| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| rotación |
APPLICATION |
veccalc1 |
curl |
This symbol is used to represent the curl function. It takes one
argument which should be a vector of scalar valued functions, intended
to represent a vector valued function and returns a vector of
functions. It should satisfy the defining relation:
curl(F) = i X \partial(F)/\partial(x) + j X \partial(F)/\partial(y) +
j X \partial(F)/\partial(Z) where i,j,k are the unit vectors
corresponding to the x,y,z axes respectively and the multiplication X
is cross multiplication.
|
| rot |
APPLICATION |
| divergencia |
APPLICATION |
veccalc1 |
divergence |
This symbol is used to represent the divergence function. It takes one
argument which should be a vector of scalar valued functions,
intended to represent a vector valued function and returns a
scalar value. It should satisfy the defining relation:
divergence(F) = \partial(F_(x_1))/\partial(x_1) + ...
+ \partial(F_(x_n))/\partial(x_n)
|
| div |
APPLICATION |
| grad |
APPLICATION |
veccalc1 |
grad |
This symbol is used to represent the grad function. It takes one
argument which should be a scalar valued function and returns a
vector of functions. It should satisfy the defining relation:
grad(F) = (\partial(F)/\partial(x_1), ... ,\partial(F)/partial(x_n))
|
| gradiente |
APPLICATION |
| laplaciana |
APPLICATION |
veccalc1 |
Laplacian |
This symbol is used to represent the laplacian function. It takes one
argument which should be a vector of scalar valued functions, intended
to represent a vector valued function and returns a vector of
functions. It should satisfy the defining relation:
laplacian(F) = \partial^2(F)/\partial(x_1)^2 + ... +
\partial^2(F)/\partial(x_n)^2
|
| ∆ |
APPLICATION |
| ∇² |
APPLICATION |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| ! |
OP_FACT |
integer1 |
factorial |
The symbol to represent a unary factorial function on non-negative integers.
|
| factor_de |
APPLICATION |
integer1 |
factorof |
This is the binary OpenMath operator that is used to indicate the
mathematical relationship a "is a factor of" b, where a is the
first argument and b is the second. This relationship is
true if and only if b mod a = 0.
|
| cociente |
APPLICATION |
integer1 |
quotient |
The symbol to represent the integer (binary) division operator. That is,
for integers a and b, quotient(a,b) denotes q such that a=b*q+r, with |r|
less than |b| and a*r positive.
|
| / |
APPLICATION |
| resto |
APPLICATION |
integer1 |
remainder |
The symbol to represent the integer remainder after (binary) division.
For integers a and b, remainder(a,b) denotes r such that a=b*q+r, with |r| less
than |b| and a*r positive.
|
| \ |
APPLICATION |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| entero_base |
APPLICATION |
nums1 |
based_integer |
This symbol represents the constructor function for integers,
specifying the base. It takes two arguments, the first is a positive
integer to denote the base to which the number is represented, the
second argument is a string which contains an optional sign and the
digits of the integer, using 0-9a-z (as a consequence of this no radix
greater than 35 is supported). Base 16 and base 10 are already
covered in the encodings of integers.
|
| e |
SYMBOL |
nums1 |
e |
This symbol represents the base of the natural logarithm, approximately 2.718.
See Abramowitz and Stegun, Handbook of Mathematical Functions, section 4.1.
|
| gama |
SYMBOL |
nums1 |
gamma |
A symbol to convey the notion of the gamma constant
as defined in Abramowitz and Stegun, Handbook of Mathematical
Functions, section 6.1.3. It is the limit of
1 + 1/2 + 1/3 + ... + 1/m - ln m
as m tends to infinity, this is approximately 0.5772 15664.
|
| γ |
SYMBOL |
| i |
SYMBOL |
nums1 |
i |
This symbol represents the square root of -1.
|
| inf |
SYMBOL |
nums1 |
infinity |
A symbol to represent the notion of infinity.
|
| ∞ |
SYMBOL |
| NaN |
SYMBOL |
nums1 |
NaN |
A symbol to convey the notion of not-a-number.
The result of an ill-posed floating computation.
See IEEE standard for floating point representations.
|
| pi |
SYMBOL |
nums1 |
pi |
A symbol to convey the notion of pi, approximately 3.142.
The ratio of the circumference of a circle to its diameter.
|
| π |
SYMBOL |
| racional |
APPLICATION |
nums1 |
rational |
This symbol represents the constructor function for rational numbers.
It takes two arguments, the first is an integer p to denote the
numerator and the second a nonzero integer q to denote the denominator
of the rational p/q.
|
| frac |
APPLICATION |
| / |
OP_PROD |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| dist_media |
APPLICATION |
s_dist1 |
mean |
This symbol represents a unary function denoting the mean of a
distribution. The argument is a univariate function to describe the
distribution. That is, if f is the function describing the
distribution. The mean is the expression integrate(x*f(x)) w.r.t. x over the
range (-infinity,infinity).
|
| dist_moda |
APPLICATION |
s_dist1 |
mode |
|
| dist_momento |
APPLICATION |
s_dist1 |
moment |
This symbol represents a ternary function to denote the i'th moment of a
distribution. The first argument should be the degree of the moment
(that is, for the i'th moment the first argument should be i), the
second argument is the value about which the moment is to be taken and
the third argument is a univariate function to describe the distribution. That
is, if f is the function which describe the distribution. The i'th
moment of f about a is the integral of (x-a)^i*f(x) with respect to x,
over the interval (-infinity,infinity).
|
| dist_desv_típica |
APPLICATION |
s_dist1 |
sdev |
This symbol represents a unary function denoting the standard
deviation of a distribution. The argument is a univariate function
to describe the distribution. The standard deviation of a distribution
is the arithmetical mean of the squares of the deviation of the
distribution from the mean.
|
| dist_varianza |
APPLICATION |
s_dist1 |
variance |
This symbol represents a unary function denoting the variance of a
distribution. The argument is a function to describe the distribution.
That is if f is the function which describes the distribution.
The variance of a distribution is the square of the standard deviation
of the distribution.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| producto_cartesiano |
APPLICATION |
set1 |
cartesian_product |
This symbol represents an n-ary construction function for constructing
the Cartesian product of sets. It takes n set arguments in order to
construct their Cartesian product.
|
| × |
OP_PROD |
| vacío |
SYMBOL |
set1 |
emptyset |
This symbol is used to represent the empty set, that is the set which
contains no members. It takes no parameters.
|
| ∅ |
SYMBOL |
| pert |
OP_PLUS |
set1 |
in |
This symbol has two arguments, an element and a set. It is used to
denote that the element is in the given set.
|
| ∈ |
OP_PLUS |
| inter |
OP_PROD |
set1 |
intersect |
This symbol is used to denote the n-ary intersection of sets. It takes
sets as arguments, and denotes the set that contains all the
elements that occur in all of them.
|
| ∩ |
OP_PROD |
| aplicación |
APPLICATION |
set1 |
map |
This symbol represents a mapping function which may be used to
construct sets, it takes as arguments a function from X to Y and a
set over X in that order. The value that is returned is a set of
values in Y. The argument list may be a set or an integer_interval.
|
| aplic |
APPLICATION |
| -> |
OP_AND |
| → |
OP_AND |
| no_pert |
OP_PLUS |
set1 |
notin |
This symbol has two arguments, an element and a set. It is used to
denote that the element is not in the given set.
