14.2 Listing of Content Elements
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| < Day Day Up > |
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14.2 Listing of Content Elements
abs
Syntax
<apply><abs/>arg1</apply>
Description
The abs element represents the absolute value of the number specified as an argument.
Attributes
This element accepts the attributes definitionURL and encoding.
and
Syntax
<apply><and/>...</apply>
Description
The and element represents the logical AND operator. It evaluates to the value True when all of its arguments are True, and False otherwise. It can take any number of arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
annotation
Syntax
<annotation>...</annotation>
Description
The annotation element is used as a container for alternative representations of a MathML expression, specified in a format different from XML. Each annotation element must be enclosed in a semantics element.
Attributes
This element accepts the attributes definitionURL and encoding.
annotation-xml
Syntax
<annotation-xml>...</annotation-xml>
Description
The annotation-xml element is used as a container for additional information about the meaning of an expression, specified using an XML-based format different from MathML. Each annotation-xml element must be enclosed in a semantics element.
Attributes
This element accepts the attributes definitionURL and encoding.
apply
Syntax
<apply>operator (argument)*</apply>
Description
The apply element represents the result of applying an operator or function to one or more arguments. The first child element of the apply element is the operator or function to be applied, and the subsequent child elements are the arguments of that operator or function. The type of operator or function used as the first child element determines the number of child elements.
Attributes
This element accepts the attributes definitionURL and encoding.
approx
Syntax
<apply><approx/> arg1 arg2 ...</apply>
Description
The approx element is used to indicate that two or more quantities are approximately equal.
Attributes
This element accepts the attributes definitionURL and encoding.
arccos
Syntax
<apply><arccos/> arg</apply>
Description
The arccos element represents the inverse cosine function.
Attributes
This element accepts the attributes definitionURL and encoding.
arccosec
Syntax
<apply><arccosec/> arg</apply>
Description
The arccosec element represents the inverse cosecant function.
Attributes
This element accepts the attributes definitionURL and encoding.
arccosh
Syntax
<apply><arccosh/> arg</apply>
Description
The arccosh element represents the inverse hyperbolic cosine function.
Attributes
This element accepts the attributes definitionURL and encoding.
arccosech
Syntax
<apply><arccosech/> arg</apply>
Description
The arccosech element represents the inverse hyperbolic cosecant function.
Attributes
This element accepts the attributes definitionURL and encoding.
arccot
Syntax
<apply><arccot/> arg</apply>
Description
The arccot element represents the inverse cotangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
arccoth
Syntax
<apply><arccoth/> arg</apply>
Description
The arccoth element represents the inverse hyperbolic cotangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
arcsec
Syntax
<apply><arcsec/> arg</apply>
Description
The arcsec element represents the inverse secant function.
Attributes
This element accepts the attributes definitionURL and encoding.
arcsech
Syntax
<apply><arcsech/> arg</apply>
Description
The arcsech element represents the inverse hyperbolic secant function.
Attributes
This element accepts the attributes definitionURL and encoding.
arcsin
Syntax
<apply><arcsin/> arg</apply>
Description
The arcsin element represents the inverse sine function.
Attributes
This element accepts the attributes definitionURL and encoding.
arcsinh
Syntax
<apply><arcsinh/> arg</apply>
Description
The arcsinh element represents the inverse hyperbolic sine function.
Attributes
This element accepts the attributes definitionURL and encoding.
arctan
Syntax
<apply><arctan/> arg</apply>
Description
The arctanh element represents the inverse tangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
arctanh
Syntax
<apply><arctanh/> arg</apply>
Description
The arctanh element represents the inverse hyperbolic tangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
arg
Syntax
<apply><arg/>arg1</apply>
Description
The arg element represents the argument of a complex number specified as an argument.
Attributes
This element accepts the attributes definitionURL and encoding.
bvar
Syntax
<bvar>variable</bvar>
Description
The bvar element is a qualifier element that is used in conjunction with the int, diff, and partialdiff elements to represent a bound variable.
Attributes
This element accepts the attributes definitionURL and encoding.
card
<apply><card/>set</apply>
Description
The card element represents the cardinality of a set; that is, the number of elements contained in the set.
Attributes
This element accepts the attributes definitionURL and encoding.
cartesianproduct
<apply><cartesianproduct/>set1 set2</apply>
Description
The cartesianproduct element represents the Cartesian product of two or more sets.
