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

  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

Types

Symbols

Acknowledgements

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.