Content Element Descriptions

Attributes Common to Most Content Elements

A large number of content markup elements accept two special attributes. These attributes can be used to extend content MathML markup by pointing to external definitions of mathematical objects. When these attributes are set, they are cues to MathML software systems about the precise meaning of content elements.

definitionURL is be a pointer to an external definition for a mathematical object. Ideally the definition should be online at an actual URL. However, the value may also be a general URI (i.e. a URL that doesn't point at an actual document) denoting a bibliographic reference for example.

encoding is used to specify the format of the defintion pointed to by definitionURL. Legal values are open ended, ranging from text to formal syntaxes such as computer algebra code.

WebEQ 3 accepts definitionUL and encoding attributes, but ignores the values.

1. Content Token Elements

Name:	cn
Usage:	<cn> ... </cn>
Description:	A numerical constant
Attributes:

Name	Values	Default
base	integer	10
type	string	real

Notes:

Numbers are decimal by default, but other bases can be used, by setting the appropriate base attribute (2 for binary, 16 for hexadecimal, etc.)

The type is the kind of number (real, integer, rational, complex-cartesian, complex-polar, constant).

Name:	ci
Usage:	<ci> ... </ci>
Description:	Symbolic names (variables)
Attributes:

Name	Values	Default
type	string

Notes:

The type is the kind of number (real, integer, complex, etc.) the ci represents, or the type of MathML object (as vector, array, etc.).

Name:	csymbol
Usage:	<csymbol> ... </csymbol>
Description:	A symbol, constant or function.
Attributes:	definitionURL and encoding

Notes:

The csymbol element is used to denote a symbol with a generally accepted public definition. For example, one might markup Boltzmann's constant, k with a csymbol. Typically csymbol is used with definitionURL and encoding attributes set, to point to an external symbol defintion.

2. Basic Elements

Name:	apply
Usage:	<apply> operator argument(s) </apply>
Description:	Applies a function or operator to its arguments. The first thing after the <apply> should be the function or operator, followed by the arguments.

Name:	reln
Usage:	<reln> operator argument(s) </reln>
Description:	Analogous to <apply>; used when the operator is an equation or a relation. This replaces the <e> tag that was used in WebEQ 2.2.

Name:	fn
Usage:	<fn> ... </fn>
Description:	A user-defined function.
Attributes:	definitionURL

Notes:

The fn element is deprecated in MathML 2.0. In MathML 2.0, the first child of an apply element is assumed to be a function and no extra markup is required.

Name:	interval
Usage:	<interval> left-endpoint right-endpoint </interval>
Description:	An interval of the real line.
Attributes:

Name	Values	Default
closure	open|closed|open-closed|closed-open	closed

Notes:

The closure determines whether the interval includes its endpoints or not.

Name:	inverse
Usage:	<apply> <inverse/> ... </apply>
Description:	The inverse of a function or operator (like a matrix).

Name:	sep
Usage:	<sep/>
Description:	Separates numeric values (for example, real and imaginary parts of complex numbers)

Name:	condition
Usage:	<condition> <reln> ... </reln> </condition>
or	<condition> <apply> ... </apply> </condition>
Description:	Places a condition on identifiers. This tag must contain a single reln or apply element.

Name:

declare

Not used in WebEQ

Usage:	<declare> variable definition </declare>
Description:	Defines a mathematical object (to set specific default characteristics, or give it a more convenient name: set x to denote a vector, or a to be the vector (1,2,-2)).
Attributes:

Name	Values	Default
type	MathML type	ci
scope	local | gobal	local
nargs	number	1
ocurrence	prefix | infix | function-model	function-model
definitionURL	URL

Notes:

The type is the MathML type of the identifier declared.

The scope controls the area of validity of the declaration.

The attribute nargs gives the number of arguments, for the use with the declaration of functions.

The ocurrence describes how the operator is to be used, as prefix, infix or function_usage.

Name:	lambda
Usage:	<lambda> variable(s)<apply> definition </apply> </lambda>
Description:	Defines a function. The first arguments are the variables representing the arguments of the function, while the last one is the expression defining it.