Attributes
This element accepts the attributes definitionURL and encoding.
ceiling
Syntax
<apply><ceiling/>number</apply>
Description
The ceiling element represents the smallest integer greater than or equal to the number specified as an argument.
Attributes
This element accepts the attributes definitionURL and encoding.
ci
Syntax
<ci>...</ci>
Description
The ci element is used to represent objects such as functions, variables, and symbolic constants. The type of the object is specified using an attribute. To allow precise control over rendering, this element can contain any arbitrary presentation markup.
Attributes
This element accepts the attributes definitionURL and encoding. In addition, it accepts the one attribute shown in Table 14.1.
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| Name | Values | Default |
|---|---|---|
| type | string | real |
|
The type attribute specifies the type of object encoded. It can be set to any string, including the names of MathML container elements (such as set, list, vector, matrix, and fn).
cn
Syntax
<cn>...</cn>
Description
The cn element is used to represent numerical constants. The type of the number and its base are specified via attributes. Rational, complex, and floating-point numbers require the different parts of the number to be separated by a sep element.
Attributes
This element accepts the attributes definitionURL and encoding. In addition, it accepts the two attributes shown in Table 14.2.
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| Name | Values | Default |
|---|---|---|
| type | real | integer | rational | floating-point | constant | real |
| complex-polar | complex-cartesian | e-notation | ||
| base | Integer between 2 and 36 | 10 |
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These attributes have the following meaning:
-
type: specifies the type of number encoded
-
base: specifies the base of the number being encoded
codomain
Syntax
<apply><codomain/>function</apply>
Description
The codomain element represents the codomain of a function; that is, a set that contains all values taken by the function. The codomain is also referred to as the range.
Attributes
This element accepts the attributes definitionURL and encoding.
complexes
Syntax
<complexes/>
Description
The complexes element represents the set of all complex numbers. It has the default rendering C.
Attributes
This element accepts the attributes definitionURL and encoding.
compose
Syntax
<apply><compose/>(function)+</apply>
Description
The compose element is used for composing two functions. The result is a new function whose range is the same as the range of the first function and whose domain is the same as the domain of the second function.
Attributes
This element accepts the attributes definitionURL and encoding.
condition
Syntax
<condition><apply>...</apply></condition>
or
<condition><reln>...</reln></condition>
Description
The condition element is used to encode conditional statements; that is, statements involving the phrase "such that."
Attributes
This element accepts the attributes definitionURL and encoding.
conjugate
Syntax
<apply><conjugate/>arg1</apply>
Description
The conjugate element represents the complex conjugate of a complex number specified as an argument.
Attributes
This element accepts the attributes definitionURL and encoding.
cos
Syntax
<apply><cos/> arg</apply>
Description
The cos element represents the trigonometric cosine function.
Attributes
This element accepts the attributes definitionURL and encoding.
cosec
Syntax
<apply><cosec/> arg</apply>
Description
The cosec element represents the trigonometric cosecant function.
Attributes
This element accepts the attributes definitionURL and encoding.
cosech
Syntax
<apply><cosech/> arg</apply>
Description
The cosech element represents the hyperbolic cosecant function.
Attributes
This element accepts the attributes definitionURL and encoding.
cosh
Syntax
<apply><cosh/> arg</apply>
Description
The cosh element represents the hyperbolic cosine function.
Attributes
This element accepts the attributes definitionURL and encoding.
cot
Syntax
<apply><cot/> arg</apply>
Description
The cot element represents the trigonometric cotangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
coth
Syntax
<apply><coth/> arg</apply>
Description
The coth element represents the hyperbolic cotangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
csymbol
Syntax
<csymbol>... </csymbol>
Description
The csymbol element is used to define new objects such as constants and functions, which cannot be represented using the existing content elements. To allow precise control over rendering, it can contain any arbitrary presentation markup. The meaning of the object is defined using the definitionURL and encoding attributes.
Attributes
This element accepts the attributes definitionURL and encoding.
curl
Syntax
<apply><curl/> function</apply>
Description
The curl element represents the curl operator of vector calculus.
Attributes
This element accepts the attributes definitionURL and encoding.
declare
Syntax
<declare>identifier definition</declare>
Description
The declare element is used for declaring that a given identifier is an object of a certain type and for assigning that object a specific value.
Attributes
This element accepts the attributes definitionURL and encoding. In addition, it accepts the three attributes shown in Table 14.3.