|
| ¬∈ |
OP_PLUS |
| ∉ |
OP_PLUS |
| no_es_subconj_propio |
OP_PLUS |
set1 |
notprsubset |
This symbol has two (set) arguments. It is used to denote that the
first set is not a proper subset of the second. A proper subset of a
set is a subset of the set but not actually equal to it.
|
| ¬⊊ |
OP_PLUS |
| no_es_subconj |
OP_PLUS |
set1 |
notsubset |
This symbol has two (set) arguments. It is used to denote that the
first set is not a subset of the second.
|
| ⊄ |
OP_PLUS |
| subconj_propio |
OP_PLUS |
set1 |
prsubset |
This symbol has two (set) arguments. It is used to denote that the
first set is a proper subset of the second, that is a subset of the
second set but not actually equal to it.
|
| ⊊ |
OP_PLUS |
| conjunto |
APPLICATION |
set1 |
set |
This symbol represents the set construct. It is an n-ary function. The
set entries are given explicitly. There is no implied ordering to the
elements of a set.
|
| {} |
APPLICATION |
| diferencia |
APPLICATION |
set1 |
setdiff |
This symbol is used to denote the set difference of two sets. It takes
two sets as arguments, and denotes the set that contains all the
elements that occur in the first set, but not in the second.
|
| \ |
OP_PLUS |
| cardinal |
APPLICATION |
set1 |
size |
This symbol is used to denote the number of elements in a set. It is
either a non-negative integer, or an infinite cardinal number. The
symbol infinity may be used for an unspecified infinite cardinal.
|
| card |
APPLICATION |
| subconj |
OP_PLUS |
set1 |
subset |
This symbol has two (set) arguments. It is used to denote that the
first set is a subset of the second.
|
| ⊂ |
OP_PLUS |
| tal_que |
BINDING |
set1 |
suchthat |
This symbol represents the suchthat function which may be used to
construct sets, it takes two arguments. The first argument should be the
set which contains the elements of the set we wish to represent, the
second argument should be a predicate, that is a function from the set
to the booleans which describes if an element is to be in the set returned.
|
| tq |
BINDING |
| | |
OP_BIND |
| unión |
OP_PROD |
set1 |
union |
This symbol is used to denote the n-ary union of sets. It takes
sets as arguments, and denotes the set that contains all the
elements that occur in any of them.
|
| ∪ |
OP_PROD |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| /\ |
OP_AND |
logic1 |
and |
This symbol represents the logical and function which is an n-ary
function taking boolean arguments and returning a boolean value. It
is true if all arguments are true or false otherwise.
|
| ∧ |
OP_AND |
| <--> |
OP_IMPL |
logic1 |
equivalent |
This symbol is used to show that two boolean expressions are logically
equivalent, that is have the same boolean value for any inputs.
|
| ⇔ |
OP_IMPL |
| falso |
SYMBOL |
logic1 |
false |
This symbol represents the boolean value false.
|
| ⊭ |
SYMBOL |
| --> |
OP_IMPL |
logic1 |
implies |
This symbol represents the logical implies function which takes two
boolean expressions as arguments. It evaluates to false if the first
argument is true and the second argument is false, otherwise it
evaluates to true.
|
| ⇒ |
OP_IMPL |
| no |
OP_EXP |
logic1 |
not |
This symbol represents the logical not function which takes one boolean
argument, and returns the opposite boolean value.
|
| ¬ |
OP_EXP |
| \/ |
OP_OR |
logic1 |
or |
This symbol represents the logical or function which is an n-ary
function taking boolean arguments and returning a boolean value. It
is true if any of the arguments are true or false otherwise.
|
| ∨ |
OP_OR |
| verdadero |
SYMBOL |
logic1 |
true |
This symbol represents the boolean value true.
|
| ⊨ |
SYMBOL |
| \% |
OP_OR |
logic1 |
xor |
This symbol represents the logical xor function which is an n-ary
function taking boolean arguments and returning a boolean
value. It is true if there are an odd number of true arguments or
false otherwise.
|
| ⊻ |
OP_OR |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| ._. |
OP_PLUS |
interval1 |
integer_interval |
A symbol to denote a discrete 1 dimensional interval from the first
argument to the second (inclusive), where the discretisation occurs at unit
intervals. The arguments are the start and the end points of the interval
in that order.
|
| ... |
OP_PLUS |
interval1 |
interval |
A symbol to denote a continuous 1-dimensional interval without any
information about the character of the end points (used in definite
integration). The arguments are the start and the end points of the interval
in that order.
|
| .. |
OP_PLUS |
interval1 |
interval_cc |
A symbol to denote a continuous 1-dimensional interval with both end
points included in the interval. The arguments are the start and the
end points of the interval in that order.
|
| ..< |
OP_PLUS |
interval1 |
interval_co |
A symbol to denote a continuous 1-dimensional interval with the first
point included in the interval, but the last excluded. The arguments
are the start and the end points of the interval in that order.
|
| <.. |
OP_PLUS |
interval1 |
interval_oc |
A symbol to denote a continuous 1-dimensional interval with the first
point excluded from the interval, but the last included. The arguments
are the start and the end points of the interval in that order.
|
| <..< |
OP_PLUS |
interval1 |
interval_oo |
A symbol to denote a continuous 1-dimensional interval with both end
points excluded from the interval. The arguments are the start and the end
points of the interval in that order.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| dom |
APPLICATION |
fns1 |
domain |
This symbol denotes the domain of a given function, which is the set of
values it is defined over.
|
| dom_aplic |
APPLICATION |
fns1 |
domainofapplication |
The domainofapplication element denotes the domain over which a given
function is being applied. It is intended in MathML to be a more general
alternative to specification of this domain using
such quantifier elements as bvar, lowlimit or condition.
|
| I |
APPLICATION |
fns1 |
identity |
The identity function, it takes one argument and returns the same value.
|
| imag |
APPLICATION |
fns1 |
image |
This symbol denotes the image of a given function, which is the set of
values the domain of the given function maps to.
|
| im |
APPLICATION |
| inv |
APPLICATION |
fns1 |
inverse |
This symbol is used to describe the inverse of its argument (a
function). This inverse may only be partially defined because the
function may not have been surjective. If the function is not
surjective the inverse function is
ill-defined without further stipulations. No assumptions are made on
the semantics of this inverse.
|
| lambda |
BINDING |
fns1 |
lambda |
This symbol is used to represent anonymous functions as lambda expansions.
It is used in a binder that takes two further arguments, the first of which
is a list of variables, and the second of which is an expression, and it
forms the function which is the lambda extraction of the expression
|
| λ |
BINDING |
| composición |
OP_PROD |
fns1 |
left_compose |
This symbol represents the function which forms the left-composition
of its two (function) arguments.
|
| ∘ |
OP_PROD |
| inverso_izq |
APPLICATION |
fns1 |
left_inverse |
This symbol is used to describe the left inverse of its argument (a
function). This inverse may only be partially defined because the
function may not have been surjective. If the function is not
surjective the left inverse function is
ill-defined without further stipulations. No other assumptions are made on
the semantics of this left inverse.
|
| margen |
APPLICATION |
fns1 |
range |
This symbol denotes the range of a function, that is a set that the
function will map to. The single argument should be the function whos
range is being queried. It should be noted that this is not necessarily
equal to the image, it is merely required to contain the image.
|
| inverso_der |
APPLICATION |
fns1 |
right_inverse |
This symbol is used to describe the right inverse of its argument (a
function). This inverse may only be partially defined because the
function may not have been surjective. If the function is not
surjective the right inverse function is
ill-defined without further stipulations. No other assumptions are made on
the semantics of this right inverse.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| abs |
APPLICATION |
arith1 |
abs |
A unary operator which represents the absolute value of its
argument. The argument should be numerically valued.
