Writing Word documents for multiple formats

Emma Cliffe

May 2012

Introduction

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:

 


 

 

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

 


 

 

Document structure

Global settings

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 transformations

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.

 

Writing a structured document

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.

Structure, navigation, text

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.

 

Labels and references

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.

 

Standard structures

Quotations

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.

Lists

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 and rules

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

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.

Standard

                                            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@

Greek

                                       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@

Letter-like symbols

                                 ,,,,ð,Ϝ,,,,h,,ı,,j,ϰ,,,,, 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@

                                   ,,,,,,,,,,,,,,, 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@

Operators

                                    ±,÷,×,,,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@

Arrows

                               ,,,,,,,,,,,,,,,, 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@

Negated relations

                                        ,,,,,,,,,,,,,, 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@

Scripts

Not all letters in the script alphabet will be spoken as script-letter by MathPlayer.

                                         A,,C,D,,,G,,,K,,, 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,,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.

Frakturs

Not all letters in the Fraktur alphabet will be spoken as fraktur-letter by MathPlayer.

                                        A,B,,D,E,F,G,,,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,,S,T,U,V,W,X,Y, 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@

Double struck

Not all letters in the double struck alphabet will be spoken as double struck-letter by MathPlayer.

                                        A,B,,D,E,F,G,,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@

                                        ,O,,,,S,T,U,V,W,X,Y, 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@

Geometry

                                              ,,,,,,,,,, MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamXvP5wqSX2qVr wzqf2zLnharyGqHrxyUDgaiuGaqaaaaaaaaaWdbiaa=9HicaGGSaGa eyiiIaTaaiilaiablgIisjaacYcacqWIIiYucaGGSaGaeyyPI4Laai ilamrr1ngBPrwtHrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae4hj IWOaaiilaiablwIiqjaacYcacqGFMisJcaGGSaacfaGaa0NnIiaacY cacqGH0icxcaGGSaGaeSynIefaaa@5C40@

 

Maths structures

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.

Displayed math

                    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 aaikdaa8aabaWdbiaaikdaaaGccaWG4bWdamaaDaaaleaapeGaaG4m aaWdaeaapeGaaGOmaaaakiaadIhapaWaa0baaSqaa8qacaaI0aaapa qaa8qacaaIYaaaaOGaamiEa8aadaqhaaWcbaWdbiaaiwdaa8aabaWd biaaikdaaaGccaWG4bWdamaaDaaaleaapeGaaGOnaaWdaeaapeGaaG OmaaaakiaadIhapaWaa0baaSqaa8qacaaI3aaapaqaa8qacaaIYaaa aOGaamiEa8aadaqhaaWcbaWdbiaaiIdaa8aabaWdbiaaikdaaaGcca WG4bWdamaaDaaaleaapeGaaGyoaaWdaeaapeGaaGOmaaaakiaadIha 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 a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaybCaeqal8aabaWdbiaadMgacqGH9aqpcaaIXaaapaqaa8qacaaI XaGaaG4maaqdpaqaa8qacqGHpis1aaGccaWG4bWdamaaDaaaleaape GaamyAaaWdaeaapeGaaGOmaaaakiabg2da9iaadIhapaWaa0baaSqa a8qacaaIXaaapaqaa8qacaaIYaaaaOGaeyyXICTaamiEa8aadaqhaa WcbaWdbiaaikdaa8aabaWdbiaaikdaaaGccqGHflY1caWG4bWdamaa DaaaleaapeGaaG4maaWdaeaapeGaaGOmaaaakiabgwSixlaadIhapa Waa0baaSqaa8qacaaI0aaapaqaa8qacaaIYaaaaOGaeyyXICTaamiE a8aadaqhaaWcbaWdbiaaiwdaa8aabaWdbiaaikdaaaGccqGHflY1ca WG4bWdamaaDaaaleaapeGaaGOnaaWdaeaapeGaaGOmaaaakiabgwSi xlaadIhapaWaa0baaSqaa8qacaaI3aaapaqaa8qacaaIYaaaaOGaey yXICTaamiEa8aadaqhaaWcbaWdbiaaiIdaa8aabaWdbiaaikdaaaGc 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@

Word structures

                                                        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 qal8aabaWdbiaadggaaeqan8aabaWdbiabg+GivdaakiaadIhacaGG SaWaaybuaeqal8aabaWdbiaadggaaeqan8aabaWdbiabg+Givdaaki aadIhacaGGSaWdamaavacabeWcbeqaaiaaygW7a0qaa8qacqWIqiYq aaGccaWG4bGaaiilamaawahabeWcpaqaa8qacaWGHbaapaqaa8qaca WGIbaan8aabaWdbiablcHidbaakiaadIhacaGGSaWaaybCaeqal8aa baWdbiaadggaa8aabaWdbiaadkgaa0WdaeaapeGaeSieImeaaOGaam iEaiaacYcadaGfqbqabSWdaeaapeGaamyyaaqab0WdaeaapeGaeSie ImeaaOGaamiEaiaacYcadaGfqbqabSWdaeaapeGaamyyaaqab0Wdae aapeGaeSieImeaaOGaamiEaaaa@6944@