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| Name | Values | Default |
|---|---|---|
| type | Any MathML content element | real |
| nargs | integer | none |
| occurrence | infix | prefix | infix |
|
These attributes have the following meaning:
-
type: specifies the type of object being declared. Typical values of this attribute are set, list, vector, matrix, or function.
-
nargs: specifies the number of arguments when you are declaring an operator or function.
-
occurrence: specifies the position in which an operator being declared occurs.
degree
Syntax
<degree>variable</degree>
Description
The degree element is a qualifier element that is used in conjunction with the diff and partialdiff elements to specify the order of differentiation, with the root element to specify the degree of a root, and with the moment element to specify the type of a statistical moment.
Attributes
This element accepts the attributes definitionURL and encoding.
determinant
Syntax
<apply><determinant/>matrix</apply>
Description
The determinant element represents the operator for the determinant of a matrix.
Attributes
This element accepts the attributes definitionURL and encoding.
diff
Syntax
<apply><diff/><bvar> ... </bvar><degree>...</degree> <apply>function<ci>var</ci></apply> </apply>
Description
The diff element represents the operation of taking a derivative. The variable of differentiation is specified using a bvar element. The order of differentiation is specified using a degree element.
Attributes
This element accepts the attributes definitionURL and encoding.
divergence
Syntax
<apply><divergence/> function</apply>
Description
The divergence element represents the divergence operator of vector calculus.
Attributes
This element accepts the attributes definitionURL and encoding.
divide
Syntax
<apply><divide/>dividend divisor</apply>
Description
The divide element represents the operation of division. It must have two arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
domain
Syntax
<apply><domain/>function</apply>
Description
The domain element represents the domain of a function; that is, the set of values over which that function can be applied.
Attributes
This element accepts the attributes definitionURL and encoding.
emptyset
Syntax
<emptyset/>
Description
The emptyset element represents a set without any elements. It has the default rendering Ø.
Attributes
This element accepts the attributes definitionURL and encoding.
eq
Syntax
<apply><eq/> arg1 arg2 ...</apply>
Description
The eq element is used to indicate that two or more expressions are equal. It must have at least two arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
equivalent
Syntax
<apply><equivalent/>arg1 arg2</apply>
Description
The equivalent element represents the logical equivalence function. Two Boolean expressions are equivalent if their values are equal for all values of the Boolean variables they contain. This element can take two or more arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
eulergamma
Syntax
<eulergamma/>
Description
The eulergamma element represents the Euler-Gamma constant γ (approx. 0.5772156649), which occurs as the limiting value of certain series.
Attributes
This element accepts the attributes definitionURL and encoding.
exists
Syntax
<apply> <exists/>(optional <bvar> or <condition>) <apply>...</apply> </apply>
or
<apply> <exists/>(optional <bvar> or <condition>) <reln> ... </reln> </apply>
Description
The exists element is used to indicate the existence of an element that satisfies a certain condition. It represents the mathematical concept normally denoted by the symbol ∃.
Attributes
This element accepts the attributes definitionURL and encoding.
exp
Syntax
<apply><exp/>exponent</apply>
Description
The exp element represents the exponential function, ex, where e is the base of the natural logarithm (2.71828….).
Attributes
This element accepts the attributes definitionURL and encoding.
exponentiale
Syntax
<exponentiale/>
Description
The exponentiale element represents the numerical constant e (approx. 2.71828); that is, the base of the natural logarithm.
Attributes
This element accepts the attributes definitionURL and encoding.
factorial
Syntax
<apply><factorial/>argument</apply>
Description
The factorial element represents the unary operator used to construct factorials.
Factorials are defined by n!= n *(n * 1) * (n * 2)*…*1.
Attributes
This element accepts the attributes definitionURL and encoding.
factorof
Syntax
<apply><factorof/> m n</apply>
Description
The factorof element is used to indicate that one number is a factor of the other. An integer m is a factor of another integer n if m mod n = 0.
Attributes
This element accepts the attributes definitionURL and encoding.
false
Syntax
<false/>
Description
The false element represents the Boolean constant "false."
Attributes
This element accepts the attributes definitionURL and encoding.
floor
Syntax
<apply><floor/>number</apply>
Description
The floor element represents the greatest integer less than or equal to the number specified as an argument.
