A way to plot without unit labeling errors and some suggestions for plot labels with units

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A way to plot without unit labeling errors and some suggestions for plot labels with units

Posted: C_R 2957 Product: Maple 2023

December 10 2023

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.

Simple plot example: Solar irradiance in space

(1)

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

(2)

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.

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]

(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], " ", "&lobrk;", a[1], "&robrk;"), typeset(b[2], " &lobrk;", a[2], "&robrk;")]; e := [typeset(b[1], " ", "(", a[1], ")"), typeset(b[2], " (", a[2], ")")]

(4)

Dimensionless labels

Double brackets

Parenthesis

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 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).

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

(5)