 

                                             ( x ),[ x ],{ x },| x |, [ x [ ,] x ],] x [, MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaeWaa8aabaWdbiaadIhaaiaawIcacaGLPaaacaGGSaWaamWaa8aa baWdbiaadIhaaiaawUfacaGLDbaacaGGSaWaaiWaa8aabaWdbiaadI haaiaawUhacaGL9baacaGGSaWaaqWaa8aabaWdbiaadIhaaiaawEa7 caGLiWoacaGGSaWaaKGia8aabaWdbiaadIhaaiaawUfacaGLBbaaca GGSaWaaKWma8aabaWdbiaadIhaaiaaw2facaGLDbaacaGGSaWaaKWi a8aabaWdbiaadIhaaiaaw2facaGLBbaacaGGSaaaaa@51C4@

                                            ( x, [ x ,{ x ,|x,,x|,x },x ], x ) MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Waaeqaa8aabaWdbiaadIhaaiaawIcaaiaacYcadaWabaWdaeaapeGa amiEaaGaay5waaGaaiilamaaceaapaqaa8qacaWG4baacaGL7baaca GGSaWaaqqaa8aabaWdbiaadIhaaiaawEa7aiaacYcacqGHMacVcaGG SaWaaqGaa8aabaWdbiaadIhaaiaawIa7aiaacYcadaGacaWdaeaape GaamiEaaGaayzFaaGaaiilamaadiaapaqaa8qacaWG4baacaGLDbaa caGGSaWaaeGaa8aabaWdbiaadIhaaiaawMcaaaaa@4EE1@

                                                             { a b MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Waaiqaa8aabaqbaeqabiqaaaqaa8qacaWGHbaapaqaa8qacaWGIbaa aaGaay5Eaaaaaa@393D@

                                                             { a b c MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 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 a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaci4CaiaacMgacaGGUbGaamiEaiaacYcaciGGJbGaai4Baiaacoha caWG4bGaaiilaiGacshacaGGHbGaaiOBaiaadIhacaGGSaGaci4yai 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 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaci4CaiaacMgacaGGUbWdamaaCaaaleqabaWdbiabgkHiTiaaigda aaGccaWG4bGaaiilaiGacogacaGGVbGaai4Ca8aadaahaaWcbeqaa8 qacqGHsislcaaIXaaaaOGaamiEaiaacYcaciGG0bGaaiyyaiaac6ga paWaaWbaaSqabeaapeGaeyOeI0IaaGymaaaakiaadIhacaGGSaGaci 4yaiaacohacaGGJbWdamaaCaaaleqabaWdbiabgkHiTiaaigdaaaGc caWG4bGaaiilaiGacohacaGGLbGaai4ya8aadaahaaWcbeqaa8qacq GHsislcaaIXaaaaOGaamiEaiaacYcaciGGJbGaai4BaiaacshapaWa aWbaaSqabeaapeGaeyOeI0IaaGymaaaakiaadIhaaaa@5C3D@

                                    sinhx,coshx,tanhx,cschx,sechx,cothx, MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaci4CaiaacMgacaGGUbGaaiiAaiaadIhacaGGSaGaci4yaiaac+ga caGGZbGaaiiAaiaadIhacaGGSaGaciiDaiaacggacaGGUbGaaiiAai 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 a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaci4CaiaacMgacaGGUbGaaiiAa8aadaahaaWcbeqaa8qacqGHsisl caaIXaaaaOGaamiEaiaacYcaciGGJbGaai4BaiaacohacaGGObWdam aaCaaaleqabaWdbiabgkHiTiaaigdaaaGccaWG4bGaaiilaiGacsha caGGHbGaaiOBaiaacIgapaWaaWbaaSqabeaapeGaeyOeI0IaaGymaa aakiaadIhacaGGSaGaae4yaiaabohacaqGJbGaaeiAa8aadaahaaWc beqaa8qacqGHsislcaaIXaaaaOGaamiEaiaacYcacaqGZbGaaeyzai aabogacaqGObWdamaaCaaaleqabaWdbiabgkHiTiaaigdaaaGccaWG 4bGaaiilaiGacogacaGGVbGaaiiDaiaacIgapaWaaWbaaSqabeaape GaeyOeI0IaaGymaaaakiaadIhaaaa@61B9@