Attributes
This element accepts the attributes definitionURL and encoding.
fn
Syntax
<fn>...</fn>
Description
The fn element is used to build a new function definition. This element is deprecated in MathML 2.0 since its function is now taken over by the apply and declare elements.
Attributes
This element accepts the attributes definitionURL and encoding.
forall
Syntax
<apply> <forall/> (optional <bvar> or <condition>) <apply> ... </apply> </apply>
or
<apply> <forall/> (optional <bvar> or <condition>) <reln> ... </reln> </apply>
Description
The forall element is used to indicate that some condition is true for all members of a certain set. It represents the mathematical concept normally denoted by the symbol ∀.
Attributes
This element accepts the attributes definitionURL and encoding.
gcd
Syntax
<apply><gcd/>...</apply>
Description
The gcd element represents the greatest common divisor of a set of integers, specified as arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
geq
Syntax
<apply><geq/>arg1 arg2</apply>
Description
The geq element is used to indicate that one element is greater than or equal to another. It can take two or more arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
grad
Syntax
<apply><grad/>function</apply>
Description
The grad element represents the gradient operator of vector calculus.
Attributes
This element accepts the attributes definitionURL and encoding.
gt
Syntax
<apply><gt/>arg1 arg2</apply>
Description
The gt element is used to indicate that one element is greater than another. It can take two or more arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
ident
Syntax
<ident/>
Description
The ident element represents the identity function. The domain and range of the identity function, as well as the type of operation it represents, all depend on the context in which the function is used. For example, if the ident element is used in the context of matrix multiplication, it will be interpreted as the identity matrix.
Attributes
This element accepts the attributes definitionURL and encoding.
image
Syntax
<apply><image/>function</apply>
Description
The image element represents the image of a function; that is, the set of values that results from applying the function to all points in its domain.
Attributes
This element accepts the attributes definitionURL and encoding.
imaginary
Syntax
<apply><imaginary/>arg1</apply>
Description
The imaginary element represents the imaginary part of a complex number specified as an argument.
Attributes
This element accepts the attributes definitionURL and encoding.
imaginaryi
Syntax
<imaginaryi/>
Description
The imaginaryi element represents the number i; that is, the complex square root of −1.
Attributes
This element accepts the attributes definitionURL and encoding.
implies
Syntax
<apply><implies/>arg1 arg2</apply>
Description
The implies element is used to indicate that one expression implies another.
Attributes
This element accepts the attributes definitionURL and encoding.
in
Syntax
<apply><in/>element set</apply>
Description
The in element represents the relation that an element is a member of a set.
Attributes
This element accepts the attributes definitionURL and encoding.
infinity
Syntax
<infinity/>
Description
The infinity element represents the concept of infinity. It has the default rendering ∞.
Attributes
This element accepts the attributes definitionURL and encoding.
int
Syntax
<apply><int/>variable expression</apply>
or
<apply><int/>variable limits expression</apply>
Description
The int element represents the operation of integration. Each variable of integration is specified using the qualifier element bvar. For definite integrals, you can indicate the region of integration in three different ways: using a pair of lowlimit and uplimit elements, using an interval element, or using a condition element.
Attributes
This element accepts the attributes definitionURL and encoding.
integers
Syntax
<apply><in/> expression<integers/></apply>
Description
The integers element represents the set of all integers, typically denoted by Z.
Attributes
This element accepts the attributes definitionURL and encoding.
intersect
Syntax
<apply><intersect/>set1 set2 ...</apply>
Description
The intersect element represents the intersection of two or more sets.
Attributes
This element accepts the attributes definitionURL and encoding.
interval
Syntax
<interval>left-boundary right-boundary</interval>
Description
The interval element is used to define intervals on the real line. It has two child elements, which specify the left and right boundaries of the interval.
Attributes
This element accepts the attributes definitionURL and encoding. In addition, it accepts the attribute shown in Table 14.4.
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| Name | Values | Default |
|---|---|---|
| closure | open | closed | open-closed | closed-open | closed |
|
The closure attribute specifies the closure of an interval on the real line.
inverse
Syntax
<apply><inverse/>function</apply>
Description
The inverse element represents the inverse of a function.
Attributes
This element accepts the attributes definitionURL and encoding.
lambda
Syntax
<lambda>(variable)+ <apply> definition</apply></lambda>
Description
The lambda element represents the definition of a lambda function. A lambda function with n arguments is represented as a lambda element with n + 1 child elements. The first n elements are the arguments, each enclosed in a bvar element, and the last child element is the definition of the function, typically specified using an apply element.
