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Examples of monomials for this question.

$x,x_1,x^2,xy,x_1^2x_2^3,x^2y^3,2xy$

The terminology I currently know.

Coefficient - A single positive integer at the start of the monomial. This has a coefficient of 5.

$5x^3$

Degree - The sum of all the exponents for a monomial. This has a degree of 4.

$xy^2z$

Literal - The part of the monomial less the coefficient. The has a literal of $xy^2z$.

$3xy^2z$

Variable - The single case lower case letters. This has two variables $x$ and $y$.

$2x_3^5y^3$

Index - The single subscript of a variable. This has the index of $3$.

$2x_3^5$

Since the terminology may change based on context, the context of this is cycle index and working with Pólya enumeration theorem.

The reason for names of such specific parts is for use with programming code.

The parts for which a name (terminology) is sought.

  1. What is the terminology when a single variable is combined with an index?

E.g.

$x_1$

  1. What is the terminology when a single variable is combined with an index and an exponent?

E.g.

$x_1^2$

  1. If a variable letter with an index is also called a variable, then I am seeking a more specific name for the letter.

I need names that are unambiguous or that can not have multiple meanings.

Guy Coder
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  • Here $x$ and $x_3$ seem to be both variables and $x_3^2$ is a power of a variable. – Wuestenfux Apr 04 '22 at 11:46
  • Indices are usually not perceived by mathematicians as objects. I would consider $x_1$ and $x_2$ as completely different variables, with no more in common than $y$ and $z$. – Captain Lama Apr 04 '22 at 11:48
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    @Wuestenfux Thanks. That is along a different line of thought I am thinking that the entire group of the letter, index, and power is a variable, and the parts would have terminology like variable name, variable index and variable power. – Guy Coder Apr 04 '22 at 11:53
  • @CaptainLama Yes I agree. In my code the name, index and power are part of a tuple and in your example they would both be in separate tuples. – Guy Coder Apr 04 '22 at 11:54
  • In more searching found this So what I refer to as variable name there is called base and a name for a base with an exponent is called power. – Guy Coder Apr 05 '22 at 23:16

1 Answers1

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My gut feeling would be to say that a scalar variable is a combination of a variable name with an optional index.

variable = name + index

This doesn't fit a picture where you consider the whole variable as a vector, and then use the index as a means to extract a component. With that you'd have

component = variable + index

To differentiate the two cases you could explicitly include distinguishing typing information in your names and reach something less ambiguous like

scalar variable = vector + index

Combine that with an exponent and the best term that I can think of would be “factor”.

factor = scalar variable + exponent
MvG
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  • Thanks. I didn't include the details of my code as I didn't want to sway possible answers. In my code, which is Prolog, the group of a variable name, index and power is in a functor, v(Name,Index,Power) and a list of these form with a coefficient form a monomial, E.g. m(1,[v(x,1,1),v(y,1,2)]). As the code has to access the specific parts at times, I would prefer meaningful names. – Guy Coder Apr 04 '22 at 12:02
  • factor is a descriptive name (terminology) I have not considered for this. I will give it a test drive. – Guy Coder Apr 04 '22 at 12:06
  • I took factor for a test drive and it just seems to bring up more thoughts of what it means than it eliminates, in other words factor has so many other meanings that it's many definitions may be confusing to those that read the code. On the other hand as I am not a mathematician, the word is correct and I am just not comfortable with it. – Guy Coder Apr 04 '22 at 12:34