In the complex case this is often referred to as the modulus.
|
| divide |
OP_PROD |
arith1 |
divide |
This symbol represents a (binary) division function denoting the first argument
right-divided by the second, i.e. divide(a,b)=a*inverse(b). It is the
inverse of the multiplication function defined by the symbol times in this CD.
|
| / |
OP_PROD |
| ÷ |
OP_PROD |
| mcd |
APPLICATION |
arith1 |
gcd |
The symbol to represent the n-ary function to return the gcd (greatest
common divisor) of its arguments.
|
| mcm |
APPLICATION |
arith1 |
lcm |
The symbol to represent the n-ary function to return the least common
multiple of its arguments.
|
| menos |
OP_PLUS |
arith1 |
minus |
The symbol representing a binary minus function. This is equivalent to
adding the additive inverse.
|
| - |
OP_PLUS |
| mas |
OP_PLUS |
arith1 |
plus |
The symbol representing an n-ary commutative function plus.
|
| + |
OP_PLUS |
| potencia |
OP_EXP |
arith1 |
power |
This symbol represents a power function. The first argument is raised
to the power of the second argument. When the second argument is not
an integer, powering is defined in terms of exponentials and
logarithms for the complex and real numbers.
This operator can represent general powering.
|
| ^ |
OP_EXP |
| producto |
APPLICATION |
arith1 |
product |
An operator taking two arguments, the first being the range of multiplication
e.g. an integral interval, the second being the function to
be multiplied. Note that the product may be over an infinite interval.
|
| ∏ |
APPLICATION |
| raíz |
APPLICATION |
arith1 |
root |
A binary operator which represents its first argument "lowered" to its
n'th root where n is the second argument. This is the inverse of the operation
represented by the power symbol defined in this CD.
Care should be taken as to the precise meaning of this operator, in
particular which root is represented, however it is here to represent
the general notion of taking n'th roots. As inferred by the signature
relevant to this symbol, the function represented by this symbol is
the single valued function, the specific root returned is the one
indicated by the first CMP. Note also that the converse of the second
CMP is not valid in general.
|
| √ |
APPLICATION |
| sum |
APPLICATION |
arith1 |
sum |
An operator taking two arguments, the first being the range of summation,
e.g. an integral interval, the second being the function to be
summed. Note that the sum may be over an infinite interval.
|
| ∑ |
APPLICATION |
| mult |
OP_PLUS |
arith1 |
times |
The symbol representing an n-ary multiplication function.
|
| × |
OP_PROD |
| ∙ |
OP_PROD |
| menos_unario |
APPLICATION |
arith1 |
unary_minus |
This symbol denotes unary minus, i.e. the additive inverse.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| argumento |
APPLICATION |
complex1 |
argument |
This symbol represents the unary function which returns the argument
of a complex number, viz. the angle which a straight line drawn from
the number to zero makes with the Real line (measured
anti-clockwise). The argument to the symbol is the complex number whos
argument is being taken.
|
| complejo_cartesiano |
APPLICATION |
complex1 |
complex_cartesian |
This symbol represents a constructor function for complex numbers
specified as the Cartesian coordinates of the relevant point on the
complex plane. It takes two arguments, the first is a number x to
denote the real part and the second a number y to denote the imaginary
part of the complex number x + i y. (Where i is the square root of -1.)
|
| complejo_polar |
APPLICATION |
complex1 |
complex_polar |
This symbol represents a constructor function for complex numbers
specified as the polar coordinates of the relevant point on the complex
plane. It takes two arguments, the first is a nonnegative number r to
denote the magnitude and the second a number theta (given in radians)
to denote the argument of the complex number r e^(i theta). (i and
e are defined as in this CD).
|
| conj |
APPLICATION |
complex1 |
conjugate |
A unary operator representing the complex conjugate of its argument.
|
| imaginario |
APPLICATION |
complex1 |
imaginary |
This represents the imaginary part of a complex number
|
| imagin |
APPLICATION |
| real |
APPLICATION |
complex1 |
real |
This represents the real part of a complex number
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| ~ |
OP_EQ |
relation1 |
approx |
This symbol is used to denote the approximate equality of its two arguments.
|
| ≅ |
OP_EQ |
| = |
OP_EQ |
relation1 |
eq |
This symbol represents the binary equality function.
|
| >= |
OP_EQ |
relation1 |
geq |
This symbol represents the binary greater than or equal to function
which returns true if the first argument is greater than or equal to
the second, it returns false otherwise.
|
| ≥ |
OP_EQ |
| > |
OP_EQ |
relation1 |
gt |
This symbol represents the binary greater than function which returns
true if the first argument is greater than the second, it returns false
otherwise.
|
| <= |
OP_EQ |
relation1 |
leq |
This symbol represents the binary less than or equal to function which returns
true if the first argument is less than or equal to the second, it
returns false otherwise.
|
| ≤ |
OP_EQ |
| < |
OP_EQ |
relation1 |
lt |
This symbol represents the binary less than function which returns
true if the first argument is less than the second, it returns false
otherwise.
|
| no_igual |
OP_EQ |
relation1 |
neq |
This symbol represents the binary inequality function.
|
| ¬= |
OP_EQ |
| ≠ |
OP_EQ |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| arccos |
APPLICATION |
transc1 |
arccos |
This symbol represents the arccos function. This is the inverse of the
cos function as described in Abramowitz and Stegun, section 4.4. It
takes one argument.
|
| arccosh |
APPLICATION |
transc1 |
arccosh |
This symbol represents the arccosh function as described in Abramowitz
and Stegun, section 4.6.
|
| arccot |
APPLICATION |
transc1 |
arccot |
This symbol represents the arccot function as described in Abramowitz
and Stegun, section 4.4.
|
| arccoth |
APPLICATION |
transc1 |
arccoth |
This symbol represents the arccoth function as described in Abramowitz
and Stegun, section 4.6.
|
| arccsc |
APPLICATION |
transc1 |
arccsc |
This symbol represents the arccsc function as described in Abramowitz
and Stegun, section 4.4.
|
| arccsch |
APPLICATION |
transc1 |
arccsch |
This symbol represents the arccsch function as described in Abramowitz
and Stegun, section 4.6.
|
| arcsec |
APPLICATION |
transc1 |
arcsec |
This symbol represents the arcsec function as described in Abramowitz
and Stegun, section 4.4.
|
| arcsech |
APPLICATION |
transc1 |
arcsech |
This symbol represents the arcsech function as described in Abramowitz
and Stegun, section 4.6.
|
| arcsen |
APPLICATION |
transc1 |
arcsin |
This symbol represents the arcsin function. This is the inverse of the
sin function as described in Abramowitz and Stegun, section 4.4. It
takes one argument.
|
| arcsenh |
APPLICATION |
transc1 |
arcsinh |
This symbol represents the arcsinh function as described in Abramowitz
and Stegun, section 4.6.
|
| arctan |
APPLICATION |
transc1 |
arctan |
This symbol represents the arctan function. This is the inverse of the
tan function as described in Abramowitz and Stegun, section 4.4. It
takes one argument.
|
| arctg |
APPLICATION |
| arctanh |
APPLICATION |
transc1 |
arctanh |
This symbol represents the arctanh function as described in Abramowitz
and Stegun, section 4.6.
|
| arctgh |
APPLICATION |
| cos |
APPLICATION |
transc1 |
cos |
This symbol represents the cos function as described in Abramowitz and
Stegun, section 4.3. It takes one argument.