Attributes
This element accepts the attributes definitionURL and encoding.
laplacian
Syntax
<apply><laplacian/> function</apply>
Description
The laplacian element represents the Laplacian operator of vector calculus.
Attributes
This element accepts the attributes definitionURL and encoding.
lcm
Syntax
<apply><lcm/>(number)*</apply>
Description
The lcm element represents the lowest common multiple of a set of integers, specified as arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
leq
Syntax
<apply><leq/> arg1 arg2</apply>
Description
The leq element is used to indicate that one element is less than or equal to another. It can take two or more arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
limit
Syntax
<apply><limit/>variable limit function</apply>
Description
The limit element represents the operator for the limit of a sequence or function. You can specify the limit point either by using a pair of bvar and lowlimit elements or by using a condition element.
Attributes
This element accepts the attributes definitionURL and encoding.
list
Syntax
<list>elements</list>
or
<list> (<bvar> ... </bvar>)* <condition> ... </condition> </list>
Description
The list element is used to represent a set of elements. The elements can either be specified explicitly or by using bvar and condition elements. This element is similar to the set element, the only difference being that in a list, the order of elements is relevant.
Attributes
This element accepts the attributes definitionURL and encoding. In addition, it accepts the attribute shown in Table 14.5.
|
| Name | Values | Default |
|---|---|---|
| order | lexicographic | numeric | lexicographic |
|
The order attribute specifies the criterion used for ordering the elements of the list. With the setting lexicographic, the elements are ordered alphabetically; with the setting numeric, the elements are ordered numerically.
ln
Syntax
<apply><ln/> arg</apply>
Description
The ln element represents the natural logarithmic function.
Attributes
This element accepts the attributes definitionURL and encoding.
log
Syntax
<apply><log/> arg</apply>
Description
The log element represents the logarithm function.
Attributes
This element accepts the attributes definitionURL and encoding.
lowlimit
Syntax
<lowlimit>limit</lowlimit>
Description
The lowlimit element is a qualifier element that is used in conjunction with the int element to represent the lower limit of a definite integral.
Attributes
This element accepts the attributes definitionURL and encoding.
lt
Syntax
<apply><lt/> arg1 arg2</apply>
Description
The lt element is used to indicate that one element is less than another. It can take two or more arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
matrix
Syntax
<matrix>(<matrixrow>...<matrixrow/>)*</matrix>
Description
The matrix element is used to represent a table or matrix. It contains a sequence of matrixrow elements, each corresponding to a single row of the table or matrix.
Attributes
This element accepts the attributes definitionURL and encoding.
matrixrow
Syntax
<matrixrow>(<mtd>... <mtd/>)*</matrixrow>
Description
The matrixrow element is used to represent a row of a table or matrix. It always occurs as a child element of a matrix element and contains a sequence of mtd child elements, each corresponding to a single cell of the table or matrix.
Attributes
This element accepts the attributes definitionURL and encoding.
max
Syntax
<apply><max/>...</apply>
Description
The max element represents the maximum of a set of numbers. You can specify the numbers as arguments or by using a condition.
Attributes
This element accepts the attributes definitionURL and encoding.
mean
Syntax
<apply><mean/>distribution</apply>
Description
The mean element represents the mean of a distribution or set of elements.
Attributes
This element accepts the attributes definitionURL and encoding.
median
Syntax
<apply><median/>distribution</apply>
Description
The median element represents the median of a distribution or set of elements.
Attributes
This element accepts the attributes definitionURL and encoding.
min
Syntax
<apply><min/>...</apply>
Description
The min element represents the minimum of a set of numbers. You can specify the numbers as arguments or by using a condition.
Attributes
This element accepts the attributes definitionURL and encoding.
minus
Syntax
<apply><minus/>...</apply>
Description
The minus element represents subtraction. It can take one or two arguments. By default, the subtraction is assumed to be over a real field, but the default semantics of the element can be modified using attributes, for example, to represent vector subtraction.
Attributes
This element accepts the attributes definitionURL and encoding.
mode
Syntax
<apply><mode/>distribution</apply>
Description
The mode element represents the mean of a distribution or set of elements.
