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Plots of physical quantities has significantly improved with Maple 2022. The updated useunits option makes unit conversion errors in plots very unlikely. A lot of time is saved when creating plots of physical quantities where values and units must be correct.

One final source of user errors remains: The manual entry of incorrect units in labels.

Below is a way to avoid such errors by computing labels with units for three prevalent axis labeling schemes.


Other desireable labels are given as a suggestion for future plot label enhancements where plot commands could provide formating functionality.

The rendering on this website adds double brakets ⟦ ⟧ wherever units are used. You have to open the document to see how Maple renders.

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Simple plot example: Solar irradiance in space

G__0 := 1361*Unit('W'/'m'^2)

1361*Units:-Unit(W/m^2)

 (1)

G__0*sin(2*Pi*t/(24*Unit('h')))

1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h))

 (2)

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'))

  

This plot has inconsistent axis labeling:

• 

The vertical axis has units but no name
• 

The horizontal axis has a name and units but they are not easily distinguishable. Misinterpretation is possible. Due to the close spacing the label could be read as a product of the dimension "time squared" (the time t times hours h is of the dimension time squared). Or the reader confounds name and units. (The use of italic fonts for names and roman fonts for units might not be noticeable and is a convention that is not used everywhere.)

 

The above labeling should be improved for communication, documentation or publication purposes.

 

A quick attempt using strings and the options useuints and labels.

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = ['d', kW/m^2], labels = ["Time t in days", "Exposure G in kV/m^2"])

 

Axes are now consistent and can be interpreted unambiguously. Formatting can still be improved.

 

Unfortunately, using the options useunits (for unit conversion) and labels this way introduces a new source of user error when labels are entered with the wrong units.

 

A way to address this and to ensure unit error-free plotting of expressions of physical quantities is the following:

 

Step1: Define two lists, one for the units to display and the other for the names to display

a := [Unit('s'), Unit('W'/'cm'^2)]; b := [t, G]

[t, G]

 (3)

Step2: Compute labels from the lists

This step avoids the labeling error: No manual entry of units in labels required.

c := [b[1]/a[1], typeset(b[2]/a[2])]; d := [typeset(b[1], " ", "⟦", a[1], "⟧"), typeset(b[2], " ⟦", a[2], "⟧")]; e := [typeset(b[1], " ", "(", a[1], ")"), typeset(b[2], " (", a[2], ")")]

[typeset(t, " ", "(", Units:-Unit(s), ")"), typeset(G, " (", Units:-Unit(W/cm^2), ")")]

 (4)

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Dimensionless labels

 Double brackets

Parenthesis

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = a, labels = c)

  

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = a, labels = d)

  

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = a, labels = e)

  

The axis values equal physical quantities divided by their units. The algebraic equation G*cm^2/W = 0.8e-1, for example, is physically speaking correct. Most functions of Maple can process dimensionless expression of the kind G*cm^2/W if G is given with appropriate physical units.

This way of using physical quantities is consistent with ISO 80000.  

Used in Maple to enter units in 2D-Math input mode

Can be confounded with functional notation. Units are therefore often written as a whole word (e.g. seconds instead of s).
 

 

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The time to produce the above three plots was about 10 Minutes. The most part was spent to get the typesetting of the second and third plot correct.

 

What takes significant more time (more a question of hours when Typesetting is used for the first time) are

 

Labels with "/ cm^(2) "or 1/cm^2 formatting.

 

This formatting might be preferred but is unfortunately again not free from user errors. (I would probably use it if there was a simple and safe way).

f := [b[1]/a[1], b[2]/`#mrow(mo("W "),mo(" "),mo(" / "),msup(mo("cm"),mn("2")))`]; g := [typeset(b[1], " ", "⟦", a[1], "⟧"), typeset(b[2], " ⟦", (`@`(`@`(Units:-Unit, numer), op))(a[2]), "/", (`@`(`@`(Units:-Unit, denom), op))(a[2]), "⟧")]; h := [typeset(b[1], " ", "(", Unit('s'), ")"), typeset(b[2], " (", `#mrow(mo("W"),mo(" "),msup(mo("cm"),mn("-2")))`, ")")]

[typeset(t, " ", "(", Units:-Unit(s), ")"), typeset(G, " (", `#mrow(mo("W"),mo(" "),msup(mo("cm"),mn("-2")))`, ")")]

 (5)

 

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = a, labels = f)

  

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = a, labels = g)

  

plot(1361*Units:-Unit(W/m^2)*sin((1/12)*Pi*t/Units:-Unit(h)), t = 0 .. 12*Unit('h'), useunits = a, labels = h)

  

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Remarks

• 

For two reasons, I have not given an example with the often used square brackets [ ] because:
    
    Maple uses square brackets already for lists and indexing purposes,
    and ISO 80000 uses square brackets as an operator that extracts the unit from a physical quantity (e.g.       [G] = Unit('W'/'cm'^2)).

• 

Adding a unit to each value at axes ticks would definitely be a nice labeling feature for simple units.

• 

Programmatically analyzing the units defined in list a above and converting them in a generic way to a typesetting structure is not possible with a few high-level commands.

 

• 

For inline quotients like in 1/2, an additional backslash must be entered in 2D-Math: \/  

Unit('W')/Unit('cm')^2

Units:-Unit(W)/Units:-Unit(cm)^2

 (6)

     This will not prevent evaluation to a normal quotient but the input can be used to create an atomic variable (select with mouse -> 2-D Math -> Atomic Variable)

`#mrow(mfenced(mi("W",fontstyle = "normal"),open = "⟦",close = "⟧"),mo("/"),mo("⁢"),msup(mfenced(mi("cm",fontstyle = "normal"),open = "⟦",close = "⟧"),mn("2")),mo("⁢"))`

`#mrow(mfenced(mi("W",fontstyle = "normal"),open = "⟦",close = "⟧"),mo("/"),mo("⁢"),msup(mfenced(mi("cm",fontstyle = "normal"),open = "⟦",close = "⟧"),mn("2")),mo("⁢"))`

 (7)

     This makes labeling much easier as compared to typesetting commands (compare to the above statements).

f := [b[1]/a[1], b[2]/`#mrow(mfenced(mi("W",fontstyle = "normal"),open = "⟦",close = "⟧"),mo("/"),mo("⁢"),msup(mfenced(mi("cm",fontstyle = "normal"),open = "⟦",close = "⟧"),mn("2")),mo("⁢"))`]

[t/Units:-Unit(s), G/`#mrow(mfenced(mi("W",fontstyle = "normal"),open = "⟦",close = "⟧"),mo("/"),mo("⁢"),msup(mfenced(mi("cm",fontstyle = "normal"),open = "⟦",close = "⟧"),mn("2")),mo("⁢"))`]

 (8)

In any case it is a good idea to read ?plot,typesetting before experimenting with typesetting.

 

Axes_with_unit_labels.mw

My personal preference is for dimensionless labels.

Note:

The solution to avoid labeling errors works only for Maple 2022 and higher.

Some plot commands do not support plotting with units, or they do not fully support it yet.
typesetting label units plots

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