Name:	compose
Usage:	<apply> <compose/> functions to compose </apply>
Description:	Function composition operator. WebEQ draws a small circle between each of the functions given by children of the apply.

Name:	ident
Usage:	<ident/>
Description:	Identity operator. WebEQ renders this as the symbol id.
Attributes:	definitionURL and encoding

Name:	domain
Usage:	<apply> <domain/> function </apply>
Description:	Domain of a function
Attributes:	definitionURL and encoding
Notes:	Not implemented in WebEQ 3.0

Name:	codomain
Usage:	<apply> <codomain/> function </apply>
Description:	Codomain of a function. Sometimes called range of a function.
Attributes:	definitionURL and encoding
Notes:	Not implemented in WebEQ 3.0

Name:	domainofapplication
Usage:	<apply> <int> <domainofapplication> ... </domainofapplication> ... </apply>
Description:	Specifies a domain over which a function is applied. Primarily for use with integrals to specify a domain of integration, and is a more general alternative to limits, where the domain of integration is an interval.
Notes:	Not implemented in WebEQ 3.0

Name:	piecewise
Usage:	<piecewise> <piece> ... [ <otherwise> ] </piecewise>
Description:	Used to support `piecewise' function declarations
Notes:	Not implemented in WebEQ 3.0

Name:	piece
Usage:	<piece> definition domain </piece>
Description:	A piece of a piecewise fuction definition
Notes:	Not implemented in WebEQ 3.0

Name:	otherwise
Usage:	<otherwise> definition domain </otherwise>
Description:	The default case in a piecewise function definition
Notes:	Not implemented in WebEQ 3.0

3. Arithmetic, Algebra and Logic

Name:	quotient
Usage:	<apply> <quotient/> numerator denominator </apply>
Description:	Quotient of an integer division (applied to a and b, gives the integer q such that a = q b + r, with r<b). This replaces the <idiv> tag that was used in WebEQ 2.2.
Attributes:	definitionURL and encoding

Name:	exp
Usage:	<apply> <exp/> exponent </apply>
Description:	Exponential function with base e = 2.718281828...
Attributes:	definitionURL and encoding

Name:	factorial
Usage:	<apply> <factorial/> argument </apply>
Description:	The factorial of a number.
Attributes:	definitionURL and encoding

Name:	divide
Usage:	<apply> <divide/> dividend divisor </apply>
Description:	Division. This replaces the <over> tag that was used in WebEQ 2.2.
Attributes:	definitionURL and encoding

Name:	max
Usage:	<apply> <max/> arguments or condition </apply>
Description:	Compare the values of its arguments, returning the largest one.
Attributes:	definitionURL and encoding

Name:	min
Usage:	<apply> <min/> arguments or condition </apply>
Description:	Compare the values of its arguments, returning the smallest one.
Attributes:	definitionURL and encoding

Name:	minus
Usage:	<apply> <minus/> ... </apply>
Description:	Substraction (if applied to 2 arguments), or changes sign (if applied to a single argument).
Attributes:	definitionURL and encoding

Name:	plus
Usage:	<apply> <plus/> ... </apply>
Description:	Addition (can be applied to any number of arguments).
Attributes:	definitionURL and encoding

Name:	power
Usage:	<apply> <power/> base exponent</apply>
Description:	First argument raised to the second one.
Attributes:	definitionURL and encoding

Name:	rem
Usage:	<apply> <rem/> dividend divisor </apply>
Description:	Remainder of an integer division (applied to a and b, gives the integer r such that a = q b + r, with r<b).
Attributes:	definitionURL and encoding

Name:	times
Usage:	<apply> <times/> ... </apply>
Description:	Multiplication.
Attributes:	definitionURL and encoding

Name:	root
Usage:	<apply> <root/> <degree>degree</degree> radicand </apply>
Description:	The n-th root. The second argument is the degree of the root. If it is not there, the default is 2 (i.e., square root).
Attributes:	definitionURL and encoding

Name:	gcd
Usage:	<apply> <gcd/> ... </apply>
Description:	Greatest Common Divisor of its arguments.
Attributes:	definitionURL and encoding

