Math.Singular.Factory.Variables

Variables.

Singular-factory supports only a single linear sequence of variables, indexed starting from 1, optionally having single-character names.

So what we do is to use (phantom) types to encode naming conventions.

Raw factory variables

type VarIdx = Int

A variable index.

In factory, there is a single linear sequence of variables. Variables are indexed starting from 1.

theFactoryVars :: [Var]

In factory, there is a single linear sequence of variables. We "precalculate" these (lazily).

theNthVar :: VarIdx -> Var

Variable sets

class VariableSet v where

The class of variable sets. Since Factory only supports a single linear variable set, these differ only by naming conventions.

Methods

varIdxName :: Proxy v -> VarIdx -> String

recogVarName :: Proxy v -> String -> Maybe VarIdx

Instances

VariableSet VarXYZ

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarXYZ -> VarIdx -> String

recogVarName :: Proxy VarXYZ -> String -> Maybe VarIdx

VariableSet VarXyz

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarXyz -> VarIdx -> String

recogVarName :: Proxy VarXyz -> String -> Maybe VarIdx

VariableSet VarABC

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarABC -> VarIdx -> String

recogVarName :: Proxy VarABC -> String -> Maybe VarIdx

VariableSet VarAbc

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarAbc -> VarIdx -> String

recogVarName :: Proxy VarAbc -> String -> Maybe VarIdx

KnownSymbol s => VariableSet (VarBracketN s)

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy (VarBracketN s) -> VarIdx -> String

recogVarName :: Proxy (VarBracketN s) -> String -> Maybe VarIdx

KnownSymbol s => VariableSet (Var_N s)

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy (Var_N s) -> VarIdx -> String

recogVarName :: Proxy (Var_N s) -> String -> Maybe VarIdx

KnownSymbol s => VariableSet (VarN s)

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy (VarN s) -> VarIdx -> String

recogVarName :: Proxy (VarN s) -> String -> Maybe VarIdx

data VarN (s :: Symbol)

The variable set x1, x2, x3, x4... (where "x" can be any string)

Instances

KnownSymbol s => VariableSet (VarN s)

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy (VarN s) -> VarIdx -> String

recogVarName :: Proxy (VarN s) -> String -> Maybe VarIdx

data Var_N (s :: Symbol)

The variable set x_1, x_2, x_3, x_4... (where "x" can be any string)

Instances

KnownSymbol s => VariableSet (Var_N s)

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy (Var_N s) -> VarIdx -> String

recogVarName :: Proxy (Var_N s) -> String -> Maybe VarIdx

data VarBracketN (s :: Symbol)

The variable set x[1], x[2], x[3], x[4]... (where "x" can be any string)

Instances

KnownSymbol s => VariableSet (VarBracketN s)

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy (VarBracketN s) -> VarIdx -> String

recogVarName :: Proxy (VarBracketN s) -> String -> Maybe VarIdx

data VarAbc

The variable set a, b, c, d...

Instances

VariableSet VarAbc

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarAbc -> VarIdx -> String

recogVarName :: Proxy VarAbc -> String -> Maybe VarIdx

data VarABC

The variable set A, B, C, D...

Instances

VariableSet VarABC

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarABC -> VarIdx -> String

recogVarName :: Proxy VarABC -> String -> Maybe VarIdx

data VarXyz

The variable set x, y, z, u, v, w, a, b, c...

Instances

VariableSet VarXyz

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarXyz -> VarIdx -> String

recogVarName :: Proxy VarXyz -> String -> Maybe VarIdx

data VarXYZ

The variable set X, Y, Z, U, V, W, A, B, C...

Instances

VariableSet VarXYZ

Defined in Math.Singular.Factory.Variables

Methods

varIdxName :: Proxy VarXYZ -> VarIdx -> String

recogVarName :: Proxy VarXYZ -> String -> Maybe VarIdx

Standard naming conventions of variables

indexedVars :: String -> VarIdx -> String

Eg. x1, x2, x3...

indexedVarsUnderscore :: String -> VarIdx -> String

Eg. x_1, x_2, x_3...

indexedVarsBracket :: String -> VarIdx -> String

Eg. x[1], x[2], x[3]...

abcVars :: VarIdx -> String

That is, a, b, c...

capitalAbcVars :: VarIdx -> String

That is, A, B, C...

xyzVars :: VarIdx -> String

x, y, z, u, v, w, a, b, c ... , t

capitalXyzVars :: VarIdx -> String

Variable lists

varListXyz :: [Char]

varListCapitalXYZ :: [Char]

lowerVarList :: [String]

The infinite list of variables a, b ..., z, aa, ab, ac, ...

upperVarList :: [String]

Parsing standard variable names

readPosIdxMaybe :: String -> Maybe VarIdx

recogIndexed :: String -> String -> Maybe VarIdx

recogIndexedUnderscore :: String -> String -> Maybe VarIdx

recogIndexedBracket :: String -> String -> Maybe VarIdx

recogAbc :: String -> Maybe VarIdx

recogABC :: String -> Maybe VarIdx

recogXyz :: String -> Maybe VarIdx

recogXYZ :: String -> Maybe VarIdx