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# Math context reference

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.

## Compounds

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 qualifier `!` is 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`
`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

## Acknowledgements

Much of this context has been assembled with the help of the Collins Dictionary of Mathematics by and . 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.

copyright © by Ping (e-mail) updated Mon 17 Jun 1996 at 10:19 JST
since Sun 26 May 1996