Name:	and
Usage:	<apply> <and/> ... </apply>
Description:	Boolean and operator.
Attributes:	definitionURL and encoding

Name:	or
Usage:	<apply> <or/> ... </apply>
Description:	Boolean or operator.
Attributes:	definitionURL and encoding

Name:	xor
Usage:	<apply> <xor/> ... </apply>
Description:	Boolean xor operator.
Attributes:	definitionURL and encoding

Name:	not
Usage:	<apply> <not/> operand </apply>
Description:	Boolean not operator.
Attributes:	definitionURL and encoding

Name:	implies
Usage:	<reln> <implies/> arg1 arg2 </reln>
Description:	Logical "implies" operator.
Attributes:	definitionURL and encoding

Name:	forall
Usage:	<apply> <forall/> Optional bvar's or condition <apply> ... </apply> </apply>
or	<apply> <forall/> Optional bvar's or condition <reln> ... <reln></apply>
Description:	The forall element represents the universal quantifier of logic.
Attributes:	definitionURL and encoding

Name:	exists
Usage:	<apply> <exists/> Optional bvar's or condition <apply> ... </apply> </apply>
or	<apply> <exists/> Optional bvar's or condition <reln> ... <reln></apply>
Description:	The exists element represents the existential quantifier of logic.
Attributes:	definitionURL and encoding

Name:	abs
Usage:	<apply> <abs/> operand </apply>
Description:	The absolute value of a real quantity or the modulus of a complex quantity.
Attributes:	definitionURL and encoding

Name:	conjugate
Usage:	<apply> <conjugate/> operand </apply>
Description:	The complex conjugate of a complex quantity.
Attributes:	definitionURL and encoding

Name:	arg
Usage:	<apply> <arg/> complex number </apply>
Description:	The argument of a complex number
Attributes:	definitionURL and encoding

Name:	real
Usage:	<apply> <real/> complex number </apply>
Description:	Real part of a complex number
Attributes:	definitionURL and encoding

Name:	imaginary
Usage:	<apply> <imaginary/> complex number </apply>
Description:	Imaginary part of a complex number
Attributes:	definitionURL and encoding

Name:	lcm
Usage:	<apply> <lcm/> number, number ... </apply>
Description:	Least common multiple of its arguments
Attributes:	definitionURL and encoding

Name:	floor
Usage:	<apply> <floor/> real number </apply>
Description:	Greatest integer less than or equal to its argument
Attributes:	definitionURL and encoding
Notes:	Not implemented in WebEQ 3.0

Name:	ceiling
Usage:	<apply> <ceiling/> real number </apply>
Description:	Least integer greater than or equal to its argument
Attributes:	definitionURL and encoding
Notes:	Not implemented in WebEQ 3.0

4. Relations

Name:	eq
Usage:	<reln> <eq/> arg1 ... arg2 </reln>
Description:	Equality relation.
Attributes:	definitionURL and encoding

Name:	neq
Usage:	<reln> <neq/> arg1 arg2 </reln>
Description:	"Not equal to" relation.
Attributes:	definitionURL and encoding

Name:	gt
Usage:	<reln> <gt/> arg1 ... arg2 </reln>
Description:	"Greater than" relation.
Attributes:	definitionURL and encoding

Name:	lt
Usage:	<reln> <lt/> arg1 ... arg2 </reln>
Description:	"Less than" relation.
Attributes:	definitionURL and encoding

Name:	geq
Usage:	<reln> <geq/> arg1 ... arg2 </reln>
Description:	"Greater or equal than" relation.
Attributes:	definitionURL and encoding

Name:	leq
Usage:	<reln> <leq/> arg1 arg2 </reln>
Description:	"Less or equal than" relation.
Attributes:	definitionURL and encoding

Name:	equivalent
Usage:	<reln> <equivalent/> arg1 arg2 </reln>
Description:	Logical equivalence operator
Attributes:	definitionURL and encoding

Name:	approx
Usage:	<reln> <approx/> arg1 arg2 </reln>
Description:	Approximately equal to.
Attributes:	definitionURL and encoding

