# FortranExpression(basicSymbols, subscriptedSymbols, R)ΒΆ

A domain of expressions involving functions which can be translated into standard Fortran-77, with some extra extensions from the NAG Fortran Library.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, R) -> %

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

`abs(x)` represents the Fortran intrinsic function ABS

acos: % -> %

`acos(x)` represents the Fortran intrinsic function ACOS

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
asin: % -> %

`asin(x)` represents the Fortran intrinsic function ASIN

associator: (%, %, %) -> %
atan: % -> %

`atan(x)` represents the Fortran intrinsic function ATAN

belong?: BasicOperator -> Boolean

from ExpressionSpace

box: % -> %

from ExpressionSpace

characteristic: () -> NonNegativeInteger
coerce: % -> Expression R

`coerce(x)` is undocumented.

coerce: % -> OutputForm
coerce: Integer -> %
coerce: Kernel % -> %

from CoercibleFrom Kernel %

coerce: R -> %

from CoercibleFrom R

commutator: (%, %) -> %
cos: % -> %

`cos(x)` represents the Fortran intrinsic function COS

cosh: % -> %

`cosh(x)` represents the Fortran intrinsic function COSH

D: (%, List Symbol) -> %
D: (%, List Symbol, List NonNegativeInteger) -> %
D: (%, Symbol) -> %
D: (%, Symbol, NonNegativeInteger) -> %
definingPolynomial: % -> %

from ExpressionSpace

differentiate: (%, List Symbol) -> %
differentiate: (%, List Symbol, List NonNegativeInteger) -> %
differentiate: (%, Symbol) -> %
differentiate: (%, Symbol, NonNegativeInteger) -> %
distribute: % -> %

from ExpressionSpace

distribute: (%, %) -> %

from ExpressionSpace

elt: (BasicOperator, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %, %, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %, %, %, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %, %, %, %, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %, %, %, %, %, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, %, %, %, %, %, %, %, %, %) -> %

from ExpressionSpace

elt: (BasicOperator, List %) -> %

from ExpressionSpace

eval: (%, %, %) -> %

from InnerEvalable(%, %)

eval: (%, BasicOperator, % -> %) -> %

from ExpressionSpace

eval: (%, BasicOperator, List % -> %) -> %

from ExpressionSpace

eval: (%, Equation %) -> %

from Evalable %

eval: (%, Kernel %, %) -> %

from InnerEvalable(Kernel %, %)

eval: (%, List %, List %) -> %

from InnerEvalable(%, %)

eval: (%, List BasicOperator, List(% -> %)) -> %

from ExpressionSpace

eval: (%, List BasicOperator, List(List % -> %)) -> %

from ExpressionSpace

eval: (%, List Equation %) -> %

from Evalable %

eval: (%, List Kernel %, List %) -> %

from InnerEvalable(Kernel %, %)

eval: (%, List Symbol, List(% -> %)) -> %

from ExpressionSpace

eval: (%, List Symbol, List(List % -> %)) -> %

from ExpressionSpace

eval: (%, Symbol, % -> %) -> %

from ExpressionSpace

eval: (%, Symbol, List % -> %) -> %

from ExpressionSpace

exp: % -> %

`exp(x)` represents the Fortran intrinsic function EXP

freeOf?: (%, %) -> Boolean

from ExpressionSpace

freeOf?: (%, Symbol) -> Boolean

from ExpressionSpace

height: % -> NonNegativeInteger

from ExpressionSpace

is?: (%, BasicOperator) -> Boolean

from ExpressionSpace

is?: (%, Symbol) -> Boolean

from ExpressionSpace

kernel: (BasicOperator, %) -> %

from ExpressionSpace

kernel: (BasicOperator, List %) -> %

from ExpressionSpace

kernels: % -> List Kernel %

from ExpressionSpace

kernels: List % -> List Kernel %

from ExpressionSpace

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

log10: % -> %

`log10(x)` represents the Fortran intrinsic function `LOG10`

log: % -> %

`log(x)` represents the Fortran intrinsic function LOG

mainKernel: % -> Union(Kernel %, failed)

from ExpressionSpace

map: (% -> %, Kernel %) -> %

from ExpressionSpace

minPoly: Kernel % -> SparseUnivariatePolynomial %

from ExpressionSpace

one?: % -> Boolean

from MagmaWithUnit

operator: BasicOperator -> BasicOperator

from ExpressionSpace

operators: % -> List BasicOperator

from ExpressionSpace

opposite?: (%, %) -> Boolean

from AbelianMonoid

paren: % -> %

from ExpressionSpace

pi: () -> %

`pi(x)` represents the NAG Library function X01AAF which returns an approximation to the value of `pi`

plenaryPower: (%, PositiveInteger) -> %
recip: % -> Union(%, failed)

from MagmaWithUnit

retract: % -> Kernel %

from RetractableTo Kernel %

retract: % -> R

from RetractableTo R

retract: Expression Float -> % if R has RetractableTo Float

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retract: Expression Integer -> %

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retract: Expression R -> %

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retract: Fraction Polynomial Float -> % if R has RetractableTo Float

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retract: Fraction Polynomial Integer -> %

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retract: Polynomial Float -> % if R has RetractableTo Float

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retract: Polynomial Integer -> %

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retract: Symbol -> %

`retract(e)` takes `e` and transforms it into a FortranExpression checking that it is one of the given basic symbols or subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: % -> Union(Kernel %, failed)

from RetractableTo Kernel %

retractIfCan: % -> Union(R, failed)

from RetractableTo R

retractIfCan: Expression Float -> Union(%, failed) if R has RetractableTo Float

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: Expression Integer -> Union(%, failed)

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: Expression R -> Union(%, failed)

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: Fraction Polynomial Float -> Union(%, failed) if R has RetractableTo Float

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: Fraction Polynomial Integer -> Union(%, failed)

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: Polynomial Float -> Union(%, failed) if R has RetractableTo Float

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: Polynomial Integer -> Union(%, failed)

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions, and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.

retractIfCan: Symbol -> Union(%, failed)

`retractIfCan(e)` takes `e` and tries to transform it into a FortranExpression checking that it is one of the given basic symbols or subscripted symbols which correspond to scalar and array parameters respectively.

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sin: % -> %

`sin(x)` represents the Fortran intrinsic function SIN

sinh: % -> %

`sinh(x)` represents the Fortran intrinsic function SINH

smaller?: (%, %) -> Boolean

from Comparable

sqrt: % -> %

`sqrt(x)` represents the Fortran intrinsic function SQRT

subst: (%, Equation %) -> %

from ExpressionSpace

subst: (%, List Equation %) -> %

from ExpressionSpace

subst: (%, List Kernel %, List %) -> %

from ExpressionSpace

subtractIfCan: (%, %) -> Union(%, failed)
tan: % -> %

`tan(x)` represents the Fortran intrinsic function TAN

tanh: % -> %

`tanh(x)` represents the Fortran intrinsic function TANH

tower: % -> List Kernel %

from ExpressionSpace

tower: List % -> List Kernel %

from ExpressionSpace

variables: % -> List Symbol

`variables(e)` return a list of all the variables in `e`.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

BiModule(R, R)

CancellationAbelianMonoid

Comparable

ExpressionSpace

InnerEvalable(%, %)

InnerEvalable(Kernel %, %)

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown