4.11 Setting Properties of functions on an algebra

4.11.1 SetSesquilinear[Functions]

Aliases: SetSesq
Description: SetSesquilinear[a,b,c,] sets a, b, c, to be functions of two variables which are linear in the first variable and conjugate linear in the second variable. See SetBilinear.
Arguments: Functions is one or more symbols separated by commas.
Comments / Limitations: None

4.11.2 SesquilinearQ[aFunction]

Aliases: None
Description: SesquilinearQ[x] will return True if SetSesquilinear[x] was executed previously. See SetSesquilinear.
Arguments: aFunction is a symbol.
Comments / Limitations: None

4.11.3 SetBilinear[Functions]

Aliases: None
Description: SetBilinear[a,b,c,] sets a, b, c, to be functions of two variables which is linear in the first variable and linear in the second variable. See SetSesquilinear.
Arguments: Functions is one or more symbols separated by commas.
Comments / Limitations: None

4.11.4 BilinearQ[aFunction]

Aliases: None
Description: BilinearQ[x] will return True if SetBilinear[x] was executed previously. See SetBilinear.
Arguments: aFunction is a symbol.
Comments / Limitations: None

4.11.5 SetLinear[Functions]

Aliases: None
Description: SetLinear[b,c,d,] sets b, c, d, to be functions of one variable which are linear. See LinearQ.
Arguments: Functions is one or more symbols separated by commas.
Comments / Limitations: None

4.11.6 LinearQ[aFunction]

Aliases: None
Description: LinearQ[x] will return True if SetLinear[x] was executed previously. See SetLinear.
Arguments: aFunction is a symbol.
Comments / Limitations: None

4.11.7 SetConjugateLinear[Functions]

Aliases: None
Description: SetConjugateLinear[b,c,d,] sets b, c, d, to be functions of one variable which are conjugate linear. See ConjugateLinearQ.
Arguments: Functions is one or more symbols separated by commas.
Comments / Limitations: None

4.11.8 ConjugateLinearQ[aFunction]

Aliases: None
Description: ConjugateLinearQ[x] will return True if SetConjugateLinear[x] was executed previously. See SetConjugateLinear.
Arguments: aFunction is a symbol.
Comments / Limitations: None

4.11.9 SetIdempotent[Functions]

Aliases: None
Description: SetIdempotent[b,c,d,] sets b, c, d, to be functions of one variable such that, for example, b[b[z_]] := z; Common examples are inverse, transpose and adjoint. See IdempotentQ.
Arguments: Functions is one or more symbols separated by commas.
Comments / Limitations: None

4.11.10 IdempotentQ[aFunction]

Aliases: None
Description: IdempotentQ[x] will return True if SetIdempotent[x] was executed previously and False otherwise. See SetIdempotent.
Arguments: aFunction is a symbol.
Comments / Limitations: None

4.11.11 SetCommutingFunctions[ aFunction, anotherFunction]

Aliases: None
Description: SetCommutingFunctions takes exactly two parameters. SetCommutingFunctions[b, c] will implement the definitions b[c[z___]] := c[b[z]] /; Not[LeftQ[b,c]]; and c[b[z___]] := b[c[z]] /; LeftQ[b, c]; Common examples are the adjoint commuting with the transpose. Note: The above implementation will NOT lead to infinite loops. WARNING: If one says SetCommutingFunctions[b, c] and then sets only LeftQ[c,b], then neither of the above rules will be executed. Therefore, one must remember the order of the two parameters in the statement. One obvious helpful habit would be to use alphabetical order (i.e. say SetCommutingFunctions[aj, tp] and not the reverse). See CommutatingOperators and LeftQ.
Arguments: aFunction and anotherFunction are symbols.
Comments / Limitations: None

4.11.12 SetNonCommutativeMultiplyAntihomomorphism[ Functions]

Aliases: None
Description: SetNonCommutativeMultiplyAntihomomorphism[b,c,d,] sets b, c, d, ... to be functions of one variable such that, for example, b[anything1**anything2] becomes b[anything2] **b[anything1] if ExpandQ[b] is True; b[anything2] ** b[anything1] becomes b[anything1 ** anything2] if ExpandQ[b] is False; Common examples are inverse, transpose and adjoint. NOTE: The synonym NCAntihomo is easier to type.
Arguments: Functions is one or more symbols separated by commas.
Comments / Limitations: None