Name:	factorof
Usage:	<reln> <factorof/> arg1 arg2 </reln>
Description:	Arg1 divides arg2
Attributes:	definitionURL and encoding
Notes:	Not implemented in WebEQ 3.0

5. Calculus

Name:	int
Usage:	<apply> <int/> [variable lowlimit uplimit] integrand </apply>
Description:	Integral. The limits may be given using lowlimit and uplimit. Also, the variable of integration may be given as a bvar element. The integrand is specified as the final argument. The domain of integration may also be given as an interval or a condition element.
Attributes:	definitionURL and encoding

Name:	diff
Usage:	<apply> <diff/> variable function </apply>
Description:	Differentiation operator. The variable one is differentiating with respect to is given as a bvar element.
Attributes:	definitionURL and encoding

Name:	partialdiff
Usage:	<apply> <partialdiff/> (variable order)s function </apply>
Description:	Partial differentiation operator. The variables of differentiation are given as bvar elements. In WebEQ, each of these may contain a degree, giving the order of differentiation (default is 1).
Attributes:	definitionURL and encoding

Name:	lowlimit
Usage:	<lowlimit> ... </lowlimit>
Description:	A container for the "lower limit" of an operator admitting quantifiers (integrals, sums, etc).

Name:	uplimit
Usage:	<uplimit> ... </uplimit>
Description:	A container for the "upper limit" of an operator admitting quantifiers (integrals, sums, etc).

Name:	bvar
Usage:	<bvar> ... </bvar>
Description:	A container for the "bound variable" of an operation (such as the variable of integration in an integral, or differentiation in a derivative).

Name:	degree
Usage:	<degree> ... </degree>
Description:	A container for the "degree" or "order" of an operation (for example, the order of a moment).

Name:	divergence
Usage:	<apply><divergence/> ... </apply>
Description:	Divergence of a vector field
Attributes:	definitionURL and encoding

Name:	gradient
Usage:	<apply><gradient/> ... </apply>
Description:	Gradient of a function
Attributes:	definitionURL and encoding

Name:	curl
Usage:	<apply><curl/> ... </apply>
Description:	Curl of a vector field.
Attributes:	definitionURL and encoding

Name:	laplacian
Usage:	<apply><laplacian/> ... </apply>
Description:	Laplacian differential operator.
Attributes:	definitionURL and encoding

6. Theory of Sets

Name:	set
Usage:	<set> list </set>
or	<set> bvar(s) condition </set>
Description:	Constructs a set of elements. These can be defined by an explicit list, or by a bvar and condition construction.

Name:	list
Usage:	<list> list of elements </list>
or	<list> bvar(s) condition </list>
Description:	Constructs a list of elements. These can be defined by an explicit list, or by a bvar and condition construction. The order of the elements of a list is significant, unlike that of the elements of a set.
Attributes:

Name	Values	Default
order	numeric | lexicographic	numeric

Notes:

The order controls how to order the elements of the list.

Name:	union
Usage:	<apply> <union/> sets </apply>
Description:	Union of two or more sets.
Attributes:	definitionURL and encoding

Name:	intersect
Usage:	<apply> <intersect/> sets </apply>
Description:	Intersection of two or more sets.
Attributes:	definitionURL and encoding

Name:	in
Usage:	<e> <in/> element set </e>
Description:	"Is a member of" operator.
Attributes:	definitionURL and encoding

Name:	notin
Usage:	<apply> <notin/> element set </apply>
Description:	"Is not a memeber of" operator.
Attributes:	definitionURL and encoding

Name:	subset
Usage:	<apply> <subset/> subset set </apply>
Description:	"Is a subset of" operator.
Attributes:	definitionURL and encoding

Name:	prsubset
Usage:	<apply> <prsubset/> subset set </apply>
Description:	"Is a proper subset of" operator.
Attributes:	definitionURL and encoding

Name:	notsubset
Usage:	<apply> <notsubset/> subset set </apply>
Description:	"Is not contained in" operator.
Attributes:	definitionURL and encoding