|
| cosh |
APPLICATION |
transc1 |
cosh |
This symbol represents the cosh function as described in Abramowitz
and Stegun, section 4.5. It takes one argument.
|
| cot |
APPLICATION |
transc1 |
cot |
This symbol represents the cot function as described in Abramowitz and
Stegun, section 4.3. It takes one argument.
|
| coth |
APPLICATION |
transc1 |
coth |
This symbol represents the coth function as described in Abramowitz
and Stegun, section 4.5. It takes one argument.
|
| csc |
APPLICATION |
transc1 |
csc |
This symbol represents the csc function as described in Abramowitz and
Stegun, section 4.3. It takes one argument.
|
| csch |
APPLICATION |
transc1 |
csch |
This symbol represents the csch function as described in Abramowitz
and Stegun, section 4.5. It takes one argument.
|
| exp |
APPLICATION |
transc1 |
exp |
This symbol represents the exponentiation function as described in
Abramowitz and Stegun, section 4.2. It takes one argument.
|
| ln |
APPLICATION |
transc1 |
ln |
This symbol represents the ln function (natural logarithm) as
described in Abramowitz and Stegun, section 4.1. It takes one
argument. Note the description in the CMP/FMP of the branch cut. If
signed zeros are in use, the inequality needs to be non-strict.
|
| log |
APPLICATION |
transc1 |
log |
This symbol represents a binary log function; the first argument is the base,
to which the second argument is log'ed.
It is defined in Abramowitz and Stegun, Handbook of Mathematical
Functions, section 4.1
|
| sec |
APPLICATION |
transc1 |
sec |
This symbol represents the sec function as described in Abramowitz and
Stegun, section 4.3. It takes one argument.
|
| sech |
APPLICATION |
transc1 |
sech |
This symbol represents the sech function as described in Abramowitz
and Stegun, section 4.5. It takes one argument.
|
| sen |
APPLICATION |
transc1 |
sin |
This symbol represents the sin function as described in Abramowitz and
Stegun, section 4.3. It takes one argument.
|
| senh |
APPLICATION |
transc1 |
sinh |
This symbol represents the sinh function as described in Abramowitz
and Stegun, section 4.5. It takes one argument.
|
| tan |
APPLICATION |
transc1 |
tan |
This symbol represents the tan function as described in Abramowitz and
Stegun, section 4.3. It takes one argument.
|
| tg |
APPLICATION |
| tanh |
APPLICATION |
transc1 |
tanh |
This symbol represents the tanh function as described in Abramowitz
and Stegun, section 4.5. It takes one argument.
|
| tgh |
APPLICATION |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| A |
SYMBOL |
setname2 |
A |
This symbol represents the set of algebraic numbers.
|
| Boolean |
SYMBOL |
setname2 |
Boolean |
This symbol represents the set of Booleans. That is the truth values,
true and false.
|
| GFp |
APPLICATION |
setname2 |
GFp |
This symbol represents the finite field of integers modulo p, where p is a
prime.
|
| GFpn |
APPLICATION |
setname2 |
GFpn |
This symbol represents the finite field with p^n elements, where p is a prime.
|
| H |
SYMBOL |
setname2 |
H |
This symbol represents the set of quaternions.
|
| QuotientField |
APPLICATION |
setname2 |
QuotientField |
This symbol represents the quotient field of any integral domain.
|
| Zm |
APPLICATION |
setname2 |
Zm |
This symbol represents the set of integers modulo m, where m is not necessarily
a prime. It takes one argument, the integer m.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| const_node |
APPLICATION |
polyslp |
const_node |
This constructor takes one argument, which is a value from the
coefficient ring. It is intended to represent a constant node.
|
| depth |
APPLICATION |
polyslp |
depth |
A unary function taking an slp as argument and returning the
greatest depth of any leaf node, that is the length of the longest
contiguous path to any leaf node.
|
| inp_node |
APPLICATION |
polyslp |
inp_node |
This constructor takes one argument, which is a variable. The return
value is intended to represent an input node.
|
| left_ref |
APPLICATION |
polyslp |
left_ref |
Takes as argument a node of an slp.
Returns the value of the left hand pointer of the node.
|
| length |
APPLICATION |
polyslp |
length |
A unary function taking an slp as argument and returning the
length of this slp.
|
| monte_carlo_eq |
APPLICATION |
polyslp |
monte_carlo_eq |
This is a Monte-Carlo equality test,
it takes three arguments, the first two are slps representing
polynomials, the third argument is the maximum probability of
incorrectness that is required of the equality test.
(Monte-Carlo equality tests are very important for slps as they
offer the only tractable method of solving the equality problem
in many cases)
|
| node_selector |
APPLICATION |
polyslp |
node_selector |
Takes an slp as the first argument, the second argument is the
position of the required node. Returns the node of the slp at
this position.
|
| op_node |
APPLICATION |
polyslp |
op_node |
This constructor takes three arguments.
The first argument is a symbol from opnode, meant to specify
whether the node is a plus, minus times or divide node,
the second and third arguments are integers, which are the numbers
of the lines which are the arguments of the operation
|
| poly_ring_SLP |
APPLICATION |
polyslp |
poly_ring_SLP |
The constructor of the polynomial ring. The first argument is a ring,
(the ring of the coefficients), the rest are the variables, in any order.
|
| polynomial_SLP |
APPLICATION |
polyslp |
polynomial_SLP |
The constructor of Polynomials built with Straight Line Program
representation.
The first argument is the polynomial ring containing the polynomial
built with poly_ring_SLP,
The second argument is the program body built with prog_body.
|
| prog_body |
APPLICATION |
polyslp |
prog_body |
The constructor of the body of the straight line program
the arguments represent straight line instructions, as constructed by the
following three constructors, op_node, inp_node and const_node, possibly
wrapped in the return symbol (from the opnode CD). The order
is taken to be the order in which they appear.
|
| quotient |
APPLICATION |
polyslp |
quotient |
A quotient function for polynomials represented by slps. It is a
requirement that this is an exact division.
|
| return_code |
APPLICATION |
polyslp |
return_code |
|
| right_ref |
APPLICATION |
polyslp |
right_ref |
Takes as argument a node of an slp.
Returns the value of the right hand pointer of the node.
|
| slp_degree |
APPLICATION |
polyslp |
slp_degree |
A unary function taking an slp as argument and returning the
apparent multiplicative degree of the slp, without performing
any cancellation.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| DMP |
APPLICATION |
polyd |
DMP |
The constructor of DMPs. The first argument is the polynomial
ring containing the polynomial and the second is a "SDMP".
Should be of the form DMP(PolyRingD(...), SDMP(...))
|
| DMPL |
APPLICATION |
polyd |
DMPL |
The constructor for lists of multivariate polynomial members of the
same polynomial ring. The first argument is a polynomial ring
and the rest are "SDMP"s. DMPL can be attributed with the "ordering"
symbol to indicate a particular ordering for monomials of all its
polynomials.
Should be of the form DMPL(PolyRingD(...), SDMP(...)+)
|
| elimination |
APPLICATION |
polyd |
elimination |
This is an ordering, which is partially in terms of one
ordering, and partially in terms of another.
First argument is a number of variables.
Second is ordering to apply on the first so many variables.
Third is an ordering on the rest, to be used to break ties.
|
| graded_lexicographic |
APPLICATION |
polyd |
graded_lexicographic |
Total degree order, graded with the lexicographic ordering.
