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## Formulas in reference books and in Mathcad, Maple etc  24-Ruby III

## Formulas in reference books and in Mathcad, Maple etc

There is no Polls now in this community,

what we must do now

1. Change formulas in references books

2. Change tools in Mathcad, Maple etc

3. Nothimg

4. Others 14 REPLIES 14  24-Ruby III
(To:ValeryOchkov)

Part of solution   13-Aquamarine
(To:ValeryOchkov)

Use Alt+0179 Viktor  24-Ruby III
(To:ViktorKorobov)

Yes, it is for us - for elite of Mathcad user!   24-Ruby III
(To:ValeryOchkov)

But what can we say to simple Mathcad users?  19-Tanzanite
(To:ValeryOchkov)

@ValeryOchkov wrote:

But what can we say to simple Mathcad users?

That the nomenclature in books is often ambiguous. Is "2 sin a cos a" 2*sin(a)*cos(a), or 2*sin(a*cos(a))? In the absence of any parentheses the first choice would the logical one to choose, but I have seen examples in books and papers where there really is no way to know without thinking about it very hard (even to the extent of rederiving the expression).  23-Emerald II
(To:ValeryOchkov)

I suggest a reference to ISO 80000 "Quantities and units" , mainly parts

1 (ISO 80000-1 "General" https://www.evs.ee/preview/iso-80000-1-2009-en.pdf), and

2 (ISO 80000-2 "Mathematical signs and symbols to be used in natural sciences and technology" https://www.evs.ee/preview/iso-80000-2-2009-en.pdf).

In part 1 you will find that symbols for quantities are to be written in sloping (italic) font, and units are to be presented as upright (not italic) symbols, separated from the preceding value by a space.

Example: borderlength = 15 m.

In part 2 you will find that:

Variables (x, y etc.) and running numbers (i, j etc.), parameters (a, b etc.) which may be considered constants in a particular context and functions in general (f, g etc.) are all printed in sloping (italic) font; while numbers are printed in upright (not italic) font

Example: f(x) = a·x + 123·g(b)

the symbols for well explicitly defined functions (sin, ln etc.), operators (d/dt, div etc.) and constants (e, π etc.)  are to be written in upright (not italic) font.

Example: sinewave(t) = -d cos(2·π·t)/ dt

The argument to a function is written in parentheses after the symbol for the function, without an intervening space. If the symbol for the function is 2 or more letters AND the argument contains no operation symbol (+, - etc.) THEN the parentheses may be omitted, and a thin space is to be inserted between the function and the argument. Example: arcosh 2a

If there is any risk of confusion, parentheses must be used. Hence write:  cos(a) + b, not:  cos a + b.

There are no rules set for the use of font types (Times, Arial etc.), nor for colour usage.

Further:

The symbol for:

- the tangent is tan    ( tg should NOT be used)

- the inverse trig functions are arcsin, arccos and arctan   (so not asin etc.)

- the inverse hyperbolic functions are arsinh, arcosh and artanh   (so not arcsinh etc.)

- natural, decimal, binary and a-based logarithmic functions are ln, lg, lb and log(with a in the subscript).

- the exponential function is ex  (with x in the exponent) or exp(x).

In a future release of Mathcad this should be implemented.

Luc  24-Ruby III
(To:LucMeekes)

OK!

sin^2x or sin(x)^2

and {[(a+b)*c)/c]*}  23-Emerald II
(To:ValeryOchkov)

That took a longer search through the standard (which is about 30 pages...).

The standard addresses powers, and states that x² is x squared and x³ is x cubed.
It briefly addresses powers of functions, stating that e.g. (sin x)² is often written as sin² x;
it does not say (sin(x))² = sin²(x).

You have parentheses (), square brackets [], braces {} and angle brackets <>.
The standard advises to use only parentheses for grouping, because the other items (braces and brackets) may have specific meanings in specific fields of application; the parentheses can be nested without causing misunderstanding.

The symbol for multiplication is a half-height dot · (ALT-0183) or a cross × (ALT-0215). Note that when a and b are vectors, then a·b is the scalar product of a and b, and  a×b is the vector product of a and b.
The symbol for division is a horizontal bar with numerator above it and denominator underneath, or the /.

The  :  may be used for ratios. Use of the symbol ÷ for division or ratio should be avoided.

Success!
Luc  19-Tanzanite
(To:LucMeekes)

This discussion came up in the days of Mathsoft. IMO the chance of Mathsoft implementing anything like this was 10x higher than the chance that PTC will, and Mathsoft didn't implement it.  24-Ruby III
(To:RichardJ)    24-Ruby III
(To:ValeryOchkov)

On the Wolfram Alpha log = ln!  23-Emerald II
(To:ValeryOchkov)

But Wolfram Alpha also knows: lb, lg and ln. And yes, it does interpret log(x) as ln(x), that is not conforming to the standard.

According to the standard

log

(without an indication of the base)

can be used if the base does not need to be specified....

I know one example of this:

loga(x)=log(x)/log(a)

It should be noted that the ISO 80000-2 standard exists since 2009. Before that the ISO 31-11 standard would reign, the latest version of which stems from 1992 (the first version is from 1978).

If you have old text books there's a good chance that they do not follow the rules of the ISO standards.

The NIST Handbook of mathematical functions follows the standard better than Mathcad or Prime (since it uses arctan, instead of atan) but not completely (since it uses arccosh instead of arcosh, to name an example).

Luc  24-Ruby III
(To:LucMeekes)   24-Ruby III
(To:LucMeekes)

@LucMeekes wrote:

The NIST Handbook of mathematical functions follows the standard better than Mathcad or Prime (since it uses arctan, instead of atan) but not completely (since it uses arccosh instead of arcosh, to name an example).

Luc 