Name:	notprsubset
Usage:	<apply> <notprsubset/> subset set </apply>
Description:	"Is not properly contained in" operator.
Attributes:	definitionURL and encoding

Name:	setdiff
Usage:	<apply> <setdiff/> set1 set2 </apply>
Description:	The set-theoretic difference between two sets.
Attributes:	definitionURL and encoding

Name:	card
Usage:	<apply> <card/> set </apply>
Description:	Cardinality of a set
Attributes:	definitionURL and encoding

Name:	cartesianproduct
Usage:	<apply> <cartesianproduct/> set1 set2 </apply>
Description:	Cartesian product of two sets
Attributes:	definitionURL and encoding
Notes:	Not implemented in WebEQ 3.0

7. Sequences and Series

Name:	sum
Usage:	<apply> <sum/> [variable lowlimit uplimit] argument </apply>
Description:	The summation operator. The indices for the summation are given as bvar elements. The upper and lower limits may be specified as lowlimit and uplimit, or as a condition on the bound variables.
Attributes:	definitionURL and encoding

Name:	product
Usage:	<apply> <product/> [variable lowlimit uplimit] argument </apply>
Description:	The product operator. The indices for the product are given as bvar elements. The upper and lower limits may be specified as lowlimit and uplimit, or as a condition on the bound variables.
Attributes:	definitionURL and encoding

Name:	limit
Usage:	<apply> <limit/> variable lowlimit function </apply>
Description:	Operator for the limit of a sequence or function. The limit point is specified as a bvar and a lowlimit, or as a condition.
Attributes:	definitionURL and encoding

Name:	tendsto
Usage:	<apply> <tendsto/> quantity value </apply>
Description:	Expresses that a quantity is tending to a specific value.
Attributes:

Name	Values	Default
type	string	above
definitionURL	URL

Notes:

The type attribute determines the direction from which the limiting value is being approached. The value of type may be either above or below.

8. Elementary Classical Functions:

Name:	exp
Usage:	<apply> <exp/> argument </apply>
Description:	The exponential function.
Attributes:	definitionURL and encoding

Name:	ln
Usage:	<apply> <ln/> ... </apply>
Description:	Natural logarithm (base e=2.718281828..)
Attributes:	definitionURL and encoding

Name:	log
Usage:	<apply> <log/> <logbase>base</logbase> argument </apply>
Description:	Logarithm. The base may be specified as a logbase element, as the first argument (default value is 10).
Attributes:	definitionURL and encoding

Name:	logbase
Usage:	<logbase> ... </logbase>
Description:	A container for the base of a logarithm.

Name:	sin
Usage:	<apply> <sin/> ... </apply>
Description:	Standard sine function.
Attributes:	definitionURL and encoding

Name:	cos
Usage:	<apply> <cos/> ... </apply>
Description:	Standard cosine function.
Attributes:	definitionURL and encoding

Name:	tan
Usage:	<apply> <tan/> ... </apply>
Description:	Standard tangent function.
Attributes:	definitionURL and encoding

Name:	sec
Usage:	<apply> <sec/> ... </apply>
Description:	Standard secant function.
Attributes:	definitionURL and encoding

Name:	csc
Usage:	<apply> <csc/> ... </apply>
Description:	Standard cosecant function. This replaces the <cosec/> tag that was used in WebEQ 2.2.
Attributes:	definitionURL and encoding

Name:	cot
Usage:	<apply> <cot/> ... </apply>
Description:	Standard cotangent function. This replaces the <cotan/> tag that was used in WebEQ 2.2.
Attributes:	definitionURL and encoding

Name:	sinh
Usage:	<apply> <sinh/> ... </apply>
Description:	Standard hyperbolic sine function.
Attributes:	definitionURL and encoding

Name:	cosh
Usage:	<apply> <cosh/> ... </apply>
Description:	Standard hyperbolic cosine function.
Attributes:	definitionURL and encoding

Name:	tanh
Usage:	<apply> <tanh/> ... </apply>
Description:	Standard hyperbolic tangent function.
Attributes:	definitionURL and encoding