Note that, if a poly_ring_d_named is used, lexigographic refers
to the order of the variables in the poly_ring_d_named, not to
their order as strings.
|
| graded_reverse_lexicographic |
APPLICATION |
polyd |
graded_reverse_lexicographic |
Total degree order, graded with the reverse lexicographic ordering.
Note that, if a poly_ring_d_named is used, lexigographic refers
to the order of the variables in the poly_ring_d_named, not to
their order as strings.
|
| groebner |
APPLICATION |
polyd |
groebner |
The groebner basis (lt-reduced, minimal) of a set of polynomials,
with respect to a given ordering. First argument is an ordering, the
second is a list of polynomials. A program that can compute
the basis is required to return a "groebnered" object.
|
| groebner_basis |
APPLICATION |
polyd |
groebner_basis |
|
| lexicographic |
APPLICATION |
polyd |
lexicographic |
The lexicographic ordering of terms.
Note that, if a poly_ring_d_named is used, lexigographic refers
to the order of the variables in the poly_ring_d_named, not to
their order as strings.
|
| ordering |
APPLICATION |
polyd |
ordering |
Used as an attribute to indicate an ordering of the terms in a
polynomial or list of polynomials. The value of this attribute
should be one of the constructors specifying ordering.
|
| plus |
APPLICATION |
polyd |
plus |
The sum. The argument is a DMPL. The sum lies within the same
"PolyRingD" i.e. a program implementing this operation
should return a DMP with the same "poly_ring_d"
(or "poly_ring_d_named").
|
| poly_ring_d |
APPLICATION |
polyd |
poly_ring_d |
The constructor of polynomial ring. The first argument is a ring
(the ring of the coefficients), the second is the number
of variables as an integer.
|
| power |
APPLICATION |
polyd |
power |
The power. First argument is a DMP, second
argument is the integer power. The power lies within the same
"PolyRingD" i.e. a program implementing this operation
should return a DMP with the same "poly_ring_d"
(or "poly_ring_d_named").
|
| reduce |
APPLICATION |
polyd |
reduce |
The reduction of a polynomial with respect to a Groebner basis.
First argument is a DMP, the second argument is a "groebnered"
object.
i.e. a program implementing this operation should return a DMP which
represents the polynomial reduced with respect to the Groebner basis.
|
| reverse_lexicographic |
APPLICATION |
polyd |
reverse_lexicographic |
The reverse lexicographic ordering of terms.
Note that, if a poly_ring_d_named is used, lexigographic refers
to the order of the variables in the poly_ring_d_named, not to
their order as strings.
|
| SDMP |
APPLICATION |
polyd |
SDMP |
The constructor for multivariate polynomials without
any indication of variables or domain for the coefficients.
Its arguments are just "term"s. No terms should differ only by
the coefficient (i.e it is not permitted to have both "2*x*y" and
"x*y" as terms in a SDMP). SDMP can be attributed with
the "ordering" symbol to indicate a particular ordering of its
terms. This attribute shall not be set if the SDMP is part of
DMPL that has this attribute set. If the SDMP is ordered, explicitly
or implicitly via an outer ordering, the terms must be in decreasing
order with respect to this order. The zero polynomial is represented
by an SDMP with no terms.
|
| term |
APPLICATION |
polyd |
term |
The constructor of terms. Valid applications are of the form
Term(coeff, exp1, exp2, ... expn)
which represents the term
coeff * var1^exp1*...varn^expn
where n is the number of variables, expi are non-negative integers.
coeff should be non-zero.
|
| times |
APPLICATION |
polyd |
times |
The product. The argument is a DMPL. The product lies within the same
"PolyRingD" i.e. a program implementing this operation
should return a DMP with the same "poly_ring_d"
(or "poly_ring_d_named").
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| anti_Hermitian |
APPLICATION |
linalg5 |
anti-Hermitian |
This symbol represents an anti-Hermitian matrix, it takes one
argument. The argument should be a vector of vectors of values which
determine the upper triangle of the matrix. The lower triangle of the
matrix is specified by the following relation: - M^* = transpose(M),
were M^* denotes the matrix consisting of all the complex conjugates
of M. This rules implies that the main diagonal is zero, therefore the
argument should not include it.
|
| banded_matrix |
APPLICATION |
linalg5 |
banded |
This symbol represents a (p,q) banded matrix, it takes one
argument. A (p,q) banded matrix should always be square. The lower non-zero
subdiagonal is the first element of the argument, whilst the highest non-zero
super-diagonal is given by the last element of the argument. The
argument determines the band of possibly non-zero entries which
are positioned around the diagonal. It should be a vector of vectors,
we note that they will not all be the same length, however the length
of the vectors determine p and q. The longest element specifies the
diagonal of the matrix and hence the size of the matrix. Every element
not in the band is zero.
|
| constant_matrix |
APPLICATION |
linalg5 |
constant |
This symbol represents a matrix which has all entries of the same
value. It takes two arguments, the first is the size of the matrix,
the second is the constant which determines every element.
|
| diagonal_matrix |
APPLICATION |
linalg5 |
diagonal_matrix |
This symbol denotes an n_ary function which is used to construct an
(nxn) diagonal matrix, that is a matrix where every non-diagonal
element is zero, the diagonal elements are equal to the n arguments.
|
| Hermitian |
APPLICATION |
linalg5 |
Hermitian |
This symbol represents a Hermitian matrix, it takes one
argument. The argument should be a vector of vectors of values which
determine the upper triangle of the matrix. The lower triangle of the
matrix is specified by the following relation: M^* = transpose(M),
were M^* denotes the matrix consisting of all the complex conjugates
of M.
|
| identity_matrix |
APPLICATION |
linalg5 |
identity |
This symbol denotes a unary function which is used to construct an
(nxn) identity matrix where n is the single positive integral argument.
|
| I |
APPLICATION |
| lower_Hessenberg |
APPLICATION |
linalg5 |
lower-Hessenberg |
This symbol represents a lower-Hessenberg matrix, it takes one argument,
the argument is a vector of vectors representing the non-zero
elements. The first element of the argument specifies the value of the
first super-diagonal, the subsequent elements specify the value of the
diagonal and subsequent subdiagonals, all other elements are zero.
|
| lower_triangular |
APPLICATION |
linalg5 |
lower-Triangular |
|
| scalar_matrix |
APPLICATION |
linalg5 |
scalar |
This symbol represents a matrix which is a scalar constant times the
identity matrix. It should take three arguments, the first and second
specify the number of rows and columns int he matrix respectively and
the third specifies the scalar multiplier.
|
| skew_symmetric_matrix |
APPLICATION |
linalg5 |
skew-symmetric |
This symbol represents a skew-symmetric matrix, it takes one
argument. The argument should be a vector of vectors of elements of
the matrix. For j>i the ij'th element of the matrix is the (j-i+1)'th
element of the i'th element of the argument. This determines the
elements above the diagonal of the matrix, the elements below the
diagonal of the matrix must conform to the rule M = - transpose
M. This rule implies that the elements on the diagonal must be equal
to 0, therefore we do not include these in the argument.
|
| symmetric_matrix |
APPLICATION |
linalg5 |
symmetric |
This symbol represents a symmetric matrix, it takes one argument. The
argument should be a vector of vectors of elements of the matrix. For
j>=i the ij'th element of the matrix is the (j-i+1)'th element of the i'th
element of the argument. This determines the upper triangle of the
matrix, the lower triangle is specified by the rule M = transpose M.
|
| tridiagonal_matrix |
APPLICATION |
linalg5 |
tridiagonal |
This symbol represents a tridiagonal matrix, it takes one argument
which should be a vector of vectors which should have three elements.