Attributes
This element accepts the attributes definitionURL and encoding.
moment
Syntax
<apply> <moment/>[<degree> ... </degree>] [<momentabout>...</momentabout>]distribution </apply>
Description
The moment element represents the statistical moment of a distribution or set of elements about a point. The qualifier element degree is used to indicate the type of moment, and the momentabout element is used to specify the point about which the moment is taken. If these elements are omitted, the default values, 1 and 0, are assumed.
Attributes
This element accepts the attributes definitionURL and encoding.
momentabout
Syntax
<apply> <moment/>[<degree> ... </degree>] [<momentabout> ... </momentabout>]distribution </apply>
Description
The momentabout element represents the point about which the moment of a distribution or set of elements is taken. This element is always used as a qualifier element in conjunction with the moment element.
Attributes
This element accepts the attributes definitionURL and encoding.
naturalnumbers
Syntax
<naturalnumbers/>
Description
The naturalnumbers element represents the set of all natural numbers, typically denoted by the symbol N.
Attributes
This element accepts the attributes definitionURL and encoding.
neq
Syntax
<apply> <neq/> arg1 arg2 </apply>
Description
The neq element is used to indicate that two expressions are not equal. It must have two arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
notanumber
Syntax
<notanumber/>
Description
The notanumber element represents the constant, typically denoted by NaN; that is, returned as the result of an ill-defined floating-point operation, such as division by zero.
Attributes
This element accepts the attributes definitionURL and encoding.
notin
Syntax
<apply><notin/>element set</apply>
Description
The notin element represents the relation that an element is not a member of a set.
Attributes
This element accepts the attributes definitionURL and encoding.
notprsubset
Syntax
<apply><notprsubset/>subset set</apply>
Description
The notprsubset element represents the relation that one set is not a proper subset of another set.
Attributes
This element accepts the attributes definitionURL and encoding.
notsubset
Syntax
<apply><notsubset/>subset set</apply>
Description
The notsubset element represents the relation that one set is not a subset of another set.
Attributes
This element accepts the attributes definitionURL and encoding.
or
Syntax
<apply><or/>...</apply>
Description
The or element represents the logical OR operator. It evaluates to the value True if any of its arguments are True. It can take any number of arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
otherwise
Syntax
<otherwise>definition domain</otherwise>
Description
The otherwise element represents a specific part of a piecewise declaration. It always occurs as a child element of a piecewise element.
Attributes
This element accepts the attributes definitionURL and encoding.
outerproduct
Syntax
<apply><outerproduct/>vector1 vector2</apply>
Description
The outerproduct element represents the outer product of two vectors.
Attributes
This element accepts the attributes definitionURL and encoding.
partialdiff
Syntax
<apply> <partialdiff/> (<bvar> ... </bvar>)* (<degree> ... </degree>)* <apply> function (<ci> var </ci>)* </apply> </apply>
Description
The partialdiff element represents the operation of taking a partial derivative. Each variables of differentiation is specified using a bvar element. The order of differentiation with respect to each variable is specified using a degree element.
Attributes
This element accepts the attributes definitionURL and encoding.
pi
Syntax
<pi/>
Description
The pi element represents the numerical constant π (approx. 3.14159), the ratio of the circumference of a circle to its diameter.
Attributes
This element accepts the attributes definitionURL and encoding.
piece
Syntax
<piece> definition domain </piece>
Description
The piece element represents a specific part of a piecewise declaration. It always occurs as a child element of a piecewise element.
Attributes
This element accepts the attributes definitionURL and encoding.
piecewise
Syntax
<piecewise>(<piece>)+<otherwise></apply>
Description
The piecewise element, in association with the piece and otherwise elements, represents piecewise declarations of the form f (x) = 0 if x < 0, f (x) = 1 if x ≥ 0.
Attributes
This element accepts the attributes definitionURL and encoding.
plus
Syntax
<apply><plus/>...</apply>
Description
The plus element represents addition. It can take any number of arguments. By default, the addition is assumed to be over a scalar field, but the default semantics of the element can be modified using attributes, for example, to represent vector addition.
Attributes
This element accepts the attributes definitionURL and encoding. In addition, it accepts the attribute shown in Table 14.6.
|
| Name | Values | Default |
|---|---|---|
| type | MathML type | real |
|
The type attribute specifies the type of the operand(s).
power
Syntax
<apply><power/>base exponent</apply>
Description
The power element represents the operation of raising a number or expression to a power. It must have two arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
primes
Syntax
<primes/>
Description
The primes element represents the set of all prime numbers, typically denoted by P.