Name:	sech
Usage:	<apply> <sech/> ... </apply>
Description:	Standard hyperbolic secant function.
Attributes:	definitionURL and encoding

Name:	csch
Usage:	<apply> <csch/> ... </apply>
Description:	Standard hyperbolic cosecant function. This replaces the <cosech/> tag that was used in WebEQ 2.2.
Attributes:	definitionURL and encoding

Name:	coth
Usage:	<apply> <coth/> ... </apply>
Description:	Standard hyperbolic cotangent function. This replaces the <cotanh/> tag that was used in WebEQ 2.2.
Attributes:	definitionURL and encoding

Name:	arcsin
Usage:	<apply> <arcsin/> ... </apply>
Description:	Standard inverse sine function.
Attributes:	definitionURL and encoding

Name:	arccos
Usage:	<apply> <arccos/> ... </apply>
Description:	Standard inverse cosine function.
Attributes:	definitionURL and encoding

Name:	arctan
Usage:	<apply> <arctan/> ... </apply>
Description:	Standard inverse tangent function.
Attributes:	definitionURL and encoding

Name:	arccot
Usage:	<apply> <arccot/> ... </apply>
Description:	Standard inverse cotangent function.
Attributes:	definitionURL and encoding

Name:	arccsc
Usage:	<apply> <arccsc/> ... </apply>
Description:	Standard inverse cosecant function.
Attributes:	definitionURL and encoding

Name:	arcsec
Usage:	<apply> <arcsec/> ... </apply>
Description:	Standard inverse secant function.
Attributes:	definitionURL and encoding

Name:	arccosh
Usage:	<apply> <arccosh/> ... </apply>
Description:	Standard inverse hyperbolic cosine function.
Attributes:	definitionURL and encoding

Name:	arccoth
Usage:	<apply> <arccoth/> ... </apply>
Description:	Standard inverse hyperbolic cotangent function.
Attributes:	definitionURL and encoding

Name:	arccsch
Usage:	<apply> <arccsch/> ... </apply>
Description:	Standard inverse hyperbolic cosecant function.
Attributes:	definitionURL and encoding

Name:	archsech
Usage:	<apply> <arcsech/> ... </apply>
Description:	Standard inverse hyperbolic secant function.
Attributes:	definitionURL and encoding

Name:	arcsinh
Usage:	<apply> <arcsinh/> ... </apply>
Description:	Standard inverse hyperbolic sine function.
Attributes:	definitionURL and encoding

Name:	arctanh
Usage:	<apply> <arctanh/> ... </apply>
Description:	Standard inverse hyperbolic tangent function.
Attributes:	definitionURL and encoding

9. Statistics

Name:	mean
Usage:	<apply> <mean/> ... </apply>
Description:	Mean, or average, operator.
Attributes:	definitionURL and encoding

Name:	sdev
Usage:	<apply> <sdev/> ... </apply>
Description:	Standard deviation operator.
Attributes:	definitionURL and encoding

Name:	variance
Usage:	<apply> <variance/> ... </apply>
Description:	Statistical variance operator.
Attributes:	definitionURL and encoding

Name:	median
Usage:	<apply> <median/> ... </apply>
Description:	Median operator.
Attributes:	definitionURL and encoding

Name:	mode
Usage:	<apply> <mode/> ... </apply>
Description:	Statistical mode operator.
Attributes:	definitionURL and encoding

Name:	moment
Usage:	<apply> <moment/> [<degree> ... </degree>] [<momentabout> ... <momentabout>] distribution </apply>
Description:	Moment operator. Use degree n for the "n-th moment" and momentabout to specify a point other than 0 around which to compute the moment.
Attributes:	definitionURL and encoding

Name:	momentabout
Usage:	<apply> <moment/> [<degree> ... </degree>] [<momentabout> ... <momentabout>] distribution </apply>
Description:	Used to define a point about which to compute a moment.
Notes:	Not implemented in WebEQ 3.0

10. Linear Algebra

Name:	vector
Usage:	<vector> components </vector>
Description:	Container for a vector.