                                        log a b,logb, lim a b, min a b, max a b,lnb MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaciiBaiaac+gacaGGNbWdamaaBaaaleaapeGaamyyaaWdaeqaaOWd biaadkgacaGGSaGaciiBaiaac+gacaGGNbGaamOyaiaacYcapaWaaC beaeaapeGaciiBaiaacMgacaGGTbaal8aabaWdbiaadggaa8aabeaa k8qacaWGIbGaaiila8aadaWfqaqaa8qaciGGTbGaaiyAaiaac6gaaS WdaeaapeGaamyyaaWdaeqaaOWdbiaadkgacaGGSaWdamaaxababaWd biGac2gacaGGHbGaaiiEaaWcpaqaa8qacaWGHbaapaqabaGcpeGaam OyaiaacYcaciGGSbGaaiOBaiaadkgaaaa@54CB@

                         =,==,+=,=,, x , x , x , x , x , x , x , x , x , x , x , x MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamXvP5wqSX2qVr wzqf2zLnharyGqHrxyUDgaiuaaqaaaaaaaaaWdbiaa=zJicqGH9aqp caGGSaGaeyypa0Jaeyypa0JaaiilaiabgUcaRiabg2da9iaacYcacq GHsislcqGH9aqpcaGGSaGaeSixIaKaaiila8aadaWfqaqaa8qacqGH qgcRaSWdaeaapeGaamiEaaWdaeqaaOWdbiaacYcapaWaaCbeaeaape GaeyOKH4kal8aabaWdbiaadIhaa8aabeaak8qacaGGSaWdamaaxaca baWdbiabgcziScWcpaqabeaapeGaamiEaaaakiaacYcapaWaaCbiae aapeGaeyOKH4kal8aabeqaa8qacaWG4baaaOGaaiila8aadaWfqaqa a8qacqGHqhc3aSWdaeaapeGaamiEaaWdaeqaaOWdbiaacYcapaWaaC beaeaapeGaeyO0H4nal8aabaWdbiaadIhaa8aabeaak8qacaGGSaWd amaaxacabaWdbiabgcDiCdWcpaqabeaapeGaamiEaaaakiaacYcapa WaaCbiaeaapeGaeyO0H4nal8aabeqaa8qacaWG4baaaOGaaiila8aa daWfqaqaa8qacqGHugYQaSWdaeaapeGaamiEaaWdaeqaaOWdbiaacY capaWaaCbiaeaapeGaeyiLHSkal8aabeqaa8qacaWG4baaaOGaaiil a8aadaWfqaqaa8qacqGHuhY2aSWdaeaapeGaamiEaaWdaeqaaOWdbi aacYcapaWaaCbiaeaapeGaeyi1HSnal8aabeqaa8qacaWG4baaaaaa @7EF6@

                                                            1 0 0 1 MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaauaabeqaciaaae aaqaaaaaaaaaWdbiaaigdaa8aabaWdbiaaicdaa8aabaWdbiaaicda a8aabaWdbiaaigdaaaaaaa@3962@

                                                          1 0 0 0 1 0 0 0 1 MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaauaabeqadmaaae aaqaaaaaaaaaWdbiaaigdaa8aabaWdbiaaicdaa8aabaWdbiaaicda a8aabaWdbiaaicdaa8aabaWdbiaaigdaa8aabaWdbiaaicdaa8aaba Wdbiaaicdaa8aabaWdbiaaicdaa8aabaWdbiaaigdaaaaaaa@3DA7@

                                                       ( 1 0 0 1 ) MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaeWaa8aabaqbaeqabmWaaaqaa8qacaaIXaaapaqaa8qacqWIVlct a8aabaWdbiaaicdaa8aabaWdbiabl6UinbWdaeaapeGaeSy8I8eapa qaa8qacqWIUlsta8aabaWdbiaaicdaa8aabaWdbiabl+UimbWdaeaa peGaaGymaaaaaiaawIcacaGLPaaaaaa@4557@

                                                       [ 1 0 0 1 ] MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb 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 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaeWaa8aabaqbaeqabiGaaaqaa8qacaaIXaaapaqaa8qacaaIWaaa paqaa8qacaaIWaaapaqaa8qacaaIXaaaaaGaayjkaiaawMcaaiaacY cadaWadaWdaeaafaqabeGacaaabaWdbiaaigdaa8aabaWdbiaaicda a8aabaWdbiaaicdaa8aabaWdbiaaigdaaaaacaGLBbGaayzxaaGaai ilamaaemaapaqaauaabeqaciaaaeaapeGaaGymaaWdaeaapeGaaGim aaWdaeaapeGaaGimaaWdaeaapeGaaGymaaaaaiaawEa7caGLiWoaaa a@486A@

 

Graphics

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.

Description: This is the alternative text of the PNG smily face.

Figure 1: Inserted PNG

Bibliography

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.