Attributes
This element accepts the attributes definitionURL and encoding.
product
Syntax
<apply><product/>index limits expression</apply>
Description
The product element represents the product operator. Each index of the product is specified using a single bvar element. The limits of the product can be indicated in several different ways: by using a pair of lowlimit and uplimit elements or by using a condition element.
Attributes
This element accepts the attributes definitionURL and encoding.
prsubset
Syntax
<apply><prsubset/>subset set</apply>
Description
The prsubset element represents the relation that one set is a proper subset of another set.
Attributes
This element accepts the attributes definitionURL and encoding.
quotient
Syntax
<apply><quotient/>numerator denominator</apply>
Description
The quotient element represents the quotient of integer division. In other words, if m and n are integers, the quotient is the integer q, such that m = n * q + r, where |r| < |m| and m * r > 0.
Attributes
This element accepts the attributes definitionURL and encoding.
rationals
Syntax
<rationals/>
Description
The <rationals/> element represents the set of all rational numbers, typically denoted by Q.
Attributes
This element accepts the attributes definitionURL and encoding.
real
Syntax
<apply><real/>arg1</apply>
Description
The real element represents the real part of a complex number specified as an argument.
Attributes
This element accepts the attributes definitionURL and encoding.
reals
Syntax
<apply><in/> expression<reals/></apply>
Description
The reals element represents the set of all real numbers, typically denoted by R.
Attributes
This element accepts the attributes definitionURL and encoding.
reln
Syntax
<reln>operator (argument)+</reln>
Description
The reln element is used to specify a mathematical relation, such as a = b, a < b, and a ≥ b. It contains as its first child element one of the content elements that represent relations, such as eq, lt, or geq. The reln element is deprecated in MathML 2.0 since its role is now taken over by the apply element.
Attributes
This element accepts the attributes definitionURL and encoding.
rem
Syntax
<apply><rem/>dividend divisor</apply>
Description
The rem element represents the remainder of integer division. In other words, if m and n are integers, the remainder is the integer r, such that m = n * q + r, where |r| < |m| and m * r > 0.
Attributes
This element accepts the attributes definitionURL and encoding.
root
Syntax
<apply> <root/><degree>degree</degree> radical </apply>
Description
The root element is used to take the root of a number or expression. It has two arguments. The first argument is a degree element that specifies the degree of the root. If this is omitted, a default value of 2 is assumed.
Attributes
This element accepts the attributes definitionURL and encoding.
scalarproduct
Syntax
<apply><scalarproduct/>vector1 vector2</apply>
Description
The scalarproduct element represents the scalar product of two vectors.
Attributes
This element accepts the attributes definitionURL and encoding.
sdev
Syntax
<apply><sdev/>distribution</apply>
Description
The sdev element represents the standard deviation of a distribution or set of elements.
Attributes
This element accepts the attributes definitionURL and encoding.
sech
Syntax
<apply><sech/> arg</apply>
Description
The sech element represents the hyperbolic secant function.
Attributes
This element accepts the attributes definitionURL and encoding.
selector
Syntax
<apply><selector/>vector index</apply>
or
<apply><selector/>matrix index</apply>
or
<apply><selector/>matrix index1 index2</apply>
Description
The selector element represents the operator for selecting a specific component of a vector, list, or matrix. The first argument following the selector element identifies the vector or matrix. This can be followed by one or two other arguments, which specify the position of the selected component. For a matrix, if two more arguments are given, they are interpreted as specifying the position of a row and column, respectively. In the case of a vector or list, if a second argument is given, it is ignored.
Attributes
This element accepts the attributes definitionURL and encoding.
semantics
Syntax
<semantics>...</semantics>
Description
The semantics element is used as a container for alternative representations of a given MathML expression. Each semantics element can contain any number of annotation-xml and annotation elements. XML-based representations are enclosed in an annotation-xml element, and non-XML representations are stored in an annotation element. The most common use of the semantics element is for combining presentation and content markup.
Attributes
This element accepts the attributes definitionURL and encoding.
sep
Syntax
<cn>...<sep/>...</cn>
Description
The sep element is used inside a cn element as a separator for the different parts of a rational, complex, or floating-point number.