Name:	matrix
Usage:	<matrix> matrixrows </matrix>
Description:	Container for a matrix. It contains matrixrows, which contain the matrix elements.

Name:	matrixrow
Usage:	<matrixrow> elements </matrixrow>
Description:	Container for the rows of a matrix.

Name:	determinant
Usage:	<apply> <determinant/> matrix </apply>
Description:	The determinant of a matrix.
Attributes:	definitionURL and encoding

Name:	transpose
Usage:	<apply> <transpose/> matrix </apply>
Description:	Transpose of a matrix.
Attributes:	definitionURL and encoding

Name:	selector
Usage:	<apply> <selector/> matrix row (element) </apply>
Note:	In WebEQ 3, selector just writes the indicies of the selection as subscripts. It doesn't actually display the selected subexpression.

Name:	vectorproduct
Usage:	<apply> <vectorproduct> vector1 vector2 </apply>
Description:	Classical vector product.
Attributes:	definitionURL and encoding

Name:	scalarproduct
Usage:	<apply> <scalarproduct> vector1 vector2 </apply>
Description:	Classical vector scalar product. Also called dot product.
Attributes:	definitionURL and encoding

Name:	outerproduct
Usage:	<apply> <outerproduct> vector1 vector2 </apply>
Description:	Vector outer product. Also called tensor product.
Attributes:	definitionURL and encoding

11. Semantic Mapping

Name:

annotation

Ignored by WebEQ

Usage:	<annotation> ... </annotation>
Description:	Container for a semantic annotation in a non-XML format. Always used with semantics.
Attributes:

Name	Values	Default
enconding	string

Notes:

The encoding defines the kind of sintax being used for the annotation (TeX, Maple, etc).

Name:

semantics

Usage:	<semantics> ... </semantics>
Description:	A container that associates a MathML construct with alternative representations. Representations that are XML based are enclosed in an xmlannotation element; others are enclosed in a annotation element.
Attributes:	definitionURL and encoding
Notes:	WebEQ renders the first child of semantics, but ignores any subsequent children.

Name:

annotation-xml

Ignored by WebEQ

Usage:	<annotation-xml> ... </annotation-xml>
Description:	Contains XML-based semantic annotation. Always used with semantics.
Attributes:

Name	Values	Default
enconding	string

Notes:

The encoding defines the kind of syntax being used for the annotation (TeX, Maple, etc).

12. Constant and Symbol Elements:

Name:	integers
Usage:	<apply> <in/> expr <integers/> </apply>
Description:	The set of integers

Name:	reals
Usage:	<apply> <in/> expr <reals/> </apply>
Description:	The set of real numbers

Name:	rationals
Usage:	<apply> <in/> expr <rationals/> </apply>
Description:	The set of rational numbers

Name:	naturalnumbers
Usage:	<apply> <in/> expr <naturalnumbers/> </apply>
Description:	The set of natural numbers

Name:	complexes
Usage:	<apply> <in/> expr <complexes/> </apply>
Description:	The set of complex numbers

Name:	primes
Usage:	<apply> <in/> expr <primes/> </apply>
Description:	The set of prime numbers.

Name:	exponentiale
Usage:	<apply> <eq/> expr <exponentiale/> </apply>
Description:	base for natural logarithms, approx. 2.7183.

Name:	imaginaryi
Usage:	<apply> <eq/> expr <imaginaryi/> </apply>
Description:	The square root of -1.

Name:	notanumber
Usage:	<notanumber/>
Description:	placeholder for an ill-defined floating point operation.

Name:	true
Usage:	<true/>
Description:	Boolean constant.

Name:	false
Usage:	<false/>
Description:	Boolean constant.

Name:	emptyset
Usage:	<emptyset/>
Description:	The empty set

Name:	pi
Usage:	<pi/>
Description:	Ratio of circumference to diameter for a circle, approx. 3.1416.

Name:	eulergamma
Usage:	<eulergamma/>
Description:	The Euler gamma constant, approximately 0.5772156649.

Name:	infinity
Usage:	<infinity/>
Description:	Cardinality of the integers.