These should be vectors representing the sub-diagonal, the diagonal
and the super-diagonal in that order.
|
| upper_Hessenberg |
APPLICATION |
linalg5 |
upper-Hessenberg |
This symbol represents an upper-Hessenberg matrix, it takes one argument,
the argument is a vector of vectors representing the non-zero
elements. The first element of the argument specifies the value of the
first subdiagonal, the subsequent elements specify the value of the
diagonal and subsequent super-diagonals, all other elements are zero.
|
| upper_triangular |
APPLICATION |
linalg5 |
upper-triangular |
This symbol represents an upper-triangular matrix, it takes one
argument. The argument should be a vector of vectors of elements of
the matrix.
|
| zero_matrix |
APPLICATION |
linalg5 |
zero |
This symbol denotes a function with two integral arguments m,n which
is used to construct an (mxn) zero matrix.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| antisymmetric |
APPLICATION |
relation0 |
antisymmetric |
Proposition; the type of antisymmetric binary relations.
|
| equivalence |
APPLICATION |
relation0 |
equivalence |
Proposition; the type of equivalence relations,
namely relations that are reflexive, symmetric and transitive.
|
| irreflexive |
APPLICATION |
relation0 |
irreflexive |
Proposition; the type of irreflexive binary relations.
|
| order |
APPLICATION |
relation0 |
order |
Proposition; the type of order relations,
namely relations that are reflexive, antisymmetric and transitive.
|
| partial_equivalence |
APPLICATION |
relation0 |
partial_equivalence |
Proposition; the type of partial_equivalence relations,
namely relations that are symmetric, and transitive.
|
| pre_order |
APPLICATION |
relation0 |
pre_order |
Proposition; the type of preorder relations,
namely relations that are reflexive and transitive.
|
| reflexive |
APPLICATION |
relation0 |
reflexive |
Proposition; the type of reflexive binary relations.
|
| relation |
APPLICATION |
relation0 |
relation |
Type constructor; returns the type of binary relations on a set.
|
| strict_order |
APPLICATION |
relation0 |
strict_order |
Proposition; the type of strict order relations,
namely relations that are irreflexive, antisymmetric and transitive.
|
| symmetric |
APPLICATION |
relation0 |
symmetric |
Proposition; the type of symmetric binary relations.
|
| transitive |
APPLICATION |
relation0 |
transitive |
Proposition; the type of transitive binary relations.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| characteristic_eqn |
APPLICATION |
linalg4 |
characteristic_eqn |
This symbol represents the polynomial which appears in the left hand
side of the characteristic equation of a matrix. It
takes one argument which should be the matrix. A definition of the
characteristic equation is given in Elementary Linear Algebra, Stanley
I. Grossman in Definition 2 of chapter 6, page 535.
|
| columncount |
APPLICATION |
linalg4 |
columncount |
This symbol represents the function which takes one matrix argument
and returns the number of columns in that matrix.
|
| eigenvalue |
APPLICATION |
linalg4 |
eigenvalue |
This symbol represents the eigenvalue of a matrix. It takes two
arguments the first should be the matrix, the second should be an
index to specify the eigenvalue. The ordering imposed on the
eigenvalues is first on the modulus of the value, and second on the
argument of the value. A definition of eigenvalue is
given in Elementary Linear Algebra, Stanley I. Grossman in Definition 1
of chapter 6, page 533.
|
| eigenvector |
APPLICATION |
linalg4 |
eigenvector |
This symbol represents the eigenvector of a matrix. It takes two
arguments the first should be the matrix, the second should be an
index to specify which eigenvalue this eigenvector should be paired
with. The ordering is as given in the eigenvalue symbol. A definition
of eigenvector is given in Elementary Linear Algebra, Stanley
I. Grossman in Definition 1 of chapter 6, page 533.
|
| rank |
APPLICATION |
linalg4 |
rank |
This symbol represents the function which takes one matrix argument
and returns the number of linearly independent rows (or columns) of
that matrix.
|
| rowcount |
APPLICATION |
linalg4 |
rowcount |
This symbol represents the function which takes one matrix argument
and returns the number of rows in that matrix.
|
| vector_size |
APPLICATION |
linalg4 |
size |
This symbol represents the function which takes one vector argument
and returns the length of that vector.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| convert |
APPLICATION |
poly |
convert |
Conversion between polynomial rings. The first argument is a
polynomial and the second is a polynomial ring. This represents the
conversion of the given polynomial as an element of the given ring.
A program that can compute the conversion is required to return
a polynomial in the given ring.
|
| degree |
APPLICATION |
poly |
degree |
The total degree of its argument. The value returned is a
non-negative integer. We note that the degree of 0 is undefined.
Note that this operation takes no account of any weights that have
been defined: see weighted_degree in polyd.
|
| degree_wrt |
APPLICATION |
poly |
degree_wrt |
The degree with respect to a variable (the second
argument). We note that the degree of 0 is undefined.
|
| expand |
APPLICATION |
poly |
expand |
Converts a factored or squarefreed form into the expanded
polynomial over the same ring, so that factored(recursive)
-> recursive, etc.
|
| factor |
APPLICATION |
poly |
factor |
The decomposition of its argument into irreducible
factors. A program that can compute the factorization is required
to return a "factored" object - see above.
It is currently an open question whether powers of 1 can be omitted.
|
| factored |
APPLICATION |
poly |
factored |
The constructor for a factorization. Its arguments are formal
powers (see previous operator), where the polynomials are supposed
to be irreducible (except possibly for a content from the ground
ring).
Note that "factored" is not a call to factorise something, rather
a statement that we know a factorisation.
|
| gcd |
APPLICATION |
poly |
gcd |
The n-ary greatest common divisor of its polynomial arguments.
This is unique up to units.
|
| lcm |
APPLICATION |
poly |
lcm |
The least common multiple of its polynomial arguments.
This is unique up to units, but the choice must be compatible with
that made for gcd: see the CMP/FMP.
|
| power |
APPLICATION |
poly |
power |
Takes a polynomial and a (non-negative) integer and produces a
formal power. Although OpenMath does not specify operational
semantics, the idea here is that these powers are not
evaluated. We note that the power from arith1 would suggest
the expanded form.
|
| resultant |
APPLICATION |
poly |
resultant |
Function taking three arguments, it represents the resultant
of two polynomials, which are the first two arguments, with
respect to the given variable which is the third argument.
|
| squarefree |
APPLICATION |
poly |
squarefree |
The square-free decomposition of its argument. A program that can
compute the factorization is required to return a "squarefreed"
object.
|
| squarefreed |
APPLICATION |
poly |
squarefreed |
The constructor for a square-free factorization. Its arguments
should have the structure of the above "factored", where the
polynomials should be square-free. Note that this is not necessarily
a minimal square-free decomposition: some exponents can occur more
than once.
Again, this is a statement that we have a square-free factorisation,
rather than a request to compute one.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| Bell |
APPLICATION |
combinat1 |
Bell |
The Bell numbers: Bell(n) is the total number of possible partitions of a set
of n elements.
|
| binomial |
APPLICATION |
combinat1 |
binomial |
The binomial coefficients. binomial(n, m) is the number of ways of choosing m
objects from a collection of n distinct objects without regard to the order.
|
| Fibonacci |
APPLICATION |
combinat1 |
Fibonacci |
The Fibonacci numbers, defined by the linear recurrence:
Fibonacci(0) = 0, Fibonacci(1) = 1, and
Fibonacci(n + 1) = Fibonacci(n) + Fibonacci(n - 1).
