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.
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.
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.