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common context -

Compounds consist of a single-quote followed by the compound name
and sub-elements (separated by commas) in parentheses, if any. See the
MINSE syntax page for details on syntax.
This page defines the *mathematics context* for giving
meaning to a MINSE expression. The common context
definitions are included as part of this definition.

In definitions, `A`, `B`, `C`... refer to
the respective sub-elements of the compound. Parts of the definition
within square brackets refer to optional sub-elements.

*Name Composition*`index`

- attach a quantitative index
`B`to a variable name`A` `qual`

- attach a descriptive qualifier
`B`to a variable name`A`

The special qualifieris interpreted as a "prime" mark in this context.`!`

*Arithmetic*`neg`

- form the negative of a quantity, vector, or matrix
`exp`

- raise a base
`A`to an exponent`B` `prod`

- multiply two expressions
`quot`

- form the quotient of two expressions
`divby`

- divide two expressions and suggest the dot-bar-dot symbol for visual rendering
`sum`

- add two expressions
`diff`

- subtract two expressions
`eq`

- assert that two expressions are equal
`noteq`

- assert that two expressions are not equal
`gt`

- assert that
`A`is strictly greater than`B` `gteq`

- assert that
`A`is greater than or equal to`B` `lt`

- assert that
`A`is strictly less than`B` `lteq`

- assert that
`A`is less than or equal to`B` `approxeq`

- assert that
`A`is approximately equal to`B` `propto`

- assert that
`A`is proportional to`B` `approach`

- suppose that
`A`approaches the value`B`

*Set Theory*`intersect`

- form the intersection of two sets
`union`

- form the union of two sets
`disjunion`

- form the disjoint union of two sets
`relcomp \`

- form the relative complement of
`B`in the set`A` `symdiff`

- form the symmetric difference of two sets
`superseteq`

- assert that
`A`is a superset of the set`B` `superset`

- assert that
`A`is a strict superset of the set`B` `subseteq`

- assert that
`A`is a subset of the set`B` `subset`

- assert that
`A`is a strict subset of the set`B` `notsubset`

- assert that
`A`is not a subset of the set`B` `element`

- assert that
`A`is an element of the set`B` `notelement`

- assert that
`A`is not an element of the set`B`

*Vectors*`cross`

- form the cross product of two vectors
`dot`

- form the dot product of two vectors

*Relations*`apply`

- apply a relation
`A`to an argument or tuple of arguments`B` `compose`

- compose the function
`A`with the function`B` `composen`

- compose the function
`A`with itself`B`times `tuple`

- group a list of arguments to a relation

*Geometry*`congruent`

- assert that
`A`is congruent to`B` `similar`

- assert that
`A`is similar to`B`

*Logic*`not`

- assert the negation of a proposition or truth value
`and`

- form the logical conjunction of two propositions or truth values
`or`

- form the logical inclusive disjunction of two propositions or truth values
`xor`

- form the logical exclusive disjunction of two propositions or truth values
`implies`

- assert that proposition
`A`implies proposition`B` `equiv`

- assert that two propositions or truth values are equivalent
`defeq`

- define
`A`as being equal to`B`

*Algebra*`Sum`

- add all values of
`A`as`B`takes values [in the set`C`] or [ranging from`C`to`D`] `Prod`

- multiply all values of
`A`as`B`takes values [in the set`C`] or [ranging from`C`to`D`]

*Calculus*`deriv`

- differentiate
`A`with respect to`B`, once or [`C`times] `ptderiv`

- partially differentiate
`A`with respect to`B`, once or [`C`times] `integ`

- integrate
`A`with respect to`B`, indefinitely or [over the interval from`C`to`D`]

*Trigonometry*`sin`

- compute the sine of
`A` `cos`

- compute the cosine of
`A` `tan`

- compute the tangent of
`A` `csc`

- compute the cosecant of
`A` `sec`

- compute the secant of
`A` `cot`

- compute the cotangent of
`A` `arcsin`

- compute the arcsine of
`A` `arccos`

- compute the arccosine of
`A` `arctan`

- compute the arctangent of
`A` `arccsc`

- compute the arccosecant of
`A` `arcsec`

- compute the arcsecant of
`A` `arccot`

- compute the arccotangent of
`A`

Much of this context has been assembled with the help of the
Collins Dictionary of Mathematics by *E. J. Borowski*
and *J. M. Borwein*. My favourite definition from the book,
given on page 411, is duplicated here (without permission) for your enjoyment.

null graph,n.

Fig. 257.Null graph.

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since Sun 26 May 1996