Note that some authors define Fibonacci(0) = 1.
|
| multinomial |
APPLICATION |
combinat1 |
multinomial |
The multinomial coefficient, multinomial(n, n1, ... nk) is the number of
ways of choosing ni objects of type i (i from 1 to k) without regard to
order, in such a way that the total number of objects chosen is n.
multinomial(n, n1, ... nk) is equal to n!/(n1!*n2! ...*nk!).
|
| Stirling1 |
APPLICATION |
combinat1 |
Stirling1 |
The Stirling numbers of the first kind. (-1)^(n-m)*Stirling1(n,m) is the
number of permutations of n symbols which have exactly m cycles.
Note that there are a few slightly different definitions of these numbers.
|
| Stirling2 |
APPLICATION |
combinat1 |
Stirling2 |
The Stirling numbers of the second kind. Stirling2(n, m) is the number of
partitions of a set with n elements into m non empty subsets.
Note that there are a few slightly different definitions of these numbers.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| character_table |
APPLICATION |
group1 |
character_table |
This is the constructor for a character table.
Usage:
CharacterTable(centralizer_primes, centralizer_indices,
classnames, power_map, irreducibles_matrix)
If G has n conjugacy classes then:
* centralizer_primes is of the form
[p1, .., pk] i < j implies that pi < pj and
the pi are precisely the primes which divide the order of
some centralizer of a conjugacy class
* centralizer_indices is of the form
[[i11, ...,i1k] ... [in1,...ink]]
so the centralizer of class 1 has order p1^i11 ... pk^i1k etc
* classnames is a list of n strings which name the conjugacy classes
in line with the convention used in the Atlas of Finite Groups
* power_map is of the form [list1, ..., listk]
where listi[j] is the name of the class where elements of class j go when
raised to the power pi.
* irreducibles_matrix: rows correspond to irreducible characters,
columns are conjugacy classes. Entries are the value of an element of the
column's conjugacy class under the character of the row.
|
| character_table_of_group |
APPLICATION |
group1 |
character_table_of_group |
Refers to the character table of its argument
which must be a group.
|
| conjugacy_class |
APPLICATION |
group1 |
conjugacy_class |
The binary function whose value is the set of elements which
are conjugate to the second argument in the first.
|
| declare_group |
APPLICATION |
group1 |
declare_group |
This symbol is a constructor for groups. It takes four arguments in
the following order; a set to specify the elements in the group, a
binary operation to specify the group operation, a unary operation to
specify inverses of group elements and an element to specify the
identity. Both the binary and unary operations should act on elements
of the set and return an element of the set.
|
| derived_subgroup |
APPLICATION |
group1 |
derived_subgroup |
The unary function whose value is the subgroup of argument
generated by all products of the form xyx^-1y^-1.
|
| element_set |
APPLICATION |
group1 |
element_set |
The unary function which returns the set of elements of a group.
|
| group |
APPLICATION |
group1 |
group |
The n-ary function Group. The group generated by its arguments.
The arguments must have a natural group operation associated with them.
|
| is_abelian |
APPLICATION |
group1 |
is_abelian |
The unary boolean function whose value is true iff the argument is an abelian group
|
| is_normal |
APPLICATION |
group1 |
is_normal |
If G, H are the group arguments, then IsNormal(G,H) returns true precisely when
G is normal in H. That is, g^-1*h*g is defined and contained in H for
all h in H and g in G.
|
| is_subgroup |
APPLICATION |
group1 |
is_subgroup |
The binary function whose value is true if the second argument is a subgroup of the first.
|
| normal_closure |
APPLICATION |
group1 |
normal_closure |
The binary function whose value is the set of conjugates of
the elements of the second group by elements of the first,
where multiplication between them is defined.
|
| quotient_group |
APPLICATION |
group1 |
quotient_group |
The binary function whose value is the factor group of the first argument by the
second, assuming the second is normal in the first.
|
| right_traversal |
APPLICATION |
group1 |
right_traversal |
|
| sylow_subgroup |
APPLICATION |
group1 |
sylow_subgroup |
The largest p-subgroup of the argument (up to conjugacy).
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| media |
APPLICATION |
s_data1 |
mean |
This symbol represents an n-ary function denoting the mean of its
arguments. That is, their sum divided by their number.
|
| mediana |
APPLICATION |
s_data1 |
median |
This symbol represents an n-ary function denoting the median of its
arguments. That is, if the data were placed in ascending order then it
denotes the middle one (in the case of an odd amount of data) or the
average of the middle two (in the case of an even amount of data).
|
| moda |
APPLICATION |
s_data1 |
mode |
This symbol represents an n-ary function denoting the mode of its
arguments. That is the value which occurs with the greatest frequency.
|
| momento |
APPLICATION |
s_data1 |
moment |
This symbol is used to denote the i'th moment of a set of data. The
first argument should be the degree of the moment (that is, for the
i'th moment the first argument should be i), the second argument
should be the point about which the moment is being taken and the rest of the
arguments are treated as the data. For n data values x_1, x_2, ...,
x_n the i'th moment about c is (1/n) ((x_1-c)^i + (x_2-c)^i + ... + (x_n-c)^i).
See CRC Standard Mathematical Tables and Formulae,
editor: Dan Zwillinger, CRC Press Inc., 1996, section 7.7.1.
|
| desv_típica |
APPLICATION |
s_data1 |
sdev |
This symbol represents a function requiring two or more arguments,
denoting the sample standard deviation of its arguments. That is,
the square root of (the sum of the squares of the deviations from the
mean of the arguments, divided by the number of arguments).
See CRC Standard Mathematical Tables and Formulae,
editor: Dan Zwillinger, CRC Press Inc., 1996, (7.7.11) section 7.7.1.
|
| varianza |
APPLICATION |
s_data1 |
variance |
This symbol represents a function requiring two or more arguments,
denoting the variance of its arguments. That is, the square of the
standard deviation.
|
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| determinante |
APPLICATION |
linalg1 |
determinant |
This symbol denotes the unary function which returns the determinant
of its argument, the argument should be a square matrix.
|
| det |
APPLICATION |
| matrix_selector |
APPLICATION |
linalg1 |
matrix_selector |
This symbol represents the function which allows individual entries to
be selected from a matrix. It takes three arguments, the first is the
index of the row and the second is the index of the column of the
required element, the third argument is the matrix in question. The
indexing is one based, i.e. the element in the top left hand corner is
indexed by (1,1).
|
| prod_exterior |
APPLICATION |
linalg1 |
outerproduct |
This symbol represents the outer product function. It takes two vector
arguments and returns a matrix. It is defined as follows: if we write
the {i,j}'th element of the matrix to be returned as m_{i,j}, then:
m_{i,j}=a_i * b_j where a_i,b_j are the i'th and j'th elements of a, b
respectively.
|
| prod_escalar |
APPLICATION |
linalg1 |
scalarproduct |
This symbol represents the scalar product function. It takes two
vector arguments and returns a scalar value. The scalar product of two
vectors a, b is defined as |a| * |b| * cos(\theta), where \theta is
the angle between the two vectors and |.| is a euclidean size
function. Note that the scalar product is often referred to as the dot
product.
|
| · |
OP_PROD |
| traspuesta |
APPLICATION |
linalg1 |
transpose |
This symbol represents a unary function that denotes the transpose of
the given matrix or vector
|
| vector_selector |
APPLICATION |
linalg1 |
vector_selector |
This symbol represents the function which allows individual entries to
be selected from a vector, or a matrixrow. It takes two arguments. The
first argument is the position in the vector (or matrixrow) of the
required entry, the second argument is the vector (or matrixrow) in
question. The indexing is one based, i.e. the first element is indexed by one.
|
| prod_vectorial |
APPLICATION |
linalg1 |
vectorproduct |
This symbol represents the vector product function. It takes two
three dimensional vector arguments and returns a three dimensional
vector. It is defined as follows: if we write a as [a_1,a_2,a_3] and
b as [b_1,b_2,b_3] then the vector product denoted
a x b = [a_2b_3 - a_3b_2 , a_3b_1 - a_1b_3 , a_1b_2 - a_2b_1].