Attributes
This element accepts the attributes definitionURL and encoding.
set
Syntax
<set>elements</set>
or
<set> (<bvar> ... </bvar>)*<condition>...</condition> <dis2> </set>
Description
The set element is used to represent a set of elements. The elements can either be specified explicitly or by using bvar and condition elements.
Attributes
This element accepts the attributes definitionURL and encoding.
setdiff
Syntax
<apply><setdiff/>set1 set2</apply>
Description
The setdiff element represents the set-theoretic difference between two sets.
Attributes
This element accepts the attributes definitionURL and encoding.
sin
Syntax
<apply><sin/> arg</apply>
Description
The sin element represents the trigonometric sine function.
Attributes
This element accepts the attributes definitionURL and encoding.
sinh
Syntax
<apply><sinh/> arg</apply>
Description
The sinh element represents the hyperbolic sine function.
Attributes
This element accepts the attributes definitionURL and encoding.
subset
Syntax
<apply><subset/>subset set</apply>
Description
The subset element represents the relation that one set is a subset of another set.
Attributes
This element accepts the attributes definitionURL and encoding.
sum
Syntax
<apply><sum/>index limits expression</apply>
Description
The sum element represents the summation operator. Each index of the summation is specified using a single bvar element. The limits of summation can be indicated in several different ways: using a pair of lowlimit and uplimit elements, using an interval element, or using a condition element.
Attributes
This element accepts the attributes definitionURL and encoding.
tan
Syntax
<apply><tan/> arg</apply>
Description
The tan element represents the trigonometric tangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
tanh
Syntax
<apply><tanh/> arg</apply>
Description
The tanh element represents the hyperbolic tangent function.
Attributes
This element accepts the attributes definitionURL and encoding.
tendsto
Syntax
<apply><tendsto/> variable value</apply>
Description
The tendsto element represents the operation of a variable that approaches a certain limiting value.
Attributes
This element accepts the attributes definitionURL and encoding. In addition, it accepts the attribute shown in Table 14.7.
|
| Name | Values | Default |
|---|---|---|
| type | above | below | above |
|
The type attribute specifies the direction from which the limiting value is approached.
times
Syntax
<apply><times/>...</apply>
Description
The times element represents multiplication. It can accept any number of arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
transpose
Syntax
<apply><transpose/>matrix</apply>
Description
The transpose element represents the transpose of a matrix.
Attributes
This element accepts the attributes definitionURL and encoding.
true
Syntax
<true/>
Description
The true element represents the Boolean constant True.
Attributes
This element accepts the attributes definitionURL and encoding.
union
Syntax
<apply><union/>set1 set2 ...</apply>
Description
The union element represents the union of two or more sets.
Attributes
This element accepts the attributes definitionURL and encoding.
uplimit
Syntax
<uplimit limit</uplimit>
Description
The uplimit element is a qualifier element that is used in conjunction with the <int/> element to represent the upper limit of a definite integral.
Attributes
This element accepts the attributes definitionURL and encoding.
var
Syntax
<apply><var/>distribution</apply>
Description
The var element represents the variance of a distribution or set of elements.
Attributes
This element accepts the attributes definitionURL and encoding.
vector
Syntax
<vector>components</vector>
Description
The vector element is a container element used to represent a vector. It contains a sequence of child elements, each corresponding to one component of the vector.
Attributes
This element accepts the attributes definitionURL and encoding.
vectorproduct
Syntax
<apply><vectorproduct/>vector1 vector2</apply>
Description
The vectorproduct element represents the vector product of two vectors.
Attributes
This element accepts the attributes definitionURL and encoding.
xor
Syntax
<apply><xor/>...</apply>
Description
The xor element is used to represent the logical XOR (or exclusive OR) operator. It evaluates to the value True if an odd number of its arguments are True. It can take any number of arguments.
Attributes
This element accepts the attributes definitionURL and encoding.
|
| < Day Day Up > |
|
EAN: 2147483647
Pages: 127
- Article 300: Wiring Methods
- Article 338 Service-Entrance Cable Types SE and USE
- Article 430: Motors, Motor Circuits, and Controllers
- Example No. D2(b) Optional Calculation for One-Family Dwelling, Air Conditioning Larger than Heating [See 220.82(A) and 220.82(C)]
- Example No. D2(c) Optional Calculation for One-Family Dwelling with Heat Pump(Single-Phase, 240/120-Volt Service) (See 220.82)