Note that the vector product is often referred to as the cross product.
|
| /\ |
OP_PROD |
| ∧ |
OP_PROD |
| QMath syntax |
Symbol type |
OpenMath CD |
OpenMath name |
Description |
| Def_alternativa |
PARAGRAPH_TYPE |
alternative-def |
QMath text structure. |
| Def_alternativa_simple |
PARAGRAPH_TYPE |
alternative-def@type=simple |
QMath text structure. |
| Def_alternativa_inductiva |
PARAGRAPH_TYPE |
alternative-def@type=inductive |
QMath text structure. |
| Def_alternativa_implícita |
PARAGRAPH_TYPE |
alternative-def@type=implicit |
QMath text structure. |
| Def_alternativa_obj |
PARAGRAPH_TYPE |
alternative-def@type=obj |
QMath text structure. |
| Aserto |
PARAGRAPH_TYPE |
assertion |
QMath text structure. |
| Teorema |
PARAGRAPH_TYPE |
assertion@type=theorem |
QMath text structure. |
| Lema |
PARAGRAPH_TYPE |
assertion@type=lemma |
QMath text structure. |
| Corolario |
PARAGRAPH_TYPE |
assertion@type=corollary |
QMath text structure. |
| Conjetura |
PARAGRAPH_TYPE |
assertion@type=conjecture |
QMath text structure. |
| Suposición |
PARAGRAPH_TYPE |
assumption |
QMath text structure. |
| Axioma |
PARAGRAPH_TYPE |
axiom |
QMath text structure. |
| Inclusión_de_axioma |
PARAGRAPH_TYPE |
axiom-inclusion |
QMath text structure. |
| Código |
PARAGRAPH_TYPE |
code |
QMath text structure. |
| Conclusión |
PARAGRAPH_TYPE |
conclude |
QMath text structure. |
| Definición |
PARAGRAPH_TYPE |
definition |
QMath text structure. |
| Definición_simple |
PARAGRAPH_TYPE |
definition@type=simple |
QMath text structure. |
| Definición_inductiva |
PARAGRAPH_TYPE |
definition@type=inductive |
QMath text structure. |
| Definición_implícita |
PARAGRAPH_TYPE |
definition@type=implicit |
QMath text structure. |
| Definición_obj |
PARAGRAPH_TYPE |
definition@type=obj |
QMath text structure. |
| Hecho |
PARAGRAPH_TYPE |
derive |
QMath text structure. |
| Ejemplo |
PARAGRAPH_TYPE |
example |
QMath text structure. |
| Ejemplo_favorable |
PARAGRAPH_TYPE |
example@type=for |
QMath text structure. |
| Contraejemplo |
PARAGRAPH_TYPE |
example@type=against |
QMath text structure. |
| Ejercicio |
PARAGRAPH_TYPE |
exercise |
QMath text structure. |
| Pista |
PARAGRAPH_TYPE |
hint |
QMath text structure. |
| Hipótesis |
PARAGRAPH_TYPE |
hypothesis |
QMath text structure. |
| Omlet |
PARAGRAPH_TYPE |
omlet |
QMath text structure. |
| Resumen |
PARAGRAPH_TYPE |
omtext@type=abstract |
QMath text structure. |
| Introducción |
PARAGRAPH_TYPE |
omtext@type=introduction |
QMath text structure. |
| Conclusión |
PARAGRAPH_TYPE |
omtext@type=conclusion |
QMath text structure. |
| Tesis |
PARAGRAPH_TYPE |
omtext@type=thesis |
QMath text structure. |
| Antítesis |
PARAGRAPH_TYPE |
omtext@type=antithesis |
QMath text structure. |
| Elaboración |
PARAGRAPH_TYPE |
omtext@type=elaboration |
QMath text structure. |
| Motivación |
PARAGRAPH_TYPE |
omtext@type=motivation |
QMath text structure. |
| Evidencia |
PARAGRAPH_TYPE |
omtext@type=evidence |
QMath text structure. |
| Enlace |
PARAGRAPH_TYPE |
omtext@type=linkage |
QMath text structure. |
| Narrativo |
PARAGRAPH_TYPE |
omtext@type=narrative |
QMath text structure. |
| Sequencia |
PARAGRAPH_TYPE |
omtext@type=sequence |
QMath text structure. |
| Alternativa |
PARAGRAPH_TYPE |
omtext@type=alternative |
QMath text structure. |
| General |
PARAGRAPH_TYPE |
omtext@type=general |
QMath text structure. |
| Premisa |
PARAGRAPH_TYPE |
premise |
QMath text structure. |
| Privado |
PARAGRAPH_TYPE |
private |
QMath text structure. |
| Prueba |
PARAGRAPH_TYPE |
proof |
QMath text structure. |
| Prueba_obj |
PARAGRAPH_TYPE |
proofobject |
QMath text structure. |
| Solución |
PARAGRAPH_TYPE |
solution |
QMath text structure. |
| Teoría |
PARAGRAPH_TYPE_LEVEL_0 |
theory |
QMath text structure. |
| Inclusión_de_teoría |
PARAGRAPH_TYPE |
theory-inclusion |
QMath text structure. |
| para |
METADATA |
@for |
QMath text structure. |
| xref |
METADATA |
@xref |
QMath text structure. |
| catálogo |
METADATA |
@catalogue |
QMath text structure. |
| Catálogo |
PARAGRAPH_TYPE_LEVEL_0 |
catalogue |
QMath text structure. |
| Antecedente_científico |
METADATA |
DC:Contributor@role=ant |
Dublin Core metadata. |
| Colaborador |
METADATA |
DC:Contributor@role=clb |
Dublin Core metadata. |
| Colaboradora |
METADATA |
DC:Contributor@role=clb |
Dublin Core metadata. |
| Editor |
METADATA |
DC:Contributor@role=edt |
Dublin Core metadata. |
| Supervisor_de_tesis |
METADATA |
DC:Contributor@role=ths |
Dublin Core metadata. |
| Transcriptor |
METADATA |
DC:Contributor@role=trc |
Dublin Core metadata. |
| Traductor |
METADATA |
DC:Contributor@role=trl |
Dublin Core metadata. |
| Fuente |
METADATA |
DC:Source |
Dublin Core metadata. |
| Descripción |
METADATA |
DC:Description |
Dublin Core metadata. |
| ISBN |
METADATA |
DC:Identifier@scheme=isbn |
Dublin Core metadata. |
| ISSN |
METADATA |
DC:Identifier@scheme=issn |
Dublin Core metadata. |
| Creado |
METADATA |
DC:Date@action=created |
Dublin Core metadata. |
| Actualizado |
METADATA |
DC:Date@action=updated |
Dublin Core metadata. |
| Formalizado |
PARAGRAPH_SECTION_MARKER |
qmath_paragraph_section_FMP |
QMath text structure. |
E-mail: web@matr